CN110620524B - Soft robot active-disturbance-rejection control method based on dielectric elastomer actuator - Google Patents

Soft robot active-disturbance-rejection control method based on dielectric elastomer actuator Download PDF

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CN110620524B
CN110620524B CN201910912700.0A CN201910912700A CN110620524B CN 110620524 B CN110620524 B CN 110620524B CN 201910912700 A CN201910912700 A CN 201910912700A CN 110620524 B CN110620524 B CN 110620524B
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dielectric elastomer
elastomer actuator
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state
actuator
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彭滔
***
张路
周鹏
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Chongqing University of Technology
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Abstract

The invention discloses a soft robot active disturbance rejection control method based on a dielectric elastomer actuator, which comprises the steps of firstly establishing a dynamic control model of the dielectric elastomer actuator in a virtual work simulation mode; secondly, designing an extended state observer to obtain unknown system dynamic information and state quantity of the dielectric elastomer actuator, wherein the system dynamic information and the state quantity are used as alternative quantities in the control process; calculating a state tracking error signal by using the difference between the current state quantity and a designed state expected value, and feeding the state tracking error signal back to the dielectric elastomer actuator by using a designed state error feedback controller, so that the control target of the soft robot is realized when the state tracking error converges to zero; therefore, the control strategy of the dielectric elastomer actuator does not depend on the accurate dynamic control model of the dielectric elastomer actuator, the requirement on the input signal of a control system is reduced, and the robustness and the adaptability of the soft robot control system based on the dielectric elastomer actuator are enhanced.

Description

Soft robot active-disturbance-rejection control method based on dielectric elastomer actuator
Technical Field
The invention relates to the technical field of soft robots, in particular to a soft robot active disturbance rejection control method based on a dielectric elastomer actuator.
Background
A Dielectric Elastomer Actuator (DEA) is composed of two flexible electrodes and a flexible film sandwiched therebetween, and when a voltage is applied to the electrodes, the Dielectric elastomer film stretches to reduce its thickness, so that it deforms. Because the dielectric elastomer actuator has the advantages of high strain response, high energy density, high response speed and the like, the dielectric elastomer actuator becomes a basic component of a soft robot and is widely applied to various fields such as artificial muscles, bionic robots, energy generators and the like.
Since soft body materials are elastic and can be deformed by bending, twisting, stretching, compressing, clasping, wrinkling, etc., soft bodies can be constrained to move in a plane, which may be considered to have infinite degrees of freedom, unlike rigid bodies which can be described as six degrees of freedom. Therefore, modeling and control of soft robots are challenging, requiring new modeling and control methods.
Mathematical modeling of dielectric elastomer actuators is essentially a necessary condition for understanding their characteristics and is also a prerequisite basis for achieving control. In general, mathematical modeling methods for dielectric elastomer actuators include two categories: physics-based modeling methods (phenomenological models) and phenomenological modeling methods (phenomenological models).
The modeling method based on physics is mainly based on the physical principle and has the advantages of being clear and rigorous; the phenomenological modeling method is mainly based on experimental phenomena and has the advantages of simplicity and high efficiency; the two modeling methods are the most different according to different modeling bases.
Based on a continuous medium mechanics theory and a thermodynamic theory, a materialist model of the dielectric elastomer actuator can be established by analyzing an energy conversion mechanism in the deformation process of the dielectric elastomer actuator; a phenomenological model of the dielectric elastomer actuator can be established by analyzing the behavior of the dielectric elastomer actuator during the experiment and using a combination of physical components (e.g., resistors, capacitors, springs, and bumpers) to represent a model of the dielectric elastomer actuator. For example, Sarban et al (see "r. Sarban, b. lassen, and m. willazen, Dynamic electrochemical modulation of dielectric elastomer actuators with metallic electrodes, IEEE/electromagnetic interactions on mechanical, vol.17, No.5, pp.960-967,2012") use capacitors and resistors to describe the electrical model of a dielectric elastomer actuator and springs and dampers to describe the mechanical model of a dielectric elastomer actuator, creating a phenomenological model of a dielectric elastomer actuator in which the electrical and mechanical portions are related by maxwell forces.
