CN111736550B - Nonlinear control method of single pendulum spray boom suspension system of plant protection machine - Google Patents
Nonlinear control method of single pendulum spray boom suspension system of plant protection machine Download PDFInfo
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- 239000007921 spray Substances 0.000 title claims abstract description 90
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Abstract
A nonlinear control method of a single pendulum spray boom suspension system of a plant protection machine comprises the following steps: firstly, collecting real-time data of a spray boom of a plant protection machine; secondly, inputting the data acquired in the first step into a dynamics model; and thirdly, utilizing a nonlinear controller based on Lyapunov theory to carry out servo control on the angle of the spray rod suspension of the plant protection machine, thereby realizing servo tracking of the reference track. The designed boom angle tracking controller can enable the output angle of the system to track the ground gradient, and simultaneously enables the system to meet the requirement of minimum secondary performance indexes, and has more practical use value compared with a controller designed according to a nominal system model.
Description
Technical field:
the invention relates to the field of control of intelligent large plant protection machinery, in particular to a control method for servo tracking of a single pendulum spray rod suspension system of a plant protection machine.
The background technology is as follows:
agricultural production has been playing a role as a basis for social development and progress. Crop protection is one of the important links in agricultural production. In order to meet the severe technical requirements of modern plant protection, such as large scale, precision and the like, large-scale plant protection machinery is gradually and widely applied. However, the research of the related field of large plant protection machinery in China is seriously lagged, so that the development process of modern plant protection in China is greatly restricted, and the research of the large plant protection machinery is imperative. In the use process of the plant protection machine, as the field working conditions are complex and changeable, the spray boom can vibrate and deviate from the optimal pesticide application set value in the pesticide application process of the plant protection machine, so that the pesticide application quality is greatly reduced, the situations of overspray and missed spraying of the pesticide liquid are caused, and the environment and the food safety are greatly influenced. When the spray boom vibrates too much, even the spray boom collides with the ground, so that the machine body is damaged. In order to effectively reduce the influence, a higher requirement is put forward on the performance of the large-scale spray boom type plant protection machine spray boom suspension. Up to now, the linearization processing in the modeling process and the loss generated by the machine body after long-time use are not considered in the control method of the single pendulum boom suspension system of the plant protection machine, so that the research of a nonlinear control method taking the linearization processing in the modeling process and the loss generated by the machine body after long-time use into consideration has important significance.
The invention comprises the following steps:
the invention aims to:
in order to solve the problems, the invention provides a nonlinear control method of a single pendulum spray boom suspension system of a plant protection machine.
The technical scheme is as follows:
a nonlinear control method of a pendulum type spray boom suspension system of a plant protection machine is characterized by comprising the following steps of:
the method comprises the following steps:
firstly, collecting real-time data of a spray boom of a plant protection machine;
secondly, inputting the data acquired in the first step into a dynamics model;
and thirdly, utilizing a nonlinear controller based on Lyapunov theory to carry out servo control on the angle of the spray rod suspension of the plant protection machine, thereby realizing servo tracking of the reference track.
The second step is that the dynamic model is established for a single pendulum boom suspension system and a hydraulic actuator of the plant protection machine; the kinetic model of the system is described as follows:
the pendulum type boom active suspension system of the plant protection machine comprises a boom, a suspender, a hydraulic cylinder and a frame connected with a vehicle body. A dynamic model is built for the boom suspension control system,
wherein T is the kinetic energy of the system, T is time, q j Is the generalized coordinates, operator d is used for the full derivative, Q j Is corresponding to q j Is a broad sense of force.
The plant protection machine pendulum type spray rod suspension obtains a group of constrained motion equations by Lagrangian multipliers:
r 1 +r 2 -d-r 3 ＝0 (2)
wherein the vector r i Corresponding to a fixed length of the connecting rod, d corresponding to a length-adjustable connecting rod comprising a hydraulic cylinder, vector r 1 ,r 2 ,r 3 Corresponding to a fixed length link in the suspension, and d corresponds to a length adjustable link containing a hydraulic cylinder.
According to the projection of the X axis and the Y axis, the following algebraic equation is obtained after linearization:
wherein r is i0 Is |r i I=1, 2,3 represents the modulus of the vector, d 0 Is |d|; alpha, gamma, theta and d represent minor variations in the variables around the setpoint. Wherein T and Q are represented as:
wherein I and m are respectively the moment of inertia and the mass of the plant protection machine spray lance.And->Represents angular velocity, T represents kinetic energy of the system and generalized force Q θ Associated with rotation θ; parameter a 1 And a 2 The displacement of the electrohydraulic servo valve is fixed by linearization constant, and under the condition of only gravity working, the displacement is as follows:
Q θ ＝-mgr 1 (a 1 d+a 1 θ) (6)
in the above, parameter a 1 And a 2 Is a linearization constant.
Likewise, generalized force Q d And the displacement d of the electrohydraulic servo valve is related to the displacement d of the electrohydraulic servo valve, and is calculated by fixing the rotation angle theta of the spray rod. In this case, the gravity and the work done by the electrohydraulic servo valve can be linearized:
Q d ＝F-mgr 1 (a 3 d+a 4 θ) (7)
wherein F is the initial force provided by the hydraulic actuator, parameter a 3 And a 4 Is linearizationA constant.
The following kinematics equations can be derived from equations (1) - (7):
the servo valve dynamic equation can be approximately described by a first order element:
wherein τ v ，k i I is the servo valve time constant, the valve core current gain and the control input current respectively.
And (3) making:
establishing a state space equation of the system according to the formulas (8) - (11), wherein the states are respectively as follows:
y＝x 1 (13)
then there are:
in model calculations, the state equation can be expressed as:
wherein:
the general state space of the active control system of the spray boom suspension (the general state equation of the system is obtained by establishing generalized coordinates, and the state equation is obtained by linearizing and finishing on the basis of the obtained dynamic equation) is represented as follows:
wherein x (t) ∈R n U (t) ∈R as a state vector for active control system of boom suspension m Y (t) ∈R as control vector for active control system of boom suspension p As an output vector of the active control system of the boom suspension. The matrix deltaa is a matrix with uncertainty in the same dimension as a as the model parameter error. The uncertainty matrix DeltaA depends on an uncertainty vector r, and the value range of r is [0,1]. And Δa satisfies the following characteristics:
ΔA＝EνF (17)
where matrix E, F is a dimensionality constant matrix and matrix v is a dimensionality time-varying matrix that is affected by the uncertainty vector r and satisfies the inequality v T ≤I。
The nonlinear controller based on Lyapunov theory in the third step is a controller designed according to the boom suspension active control system model,
the system performance index is described as:
in the above formula, J represents a performance index function, x (t) represents a state vector of a system, u (t) represents a control vector of the system, ε represents a specified stability, ζ represents a balance state quantity, ρ represents a control quantity weight ratio, and values of parameters ε, ζ and ρ are all larger than 0. Of the two integral terms mentioned above, the first term represents the requirement for the control process. The smaller the value of the control amount, the more excellent the system performance index thereof. The second term represents the requirement for control capability. The suspension system is required to achieve the control effect of the spray rod and meet the system stability performance index on the premise of using as little energy as possible.
(A+εI) T P+P(A+εI)-ρ -1 PBB T P+ζI＝0 (19)
u(t)＝-ρ -1 B T Px(t)＝-kx(t) (20)
The optimal control inputs are:
p represents a symmetric positive solution, I is an identity matrix of suitable dimension,is a regulating factor of the system.
As a regulating factor of the system, the following conditions should be satisfied:
the actual output angle of the system is gradually tracked to the ground inclination angle and is used as a control target in the design of the controller. At t → infinity, the difference between the actual angle of the spray boom and the inclination angle of the ground slope can be gradually converged to zero, and can be expressed by the following formula:
the above formula is combined with the state equation in the control system in the invention to obtain the augmentation system:
the augmentation system is arranged into the form of an augmentation state equation, and the formula is expressed as follows:
in the above formula:
and the following condition should be satisfied in the above formula:
the controller design work is carried out aiming at the established mathematical model, a series of uncertainties generated by linearization in the modeling process and accompanying operation process and external environment change are fully considered, and the controller design is carried out by the established second-order time-invariant uncertainty linear system.
The augmented state equation established by the pendulum type spray rod suspension active control system of the plant protection machine is as follows:
wherein:
and DeltaA z2 ＝E z2 θ z2 F z2 Matrix v Z2 Uncertainty of received quantity r 1 And r 2 Wherein r is 1 And r 2 The value range of (2) is 0-r 1 ≤1、0≤r 2 ≤1、0≤r 3 ≤1。
And designing the active control system controller of the boom suspension by a method of designing the tracking controller. And selecting a specified convergence rate epsilon 2 Trade-off parameter ζ =2 2 =2, calculated weighting parameter ρ 2 =2, substituting each parameter into the formula (22) in the text to obtain α 2 =1. Solving the symmetric matrix P in MATLAB simulation software 2 And an optimal feedback gain K 2 The method comprises the following steps:
K 2 ＝[2.1173×10 2 2.8051×10 1 1.0748×10 -2 1×10 3 ]。
in order to meet the design requirement of the controller, lyapunov theory is applied to prove the system stability.
Lemma 1: for any matrix H, F (t), E of appropriate dimensions, and F (t) satisfies F (t) T F (t) is less than or equal to I, then any epsilon is more than 0, HF (t) E+E can be obtained T F T (t)H T ≤ε -1 HH T +εE T E。
And (4) lemma 2: setting (a, B) to be controllable, proposition: there is a real symmetric matrix P that satisfies the Riccati inequality pa+a T P+PBB T X+FF T < 0 is equivalent to proposition: there is a real symmetry matrix P that satisfies the Riccati equation P ∞ A+A T P ∞ +P ∞ BB T P ∞ +FF T =0 where P ∞ ＞P。
Definition 1: for any uncertainty (satisfying the first assumption), if there is a positive definite matrix p=p T Number of normal timesThe derivative of Lyapunov function V (x, t) with respect to time t satisfies the following condition
The system is secondarily stabilized.
Theorem 1: if the symmetric positive definite matrix P calculated by the formula (3.30) satisfies the following matrix inequality
The closed loop system is stable.
And (3) proving: the closed loop system can be expressed as:
the following form of Lyapunov function was selected:
V(x,t)＝x T Px (31)
then:
by lemma 1, for:
the method can obtain the following steps:
and (3) making:
if the formula Q < 0 is satisfied according to (3.34), the following are:
wherein lambda is max (Q) represents the maximum eigenvalue of matrix Q. If takeThe method can obtain:
the closed loop system is then secondarily stable.
The advantages and effects are that:
a nonlinear control method for an uncertain spray boom position system of a plant protection machine is characterized by comprising the following steps of:
1) A dynamic model is built for a single pendulum spray boom suspension system and a hydraulic actuator of the plant protection machine;
2) The plant protection machine working ground flatness or the canopy height effective value has uncertainty external disturbance, on the other hand, the internal characteristics of a sensor, a hydraulic actuating mechanism and the like are changed due to modeling errors or long-time working of the plant protection machine, and the nonlinear controller based on the Lyapunov theory is designed by considering the influence of the factors.
The method comprises the following steps:
step 1) a mathematical model is built for a single pendulum spray rod suspension system of a plant protection machine. The mathematical model of the system is described as follows:
the pendulum type boom active suspension system of the plant protection machine comprises a boom, a suspender, a hydraulic cylinder and a frame connected with a vehicle body. A dynamic model is built for the boom suspension control system,
wherein T is the kinetic energy of the system, T is time, q j Is the generalized coordinates, operator d is used for the full derivative, Q j Is corresponding to q j Is a broad sense of force.
The plant protection machine pendulum type spray rod suspension obtains a group of constrained motion equations by Lagrangian multipliers:
r 1 +r 2 -d-r 3 ＝0 (2)
wherein the vector r i Corresponding to a fixed length of the connecting rod, d corresponds to a length-adjustable connecting rod comprising a hydraulic cylinder.