Currently, the results of the dielectric elastomer actuators are focused mainly on the material and physical properties, while the control results are few. Some researchers have proposed control strategies using the above described phenomenological and phenomenological models of dielectric elastomer actuators, but most of them are implemented using open-loop control using pressure control of pressure sensors or using volume control of strain sensors to drive a section of the soft body of a robot. However, in general, there are some unmeasured parameters in the dielectric elastomer actuator, and some estimates of them need to be considered in the control process. In this respect, it is necessary to use some achievable control of the dielectric elastomer actuator, using a control strategy that can use the dynamics of the dielectric elastomer actuator, tolerating parameter uncertainties and limited measurement conditions.
In the control field, active disturbance rejection control is an effective method for estimating and compensating all unknown information of a dynamic system in a controller, which can successfully process the dynamic system with unknown and uncertain values and is applied in many fields, such as robots, industrial control systems, and the like.
Generally, some unknown parameters and immeasurable information exist in the dielectric elastomer actuator, and the unknown dynamic information and the estimated value or observed value of the state quantity of the system caused by the unknown parameters or the immeasurable information need to be considered in the control process. Therefore, there is a pressing need to consider the dynamics of the dielectric elastomer actuators, the uncertainty of the tolerance parameters, and to design a usable controller and its control method under limited measurable conditions in the control process.
Disclosure of Invention
Aiming at the defects in the prior art, the technical problems to be solved by the invention are as follows: how to provide a soft robot active disturbance rejection control method based on a dielectric elastomer actuator to reduce the requirement on an input signal and enhance the robustness and the adaptability of a control system of the dielectric elastomer actuator.
In order to solve the technical problems, the invention adopts the following technical scheme:
a soft robot active disturbance rejection control method based on a dielectric elastomer actuator comprises the following steps:
establishing a dynamic control model of the dielectric elastomer actuator by using a virtual work simulation mode;
acquiring unknown system dynamic information and state quantity of the dielectric elastomer actuator by using an extended state observer, and using the system dynamic information and the state quantity as substitute quantity in the control process;
and a state tracking error signal obtained by calculating the difference between the state quantity which can be measured in the dielectric elastomer actuator and the observed state quantity obtained by the extended state observer and a designed expected value is utilized, and the state tracking error signal is fed back to the dielectric elastomer actuator by utilizing a designed state error feedback controller, so that the control target of the soft robot is realized when the tracking error converges to zero.
In the above method for controlling active disturbance rejection of a soft robot based on a dielectric elastomer actuator, specifically, the dynamic control model of the dielectric elastomer actuator is:
Figure BDA0002215200420000031
wherein u is Φ2Is the control input to the dielectric elastomer actuator, Φ is the control voltage of the dielectric elastomer actuator; y is the output signal of the dielectric elastomer actuator and has:
Figure BDA0002215200420000032
Figure BDA0002215200420000033
wherein x ═ x1,x2]TIs a state quantity of a dielectric elastomer actuator, where x1Is the transverse deformation ratio of the dielectric elastic film in the dielectric elastic body actuator, i.e. the ratio of the transverse length value after the deformation of the dielectric elastic film to the transverse length value before the deformation, x2For the rate of deformation of the dielectric elastomeric film in the dielectric elastomeric actuator,
Figure BDA0002215200420000034
and
Figure BDA0002215200420000035
respectively represent state quantities x1、x2Differentiation of (1); l is a value of a transverse length before deformation of the dielectric elastic film, L3Dielectric bulletThickness of the sexual membrane before deformation; p is the transverse tension to which the dielectric elastic film is subjected when deformed; t is the temperature of the environment and,
Figure BDA0002215200420000036
is the dielectric constant of the dielectric elastomer actuator, μ (T) is the shear modulus of the dielectric elastomer actuator dependent on the ambient temperature T, JmIs the limit of the transverse deformation ratio of the dielectric elastomer actuator after deformation relative to the actuator before deformation; ρ is the density of the dielectric elastomer actuator, c is the damping coefficient of the dielectric elastomer actuator,
Figure BDA0002215200420000037
is dielectric constant
Figure BDA0002215200420000038
At x1The amount of change in the deformation process.