According to the projection of the X axis and the Y axis, the following algebraic equation is obtained after linearization:
wherein r is i0 Is |r i |，d 0 Is |d|; alpha, gamma, theta and d represent minor variations in the variables around the setpoint. In order to calculate equation (1), the kinetic energy T and the generalized force Q need to be determined j 。
Wherein I and m are respectively the moment of inertia and the mass of the plant protection machine spray lance. Generalized force Q θ Associated with rotation θ; during calculation, the displacement of the fixed electrohydraulic servo valve is as follows under the condition that only gravity works:
Q θ ＝-mgr 1 (a 1 d+a 1 θ) (6)
in the above, parameter a 1 And a 2 Is a linearization constant.
Likewise, generalized force Q d And the displacement d of the electrohydraulic servo valve is related to the displacement d of the electrohydraulic servo valve, and is calculated by fixing the rotation angle theta of the spray rod. In this case, the gravity and the work done by the electrohydraulic servo valve can be linearized:
Q d ＝F-mgr 1 (a 3 d+a 4 θ) (7)
wherein F is the initial force provided by the hydraulic actuator, parameter a 3 And a 4 Is a linearization constant.
The following kinematics equations can be derived from equations (1) - (7):
the servo valve dynamic equation can be approximately described by a first order element:
wherein τ v ，k i U is the servo valve time constant, the spool current gain and the control input current, respectively.
And (3) making:
establishing a state space equation of the system according to the formulas (8) - (11), wherein the states are respectively as follows:
y＝x 1 (13)
then there are:
in model calculations, the state equation can be expressed as:
wherein:
step 2) taking into account that certain linearization treatment is carried out in the process of establishing a system mathematical model, and the characteristics of the researched controlled object per se can generate unavoidable abrasion and aging of a mechanical structure along with the increase of the service time, so that the obtained mathematical model has certain parameter uncertainty. In order to effectively solve the influence of the uncertainty of the model on the system, a control method is applied to the chapter, and the active control system of the spray rod suspension with the uncertainty is researched.
The state space general formula of the active control system of the spray rod suspension is expressed as follows:
wherein x (t) ∈R n U (t) ∈R as a state vector for active control system of boom suspension m Y (t) ∈R as control vector for active control system of boom suspension p As an output vector of the active control system of the boom suspension. The matrix A, B, C is a nominal matrix with proper dimension in the established plant protection machine spray boom suspension system model, and the matrix delta A is taken as a model parameter error and is a matrix with uncertainty with the same dimension as A. The uncertainty matrix DeltaA depends on the uncertainty directionThe value range of the quantity r, r is [0,1 ]]. And Δa satisfies the following characteristics:
ΔA＝EνF (17)
where matrix E, F is a dimensionality constant matrix and matrix v is a dimensionality time-varying matrix that is affected by the uncertainty vector r and satisfies the inequality v T ≤I。
According to the boom suspension active control system model, an improved control method is provided for designing a controller to control the output angle of a boom suspension system, so that the boom can be stabilized as soon as possible, and the minimum requirement of the system output energy is met.
In order to achieve the purpose of stabilizing the system by the controller, the performance index designed by the invention needs to meet the controllability of the linear system. The optimal control not only can calm the spray rod, but also can enable the performance index to reach the minimum value. The system performance index is described as:
in the above formula, epsilon represents the designated stability, zeta represents the weighing state quantity, rho represents the weight ratio of the control quantity, and the values of the parameters epsilon, zeta and rho are all larger than 0. Of the two integral terms mentioned above, the first term represents the requirement for the control process. The smaller the value of the control amount, the more excellent the system performance index thereof. The second term represents the requirement for control capability. The suspension system is required to achieve the control effect of the spray rod and meet the system stability performance index on the premise of using as little energy as possible.
According to the traditional optimal control method, the control quantity is as follows:
u(t)＝-ρ -1 B T Px(t)＝-kx(t) (19)
where P is a symmetric positive definite solution and is a stable solution of the Riccati equation as follows:
(A+εI) T P+P(A+εI)-ρ -1 PBB T P+ζI＝0 (20)
wherein I is a unit matrix with proper dimension.
Because of the uncertainty in the system, a new optimal control input is derived as:
as a regulating factor of the system, the following conditions should be satisfied:
step 3) to achieve the design of the controller, it is decided to augment the above system. The actual output angle of the system is gradually tracked to the ground inclination angle and is used as a control target in the design of the controller. At t → infinity, the difference between the actual angle of the spray boom and the inclination angle of the ground slope can be gradually converged to zero, and can be expressed by the following formula:
the above formula is combined with the state equation in the control system in the invention to obtain the augmentation system:
the augmentation system is arranged into the form of an augmentation state equation, and the formula is expressed as follows:
in the above formula:
and the following condition should be satisfied in the above formula:
the controller design work is carried out aiming at a mathematical model established by a Lagrange second equation, a series of uncertainties generated by linearization in a modeling process and accompanying operation process and external environment changes are fully considered, and the controller design is carried out by the established second-order time-invariant uncertainty linear system.
The augmented state equation established by the pendulum type spray rod suspension active control system of the plant protection machine is as follows:
wherein:
and DeltaA z2 ＝E z2 θ z2 F z2 Matrix v Z2 Uncertainty of received quantity r 1 And r 2 Wherein r is 1 And r 2 The value range of (2) is 0-r 1 ≤1、0≤r 2 ≤1、0≤r 3 ≤1。
Active control system controller of spray rod suspension by designing robust tracking controllerAnd (5) designing. And selecting a specified convergence rate epsilon 2 Trade-off parameter ζ =2 2 =2, calculated weighting parameter ρ 2 =2, substituting each parameter into the formula (22) in the text to obtain α 2 =1. Solving the symmetric matrix P in MATLAB simulation software 2 And an optimal feedback gain K 2 The method comprises the following steps:
K 2 ＝[2.1173×10 2 2.8051×10 1 1.0748×10 -2 1×10 3 ]
and 4) adopting a CAN bus serial communication protocol to transmit data, and utilizing an STM32 microprocessor to track and control the angle of the spray rod of the plant protection machine. The method is characterized in that: the STM32 microprocessor is used as a main controller, and the input of the main controller is connected with the angle detection module, and the output of the main controller is connected with the motor driving module; a CAN bus communication module; and the power supply module is used for supplying power to the power supply.
And 5) providing an output signal for a driving unit based on the STM32 microprocessor, so that the real-time control of the angle of the spray rod is realized. The method is characterized in that: the control method of the main controller is to read the feedback signal of the angle detection unit and the control command signal x given by the main controller L And y d An error signal is calculated. According to the error signal, the main controller sends the angle of the spray rod calculated by a preset control algorithm and the control quantity of the current signal for driving the servo valve to the servo valve driving unit, so that the spray rod of the plant protection machine keeps tracking the ground angle to work.
Considering the linearization process existing in the model building process, and the damage and aging of the machine body caused by the interference of external non-artificial and uncontrollable factors such as the change of the working environment and the like of the control system along with the increase of the working time in the production operation process, the dynamic characteristics of the machine body can also generate certain change, so that the errors existing between the mathematical model describing the controlled object and the actual object are caused. The designed output tracking controller has stronger applicability. The control method can effectively improve the utilization rate of pesticides and the control of plant diseases and insect pests of crops. The designed boom angle tracking controller can enable the output angle of the system to track the ground gradient, and simultaneously enables the system to meet the requirement of minimum secondary performance indexes, and has more practical use value compared with a controller designed according to a nominal system model.
Description of the drawings:
FIG. 1 is a block diagram of the operation of a controller according to the present invention;
FIG. 2 is a DC regulated power supply;
FIG. 3 is CAN bus communication;
FIG. 4 is a hydraulic control signal output;
FIG. 5 is an angle signal input;
FIG. 6 is a controller master chip;
the specific embodiment is as follows:
a nonlinear control method of a pendulum type spray boom suspension system of a plant protection machine is characterized by comprising the following steps of:
the method comprises the following steps:
firstly, collecting real-time data of a spray boom of a plant protection machine; (actual parameters of position, height, angle, etc. of the boom relative to the ground)
Secondly, inputting the data acquired in the first step into a dynamics model;
and thirdly, utilizing a nonlinear controller based on Lyapunov theory to carry out servo control on the angle of the spray rod suspension of the plant protection machine, thereby realizing servo tracking of the reference track.
Establishing a mathematical model for a single pendulum spray rod suspension system of a plant protection machine; the output tracking controller is designed by fully considering linearization processing in the modeling process and loss generated by a machine body after long-time use. The method comprises the following steps:
1) A dynamic model is built for a single pendulum spray boom suspension system and a hydraulic actuator of the plant protection machine;
2) The plant protection machine working ground flatness or the canopy height effective value has uncertainty external disturbance, on the other hand, the internal characteristics of a sensor, a hydraulic actuating mechanism and the like are changed due to modeling errors or long-time working of the plant protection machine, and the nonlinear controller based on the Lyapunov theory is designed by considering the influence of the factors.
The second step is that the dynamic model is established for a single pendulum boom suspension system and a hydraulic actuator of the plant protection machine; the kinetic model of the system is described as follows:
the pendulum type boom active suspension system of the plant protection machine comprises a boom, a suspender, a hydraulic cylinder and a frame connected with a vehicle body. A dynamic model is built for the boom suspension control system,
wherein T is the kinetic energy of the system, T is time, q j Is the generalized coordinates, operator d is used for the full derivative, Q j Is corresponding to q j Is a broad sense of force. dt is the total derivative with respect to time,represents the partial derivative->Represents q j Is a derivative of (a).
The plant protection machine pendulum type spray rod suspension obtains a group of constrained motion equations by Lagrangian multipliers:
r 1 +r 2 -d-r 3 ＝0 (2)
wherein the vector r i Corresponding to a fixed length of the connecting rod, d corresponding to a length-adjustable connecting rod comprising a hydraulic cylinder, vector r 1 ,r 2 ,r 3 And d corresponds to a length-adjustable connecting rod with a hydraulic cylinder (two ends of the hydraulic cylinder are respectively connected with the spray boom and the suspender).
According to the projection of the X axis and the Y axis, the following algebraic equation is obtained after linearization:
wherein r is i0 Is |r i I=1, 2,3 represents the modulus of the vector, d 0 Is |d|; alpha, gamma, theta and d represent the variables micro-scale around the setpoint
Small variations. Wherein T and Q are represented as:
wherein I and m are respectively the moment of inertia and the mass of the plant protection machine spray lance.And->Represents angular velocity, T represents kinetic energy of the system and generalized force Q θ Associated with rotation θ; parameter a 1 And a 2 The displacement of the electrohydraulic servo valve is fixed by linearization constant, and under the condition of only gravity working, the displacement is as follows:
Q θ ＝-mgr 1 (a 1 d+a 1 θ) (6)
in the above, parameter a 1 And a 2 Is a linearization constant.
Likewise, generalized force Q d And the displacement d of the electrohydraulic servo valve is related to the displacement d of the electrohydraulic servo valve, and is calculated by fixing the rotation angle theta of the spray rod. In this case, the gravity and the work done by the electrohydraulic servo valve can be linearized:
Q d ＝F-mgr 1 (a 3 d+a 4 θ) (7)
wherein F is the initial force provided by the hydraulic actuator, parameter a 3 And a 4 Is a linearization constant.
The following kinematics equations can be derived from equations (1) - (7):
the servo valve dynamic equation can be approximately described by a first order element:
wherein τ v ，k i I is the servo valve time constant, the valve core current gain and the control input current respectively.
And (3) making:
establishing a state space equation of the system according to the formulas (8) - (11), wherein the states are respectively as follows:
/>
y＝x 1 (13)
then there are:
in model calculations, the state equation can be expressed as:
wherein:
the general state space of the active control system of the spray boom suspension (the general state equation of the system is obtained by establishing generalized coordinates, and the state equation is obtained by linearizing and finishing on the basis of the obtained dynamic equation) is represented as follows:
wherein x (t) ∈R n U (t) ∈R as a state vector for active control system of boom suspension m Y (t) ∈R as control vector for active control system of boom suspension p As an output vector of the active control system of the boom suspension. The matrix deltaa is a matrix with uncertainty in the same dimension as a as the model parameter error. The uncertainty matrix DeltaA depends on an uncertainty vector r, and the value range of r is [0,1]. And Δa satisfies the following characteristics:
ΔA＝EνF (17)
where matrix E, F is a dimensionality constant matrix and matrix v is a dimensionality time-varying matrix that is affected by the uncertainty vector r and satisfies the inequality v T ≤I。
The nonlinear controller based on Lyapunov theory in the third step is designed according to the boom suspension active control system model (state space general formula of the boom suspension active control system), so that the purpose of controlling the output angle of the boom suspension system is achieved, the boom can be calmed as soon as possible, and meanwhile, the requirement of minimum system output energy is met.