In the above method for controlling active disturbance rejection of a soft robot based on a dielectric elastomer actuator, specifically, the extended state observer is:
Figure BDA0002215200420000039
wherein x iso1、xo2And xo3Are the three observed state quantities output by the extended state observer,
Figure BDA00022152004200000310
and
Figure BDA00022152004200000311
respectively representing the observed state quantities xo1、xo2And xo3Differentiation of (1); k is a radical ofo1、ko2And ko3The method is a design parameter of the extended state observer, and the design parameters are positive values; e.g. of the typeo1＝xo1-x1For x to expand the state observer1The observation error of (2).
In the above method for controlling active disturbance rejection of a soft robot based on a dielectric elastomer actuator, specifically, the error feedback controller is:
Figure BDA0002215200420000041
wherein u is0Tracking error, x, output by error feedback controllero1、xo2And xo3Three observed state quantities, x, output by the extended state observer1d、x2dAnd x3dRespectively, are observed state quantities xo1、xo2And xo3A corresponding state quantity expected value; k is a radical ofc1、kc2Are design parameters of the error feedback controller and are all positive values.
In summary, the software robot active-disturbance-rejection control method based on the dielectric elastomer actuator provided by the invention establishes a dynamic control model of the dielectric elastomer actuator in a virtual work simulation manner; acquiring unknown system dynamic information and state quantity of the dielectric elastomer actuator by using an extended state observer, and using the system dynamic information and the state quantity as substitute quantity in the control process; and a state tracking error signal obtained by calculating the difference between the state quantity which can be measured in the dielectric elastomer actuator and the observed state quantity obtained by the extended state observer and the designed state expected value is used, and the designed state error feedback controller is used for feeding back the state tracking error signal to the dielectric elastomer actuator, so that the control target of the soft robot is realized when the state tracking error converges to zero. Theoretical analysis derivation and simulation experiments prove that the soft robot active disturbance rejection control method based on the dielectric elastomer actuator can effectively converge the observation error and the tracking error of a closed-loop control system and can control the dielectric elastomer actuator to successfully converge to a desired value. Therefore, the control strategy does not need to depend on an accurate dynamic control model, the requirement on input signals is reduced, and the robustness and the adaptability of the soft robot control system based on the dielectric elastomer actuator are enhanced.
Drawings
FIG. 1 is a diagram of a dielectric elastomer actuator before and after deformation; fig. 1(a) shows a state before deformation of the dielectric elastomer actuator, and fig. 1(b) shows a state after deformation of the dielectric elastomer actuator.
Fig. 2 is a schematic block diagram of a control logic structure of the method for controlling the active-disturbance-rejection of the soft robot based on the dielectric elastomer actuator according to the present invention, that is, a schematic block diagram of a structure of the system for controlling the active-disturbance-rejection of the soft robot based on the dielectric elastomer actuator according to the present invention.
FIG. 3 is a graph of an error curve of an extended state observer in a simulation experiment of the present invention.
FIG. 4 is a graph of an error curve of a nonlinear state error feedback controller in a simulation experiment of the present invention.
FIG. 5 is a control input curve diagram in a simulation experiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings.
1. Summary of the invention
In the invention, a track tracking controller is designed for a soft robot based on a dielectric elastomer actuator by utilizing an active disturbance rejection control technology. Firstly, describing elastic energy by using a Gent model based on a virtual work simulation mode, and establishing a dynamic control model of a dielectric elastomer actuator; second, some model parameters are difficult to obtain due to the dielectric elastomer actuator, and the rate of deformation of the dielectric elastomer actuator is difficult to measure by the sensor. Therefore, using the output measurement values of the dielectric elastomer actuator as input signals, an extended state observer is designed to acquire unknown system dynamics information in the dielectric elastomer actuator, and state quantities that are difficult to measure by sensors, as alternative quantities that can be used in the control process. Finally, on the basis of the extended state observer, in order to realize the track tracking control of the soft robot based on the dielectric elastomer actuator, a nonlinear error feedback controller is designed, a state tracking error signal obtained by calculating the difference between the state quantity which can be measured in the dielectric elastomer actuator and the observed state quantity obtained by the extended state observer and a set expected value is utilized, and the designed state error feedback controller is utilized to feed back the state tracking error signal to the dielectric elastomer actuator, so that the control target of the soft robot is realized when the tracking error converges to zero.