In order to achieve the purpose of stabilizing the system by the controller, the performance index designed by the invention needs to meet the controllability of the linear system. The optimal control not only can calm the spray rod, but also can enable the performance index to reach the minimum value. The system performance index is described as:
in the above formula, J represents a performance index function, x (t) represents a state vector of a system, u (t) represents a control vector of the system, ε represents a specified stability, ζ represents a balance state quantity, ρ represents a control quantity weight ratio, and values of parameters ε, ζ and ρ are all larger than 0. Of the two integral terms mentioned above, the first term represents the requirement for the control process. The smaller the value of the control amount, the more excellent the system performance index thereof. The second term represents the requirement for control capability. The suspension system is required to achieve the control effect of the spray rod and meet the system stability performance index on the premise of using as little energy as possible.
(A+εI) T P+P(A+εI)-ρ -1 PBB T P+ζI＝0 (19)
u(t)＝-ρ -1 B T Px(t)＝-kx(t) (20)
The optimal control inputs are:
p represents a symmetric positive solution, I is an identity matrix of suitable dimension,is a regulating factor of the system.
As a regulating factor of the system, the following conditions should be satisfied:
the actual output angle of the system is gradually tracked to the ground inclination angle and is used as a control target in the design of the controller. At t → infinity, the difference between the actual angle of the spray boom and the inclination angle of the ground slope can be gradually converged to zero, and can be expressed by the following formula:
the above formula is combined with the state equation in the control system in the invention to obtain the augmentation system:
the augmentation system is arranged into the form of an augmentation state equation, and the formula is expressed as follows:
in the above formula:
and the following condition should be satisfied in the above formula:
the controller design work is carried out aiming at the established mathematical model, a series of uncertainties generated by linearization in the modeling process and accompanying operation process and external environment change are fully considered, and the controller design is carried out by the established second-order time-invariant uncertainty linear system.
The augmented state equation established by the pendulum type spray rod suspension active control system of the plant protection machine is as follows:
wherein:
and DeltaA z2 ＝E z2 θ z2 F z2 Matrix v Z2 Uncertainty of received quantity r 1 And r 2 Wherein r is 1 And r 2 The value range of (2) is 0-r 1 ≤1、0≤r 2 ≤1、0≤r 3 ≤1。
And designing the active control system controller of the boom suspension by a method of designing the tracking controller. And selecting a specified convergence rate epsilon 2 Trade-off parameter ζ =2 2 =2, calculated weighting parameter ρ 2 =2, substituting each parameter into the formula (22) in the text to obtain α 2 =1. Solving the symmetric matrix P in MATLAB simulation software 2 And an optimal feedback gain K 2 The method comprises the following steps:
K 2 ＝[2.1173×10 2 2.8051×10 1 1.0748×10 -2 1×10 3 ]. (Single pendulum suspension systems are designed to indirectly change the angle of the boom relative to the ground by adjusting the angle between the cylinder and the boom via solenoid valves, maintaining the boom relatively parallel to the ground.)
In order to meet the design requirement of the controller, lyapunov theory is applied to prove the system stability.
Lemma 1: for any matrix H, F (t), E of appropriate dimensions, and F (t) satisfies F (t) T F (t) is less than or equal to I, then any epsilon is more than 0, HF (t) E+E can be obtained T F T (t)H T ≤ε -1 HH T +εE T E。
And (4) lemma 2: the (A, B) is a combination ofControlled, proposition: there is a real symmetric matrix P that satisfies the Riccati inequality pa+a T P+PBB T X+FF T < 0 is equivalent to proposition: there is a real symmetry matrix P that satisfies the Riccati equation P ∞ A+A T P ∞ +P ∞ BB T P ∞ +FF T =0 where P ∞ ＞P。
Definition 1: for any uncertainty (satisfying the first assumption), if there is a positive definite matrix p=p T Number of normal timesThe derivative of Lyapunov function V (x, t) with respect to time t satisfies the following condition
The system is secondarily stabilized.
Theorem 1: if the symmetric positive definite matrix P calculated by the formula (3.30) satisfies the following matrix inequality
The closed loop system is stable.
And (3) proving: the closed loop system can be expressed as:
the following form of Lyapunov function was selected:
V(x,t)＝x T Px (31)
then:
by lemma 1, for:
the method can obtain the following steps:
and (3) making:
if the formula Q < 0 is satisfied according to (3.34), the following are:
wherein lambda is max (Q) represents the maximum eigenvalue of matrix Q. If takeThe method can obtain: />
The closed loop system is then secondarily stable.
( This part is the controller parameter solving process finally obtained in step 3. Firstly, constructing a Lyapunov function according to expected performance indexes to prove the stability of a system, then obtaining sufficient conditions meeting the establishment of the performance indexes according to equivalent substitution conditions of theorem and quotients, and finally obtaining controller parameters by solving matrix inequality )
And the CAN bus serial communication protocol is adopted to transmit data, and the STM32 microprocessor is utilized to control the angle of the spray rod of the plant protection machine. The STM32 microprocessor is used as a main controller, and the input of the main controller is connected with the angle detection module, and the output of the main controller is connected with the motor driving module; a CAN bus communication module; and the power supply module is used for supplying power to the power supply. The STM32 microprocessor is based to provide the output signal for the driving unit, so that the real-time control on the position of the spray rod is realized. The control method of the main controller is to read the feedback signal of the angle detection unit and the control command signals x and y given by the main controller, and calculate an error signal. According to the error signal, the main controller sends the angle of the spray rod calculated by a preset control algorithm and the control quantity of the current signal for driving the servo valve to the servo valve driving unit, so that the spray rod of the plant protection machine keeps tracking the ground angle to work.