2. Dynamic control virtual model of dielectric elastomer actuator
And establishing a dynamic control model of the dielectric elastomer actuator based on a virtual work simulation mode. Fig. 1 is a state diagram before and after deformation of the dielectric elastomer actuator, in which fig. 1(a) is a state before deformation of the dielectric elastomer actuator, and fig. 1(b) is a state after deformation of the dielectric elastomer actuator. In FIG. 1, L1，L2And L3Is the length, width, height, l, of the dielectric elastomer actuator before deformation1，l2And l3Is the length, width, height, P, of the dielectric elastomer actuator after deformation1And P2The tensile force is applied to the dielectric elastomer actuator in the transverse length and width directions when the dielectric elastomer actuator is deformed, phi is the control voltage of the dielectric elastomer actuator,
Figure BDA0002215200420000051
is the corresponding electrical quantity.
Order to
Figure BDA0002215200420000052
And
Figure BDA0002215200420000053
λ1、λ2、λ3then the ratio of the length, width, and height directions of the dielectric elastomer actuator after deformation relative to the dielectric elastomer actuator before deformation, respectively, and λ is given by the incompressibility of the dielectric elastomer actuator1λ2λ3＝1；
Electric quantity
Figure BDA0002215200420000054
The relationship to the voltage Φ is:
Figure BDA0002215200420000055
wherein T is the temperature of the environment,
Figure BDA0002215200420000056
is the dielectric constant of a dielectric elastomer actuator, which is λ1，λ2And a non-linear function of T.
λ occurs when the length and width of the dielectric elastomer actuator, respectively1And λ2When deformed, the tension will change P1L1λ1And P2L2λ2The change amount of the deformation process of the voltage is phi
Figure BDA0002215200420000057
Therefore, the deformation process variation of the electric quantity
Figure BDA0002215200420000058
Comprises the following steps:
Figure BDA0002215200420000061
the inertial forces along the x and y directions of the coordinate system in the dielectric elastomer actuator are respectively ρ L2L3x2(d2λ1/dt2) And ρ L1L3y2(d2λ2/dt2) Damping forces are cx (d λ)1Dt) and cy (d lambda)2Dt). Thus, the inertial and damping forces act as:
Figure BDA0002215200420000062
Figure BDA0002215200420000063
where ρ is the density of the dielectric elastomer actuator and c is the damping coefficient of the dielectric elastomer actuator.
The deformation process change quantity W of the free energy W of the dielectric elastomer actuator is influenced by voltage, tension, inertia force and damping force, and then:
Figure BDA0002215200420000064
and W is the elastic energy WelaAnd electric energy WeleConsists of the following components:
Figure BDA0002215200420000065
where μ (T) is the shear modulus of the dielectric elastomer actuator as a function of ambient temperature T, JmIs the dielectric elastomer actuator deformation limit.
Note 1: the elastic energy in the above process is described using the Gent model. In addition to the Gent model, there are other models that describe elastic energy, such as the Neo-Hookean model, the Mooney-Rivlin model, the Ogden model, the Arruda-Boyce model, and the like.