The invention is further described below with reference to the accompanying drawings.
A nonlinear control method for an uncertain spray boom position system of a plant protection machine is characterized by comprising the following steps of:
1) Establishing a mathematical model of a single pendulum spray rod suspension system of the plant protection machine by adopting a second Lagrange dynamic equation;
2) According to the actual working demand, linearization processing in the modeling process and loss generated by a machine body after long-time use are fully considered, and an output tracking controller based on optimal control is designed;
3) The CAN bus serial communication protocol is adopted to transmit data, and the STM32 microprocessor is utilized to carry out servo control on the angle of the spray rod of the plant protection machine, so that the servo tracking of the reference track is realized.
The method comprises the following steps:
and 1) establishing a dynamic model for the single pendulum spray rod suspension system of the plant protection machine by adopting a second Lagrange dynamic equation.
The kinetic model of the system is described as follows:
the pendulum type boom active suspension system of the plant protection machine comprises a boom, a suspender, a hydraulic cylinder and a frame connected with a vehicle body. A second Lagrangian equation is used to build a dynamic model for the boom suspension control system,
wherein T is the kinetic energy of the system, T is time, q j Is the generalized coordinates, operator d is used for the full derivative, Q j Is corresponding to q j Is a broad sense of force.
In general, the change in the generalized coordinates of a passive system is a closed kinematic chain, which means that the different coordinates are interrelated. This correlation is obtained by expressing the geometric relationships of the system, thereby producing as many algebraic constraint equations as there are coordinates. The number of constraint equations is given by the difference between the selected total number of coordinates and the degree of freedom of the mechanism. In general, these algebraic equations need to be introduced into the differential equations, derived from the equations.
The plant protection machine pendulum type spray rod suspension obtains a group of constrained motion equations by Lagrangian multipliers:
r 1 +r 2 -d-r 3 ＝0 (2)
wherein the vector r i Corresponding to a fixed length of the connecting rod, d corresponds to a length-adjustable connecting rod comprising a hydraulic cylinder.
According to the projection of the X axis and the Y axis, the following algebraic equation is obtained after linearization:
wherein r is i0 Is |r i |，d 0 Is |d|; alpha, gamma, theta and d represent minor variations in the variables around the setpoint. In order to calculate equation (1), the kinetic energy T and the generalized force Q need to be determined j 。
Wherein I and m are respectively the moment of inertia and the mass of the plant protection machine spray lance. Generalized force Q θ Associated with rotation θ; during calculation, the displacement of the fixed electrohydraulic servo valve is as follows under the condition that only gravity works:
Q θ ＝-mgr 1 (a 1 d+a 1 θ) (6)
in the above, parameter a 1 And a 2 Is a linearization constant.
Likewise, generalized force Q d And the displacement d of the electrohydraulic servo valve is related to the displacement d of the electrohydraulic servo valve, and is calculated by fixing the rotation angle theta of the spray rod. In this case, the gravity and the work done by the electrohydraulic servo valve can be linearized:
Q d ＝F-mgr 1 (a 3 d+a 4 θ) (7)
wherein F is the initial force provided by the hydraulic actuator, parameter a 3 And a 4 Is a linearization constant.
The following kinematics equations can be derived from equations (1) - (7):
the servo valve dynamic equation can be approximately described by a first order element:
wherein τ v ，k i U is the servo valve time constant, the spool current gain and the control input current, respectively.
And (3) making:
establishing a state space equation of the system according to the formulas (8) - (11), wherein the states are respectively as follows:
y＝x 1 (13)
then there are:
in model calculations, the state equation can be expressed as:
wherein:
step 2) taking into account that certain linearization treatment is carried out in the process of establishing a system mathematical model, and the characteristics of the researched controlled object per se can generate unavoidable abrasion and aging of a mechanical structure along with the increase of the service time, so that the obtained mathematical model has certain parameter uncertainty. In order to effectively solve the influence of the uncertainty of the model on the system, the control method is applied to the seal, and the stability of the active control system of the boom suspension with the uncertainty is researched.
The state space general formula of the active control system of the spray rod suspension is expressed as follows:
wherein x (t) ∈R n U (t) ∈R as a state vector for active control system of boom suspension m Y (t) ∈R as control vector for active control system of boom suspension p As an output vector of the active control system of the boom suspension. Wherein the matrix A, B, C is a nominal matrix with proper dimension in the established plant protection machine spray rod suspension system model, and the matrix delta A is taken as the modelThe parameter error is a matrix with uncertainty in the same dimension as a. The uncertainty matrix DeltaA depends on an uncertainty vector r, and the value range of r is [0,1]. And Δa satisfies the following characteristics:
ΔA＝EνF (17)
where matrix E, F is a dimensionality constant matrix and matrix v is a dimensionality time-varying matrix that is affected by the uncertainty vector r and satisfies the inequality v T ≤I。
According to the active control system model of the spray boom suspension, a control method is provided for designing a controller, so that the purpose of controlling the output angle of the spray boom suspension system is achieved, the spray boom can be calmed as soon as possible, and the requirement of minimum system output energy is met.
In order to achieve the purpose of stabilizing the system by the controller, the performance index designed by the invention needs to meet the controllability of the linear system. The optimal control not only can calm the spray rod, but also can enable the performance index to reach the minimum value. The system performance index is described as:
in the above formula, J represents a performance index function, x (t) represents a state vector of a system, u (t) represents a control vector of the system, ε represents a specified stability, ζ represents a balance state quantity, ρ represents a control quantity weight ratio, and values of parameters ε, ζ and ρ are all larger than 0. Of the two integral terms mentioned above, the first term represents the requirement for the control process. The smaller the value of the control amount, the more excellent the system performance index thereof. The second term represents the requirement for control capability. The suspension system is required to achieve the control effect of the spray rod and meet the system stability performance index on the premise of using as little energy as possible.
According to the traditional optimal control method, the control quantity is as follows:
u(t)＝-ρ -1 B T Px(t)＝-kx(t) (19)
where P is a symmetric positive definite solution and is a stable solution of the Riccati equation as follows:
(A+εI) T P+P(A+εI)-ρ -1 PBB T P+ζI＝0 (20)
wherein I is a unit matrix with proper dimension.
Because of the uncertainty in the system, a new optimal control input is derived as:
as a regulating factor of the system, the following conditions should be satisfied:
step 3) to achieve the design of the controller, it is decided to augment the above system. The actual output angle of the system is gradually tracked to the ground inclination angle and is used as a control target in the design of the controller. At t → infinity, the difference between the actual angle of the spray boom and the inclination angle of the ground slope can be gradually converged to zero, and can be expressed by the following formula:
to make the output error vector e (t) =y (t) -y of the system r Gradually converging towards zero, so that the error vector is integrated, and the error can be eliminated after the integration treatment, so that the goal of enabling the error to be zero is realized, and the error vector can be described by the following equation:
the above formula is combined with the state equation in the control system in the invention to obtain the augmentation system:
the augmentation system is arranged into the form of an augmentation state equation, and the formula is expressed as follows:
in the above formula:
and the following condition should be satisfied in the above formula:
the controller design work is carried out aiming at the established mathematical model, a series of uncertainties generated by linearization in the modeling process and accompanying operation process and external environment change are fully considered, and the controller design is carried out by the established second-order time-invariant uncertainty linear system.
The augmented state equation established by the pendulum type spray rod suspension active control system of the plant protection machine is as follows:
wherein:
and DeltaA z2 ＝E z2 θ z2 F z2 Matrix v Z2 Uncertainty of received quantity r 1 And r 2 Wherein r is 1 And r 2 The value range of (2) is 0-r 1 ≤1、0≤r 2 ≤1、0≤r 3 ≤1。
And designing the active control system controller of the boom suspension by a method for designing a robust tracking controller. And selecting a specified convergence rate epsilon 2 Trade-off parameter ζ =2 2 =2, calculated weighting parameter ρ 2 =2, substituting each parameter into the formula (22) in the text to obtain α 2 =1. Solving the symmetric matrix P in MATLAB simulation software 2 And an optimal feedback gain K 2 The method comprises the following steps:
K 2 ＝[2.1173×10 2 2.8051×10 1 1.0748×10 -2 1×10 3 ]
and 4) adopting a CAN bus serial communication protocol to transmit data, and utilizing an STM32 microprocessor to track and control the angle of the spray rod of the plant protection machine. The method is characterized in that: the STM32 microprocessor is used as a main controller, and the input of the main controller is connected with the angle detection module, and the output of the main controller is connected with the motor driving module; a CAN bus communication module; and the power supply module is used for supplying power to the power supply.
And 5) providing an output signal for a driving unit based on the STM32 microprocessor, so that the real-time control of the angle of the spray rod is realized. The method is characterized in that: the control method of the main controller is to read the feedback signal of the angle detection unit and the control command signal x given by the main controller L And y d An error signal is calculated. According to the error signal, the main controller sends the angle of the spray rod calculated by a preset control algorithm and the control quantity of the current signal for driving the servo valve to the servo valve driving unit, so that the spray rod of the plant protection machine keeps tracking the ground angle to work.
In summary, the linearization process existing in the model building process is considered, and the control system causes damage and aging of the machine body along with the increase of the working time in the production operation process and the interference of external non-artificial and uncontrollable factors such as the change of the working environment, and the dynamic characteristics of the machine body also generate certain change, so that errors exist between the mathematical model describing the controlled object and the actual object. The designed output tracking controller has stronger applicability. The controller based on the method has been verified in a MATLAB environment by simulation, and the actual conditions of various complex terrains, working conditions and the like in the spraying operation of the plant protection machine are simulated. The control method can effectively improve the utilization rate of pesticides and the control of plant diseases and insect pests of crops. The designed boom angle tracking controller can enable the output angle of the system to track the ground gradient, and simultaneously enables the system to meet the requirement of minimum secondary performance indexes, and has more practical use value compared with a controller designed according to a nominal system model.
Claims (3)
1. A nonlinear control method of a pendulum type spray boom suspension system of a plant protection machine is characterized by comprising the following steps of:
the method comprises the following steps:
firstly, collecting real-time data of a spray boom of a plant protection machine;
secondly, inputting the data acquired in the first step into a dynamics model;
thirdly, servo control is carried out on the angle of the spray rod suspension of the plant protection machine by using a nonlinear controller based on Lyapunov theory, so that servo tracking of a reference track is realized;
the second step is to build a dynamic model for a single pendulum boom suspension system and a hydraulic actuator of the plant protection machine; the kinetic model of the system is described as follows:
the pendulum type boom active suspension system of the plant protection machine comprises a boom, a suspender, a hydraulic cylinder and a frame connected with a vehicle body; a dynamic model is built for the boom suspension control system,
wherein T is the kinetic energy of the system, T is time, q j Is the generalized coordinates, operator d is used for the full derivative, Q j Is corresponding to q j Is a broad sense of force;
the plant protection machine pendulum type spray rod suspension obtains a group of constrained motion equations by Lagrangian multipliers:
r 1 +r 2 -d-r 3 ＝0 (2)
wherein the vector r i Corresponding to a fixed length of the connecting rod, d corresponding to a length-adjustable connecting rod comprising a hydraulic cylinder, vector r 1 ,r 2 ,r 3 Corresponding to a fixed length link in the suspension, d corresponding to a length-adjustable link comprising a hydraulic cylinder;
according to the projection of the X axis and the Y axis, the following algebraic equation is obtained after linearization:
wherein r is i0 Is |r i I=1, 2,3 represents the modulus of the vector, d 0 Is |d|; α, γ, θ and d represent minor variations in the variables around the setpoint; wherein T and Q are represented as:
wherein I and m are respectively the moment of inertia and the mass of a spray rod of the plant protection machine;and->Represents angular velocity, T represents kinetic energy of the system and generalized force Q θ Associated with rotation θ; parameter a 1 And a 2 The displacement of the electrohydraulic servo valve is fixed by linearization constant, and under the condition of only gravity working, the displacement is as follows:
Q θ ＝-mgr 1 (a 1 d+a 1 θ) (6)
in the above, parameter a 1 And a 2 Is a linearization constant;
likewise, generalized force Q d The displacement d of the electrohydraulic servo valve is related to the displacement d of the electrohydraulic servo valve, and is calculated by fixing the rotation angle theta of the spray rod; in this case, the work performed by the gravity and electrohydraulic servo valve is linearized:
Q d ＝F-mgr 1 (a 3 d+a 4 θ) (7)
wherein F is the initial force provided by the hydraulic actuator, parameter a 3 And a 4 Is a linearization constant;
the following kinematic equations are obtained according to equations (1) - (7):
the servo valve dynamic equation is approximately described by a first-order link:
wherein τ v ，k i I is the servo valve time constant, the valve core current gain and the control input current respectively;
and (3) making:
establishing a state space equation of the system according to the formulas (8) - (11), wherein the states are respectively as follows:
y＝x 1 (13)
then there are:
in model calculation, the state equation is expressed as:
wherein:
F C 2 ＝[100]
the state space general formula of the active control system of the spray rod suspension is expressed as follows:
wherein x (t) ∈R n U (t) ∈R as a state vector for active control system of boom suspension m Y (t) ∈R as control vector for active control system of boom suspension p Active as boom suspensionControlling an output vector of the system; the matrix delta A is used as a model parameter error and is a matrix with uncertainty of the same dimension as A; the uncertainty matrix DeltaA depends on an uncertainty vector Deltar, and the Deltar takes the value range of [0,1 ]]The method comprises the steps of carrying out a first treatment on the surface of the And Δa satisfies the following characteristics:
ΔA＝EνF (17)
where matrix E, F is a dimensionality constant matrix, matrix v is a dimensionality time-varying matrix, the matrix is affected by an uncertainty vector Deltar and satisfies an inequality nu v T ≤I。
2. The nonlinear control method of the pendulum type spray rod suspension system of the plant protection machine according to claim 1, wherein the nonlinear control method comprises the following steps: the nonlinear controller based on Lyapunov theory in the third step is a controller designed according to the boom suspension active control system model,
the system performance index is described as:
in the above formula, J represents a performance index function, x (t) represents a state vector of a system, u (t) represents a control vector of the system, epsilon represents a designated stability, zeta represents a weighing state quantity, rho represents a control quantity weight ratio, and values of parameters epsilon, zeta and rho are all larger than 0;
(A+εI) T P+P(A+εI)-ρ -1 PBB T P+ζI＝0 (19)
u(t)＝-ρ -1 B T Px(t)＝-kx(t) (20)
the optimal control inputs are:
p represents a symmetric positive solution, I is an identity matrix of suitable dimension,is a regulating factor of the system; />As a regulating factor of the system, the following conditions should be satisfied:
progressively tracking the actual output angle of the system to the ground inclination angle to be used as a control target in the design of the controller; at t → infinity, the difference between the actual angle of the spray boom and the inclination angle of the ground slope can be gradually converged to zero, which is expressed by the following formula:
the above formula is combined with the state equation in the control system in the invention to obtain the augmentation system:
the augmentation system is arranged into the form of an augmentation state equation, and the formula is expressed as follows:
in the above formula:
and the following condition should be satisfied in the above formula:
aiming at the established mathematical model, the controller design work is carried out, a series of uncertainties generated by linearization in the modeling process and accompanying operation process and external environment change are fully considered, and the established second-order time-invariant uncertainty linear system is used for the controller design;
the augmented state equation established by the pendulum type spray rod suspension active control system of the plant protection machine is as follows:
wherein:
and DeltaA z2 ＝E z2 θ z2 F z2 Matrix v Z2 Uncertainty of Deltar 1 And Deltar 2 Wherein Δr is the influence of 1 And Deltar 2 The range of the value of (a) is 0-deltar 1 ≤1、0≤Δr 2 ≤1、0≤Δr 3 ≤1；
Opposed spray by designing tracking controllerThe controller of the active control system of the rod suspension is designed; and selecting a specified convergence rate epsilon 2 Trade-off parameter ζ =2 2 =2, calculated weighting parameter ρ 2 =2, substituting each parameter into the formula (22) to obtain α 2 =1; solving the symmetric matrix P in MATLAB simulation software 2 And an optimal feedback gain K 2 The method comprises the following steps:
K 2 ＝[2.1173×10 2 2.8051×10 1 1.0748×10 -2 1×10 3 ]。
3. the nonlinear control method of the pendulum type spray rod suspension system of the plant protection machine according to claim 1, wherein the nonlinear control method comprises the following steps: in order to meet the design requirement of the controller, the Lyapunov theory is applied to prove the system stability;
lemma 1: for any matrix H, F (t), E of appropriate dimensions, and F (t) satisfies F (t) T F (t) is less than or equal to I, and then any epsilon is more than 0, HF (t) E+E is obtained T F T (t)H T ≤ε -1 HH T +εE T E；
And (4) lemma 2: setting (a, B) to be controllable, proposition: there is a real symmetric matrix P that satisfies the Riccati inequality pa+a T P+PBB T X+FF T < 0 is equivalent to proposition: there is a real symmetry matrix P that satisfies the Riccati equation P ∞ A+A T P ∞ +P ∞ BB T P ∞ +FF T =0 where P ∞ ＞P；
Definition 1: for arbitrary uncertainty, if there is a positive definite matrix p=p T Number of normal timesThe derivative of Lyapunov function V (x, t) with respect to time t satisfies the following condition
The system is secondarily stabilized;
theorem 1: if the symmetric positive definite matrix P calculated by the formula (3.30) satisfies the following matrix inequality
The closed loop system is stable;
and (3) proving: the closed loop system is expressed as:
the following form of Lyapunov function was selected:
V(x,t)＝x T Px (31)
then:
by lemma 1, for:
the method comprises the following steps:
and (3) making:
if the formula Q < 0 is satisfied according to (3.34), the following are:
wherein lambda is max (Q) represents the maximum eigenvalue of matrix Q; if takeObtaining:
the closed loop system is then secondarily stable.
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| CN111736550A (en) | 2020-10-02 |
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| CN111679581A (en) | 2020-09-18 |
| CN112327610B (en) | 2022-06-24 |
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| CN111679581B (en) | 2022-06-24 |
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