Substituting formula (1) into formula (2) includes:
Figure BDA0002215200420000071
according to the formula (4), there are:
Figure BDA0002215200420000072
Figure BDA0002215200420000073
from equations (3), (5) and (6), the virtual model for dynamic control of the dielectric elastomer actuator can be derived as:
Figure BDA0002215200420000074
Figure BDA0002215200420000075
dielectric elastomer actuators can be generally considered isotropic and for simplicity of representation can be written as L1＝L2L and P1＝P2＝P，λ1＝λ2λ. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002215200420000076
can be simplified into
Figure BDA0002215200420000077
(7) And (8) can be simplified as:
Figure BDA0002215200420000078
let x1＝λ，
Figure BDA0002215200420000079
And order
Figure BDA00022152004200000710
The dynamic control virtual model of the dielectric elastomer actuator can be derived from (9) as:
Figure BDA0002215200420000081
wherein u is Φ2Is a control input signal of the dynamic control virtual model of the dielectric elastomer actuator, phi is a control voltage of the dielectric elastomer actuator; y is the control output signal of the dynamic control virtual model of the dielectric elastomer actuator. When x is ordered1When the number is equal to lambda, the second phase is,
Figure BDA0002215200420000082
can be written as
Figure BDA0002215200420000083
And has the following components:
Figure BDA0002215200420000084
Figure BDA0002215200420000085
3. description of control problems
In practical application, the process of the soft robot composed of the dielectric elastic film to complete a task is essentially the process of dynamic deformation of the body of the soft robot, and the process is realized by the dielectric elastic body actuator. Thus, this process can be characterized as state x in the system (10)1And x2Tracking the expected states x separately1dAnd x2dAnd a state x is desired1dAnd x2dIs an ideal track for describing the target task design. This means, therefore, that in order to accomplish this task, a controller u needs to be designed such that:
Figure BDA0002215200420000086
in the actual control process, x is used2Is to express the deformation speed of the dielectric elastic film, so it is difficult to directly measure with a sensor, and since many parameters in the dielectric elastic film are unknown, so that f (x) and g (x) are unknown system dynamic information. This makes these signals not directly usable in the control process, which presents two challenges to the design of soft-body robot controllers based on dielectrophoretic actuators.
4. Active disturbance rejection control design
In this section, to overcome the above two difficulties in controller design, an auto-disturbance-rejection controller for trajectory tracking is designed to achieve the control objective (11) using the auto-disturbance-rejection control technique. The active disturbance rejection controller comprises an extended state observer and a nonlinear error feedback controller.
4.1. Extended state observer
The dielectric elastomer actuator contains some unknown parameters, such as p,
Figure BDA0002215200420000091
and JmThis makes f (x) and g (x) unknown system dynamics information. In addition, the state quantity x2Which is indicative of the rate of deformation of the dielectric elastomer actuator, is also relatively difficult to measure directly with a sensor.
Therefore, in this section, an extended state observer pair is designed from state x2And unknown system dynamic information f (x) and g (x) are used for observing the disturbance caused by the unknown system sum. Let x be before designing the extended state observer3(x) 1 (g) and (x) 1 ═ f
Figure BDA0002215200420000092
The system (10) can be converted into:
Figure BDA0002215200420000093
for the system (14), a state-extended observer is designed as follows:
Figure BDA0002215200420000094
wherein x iso1、xo2And xo3Are the three observed state quantities output by the extended state observer,
Figure BDA0002215200420000095
and
Figure BDA0002215200420000096
respectively representing the observed state quantities xo1、xo2And xo3Differentiation of (1); k is a radical ofo1、ko2And ko3The method is a design parameter of the extended state observer, and the design parameters are positive values; e.g. of the typeo1＝xo1-x1For x to expand the state observer1The observation error of (2).
And (3) convergence derivation:
let eo2＝xo2-x2And eo3＝xo3-x3According to the formulae (14) and (15),the following observation error system can be derived:
Figure BDA0002215200420000097
let eo＝[eo1,eo2,eo3]T，
Figure BDA0002215200420000098
And
Figure BDA0002215200420000099
thus, the system (16) can be abbreviated as:
Figure BDA00022152004200000910
due to the fact that
Figure BDA00022152004200000911
By selecting the appropriate koi(i ═ 1,2,3), there is a normal number λo1＜λo2＜λo3Such that:
Figure BDA0002215200420000101
this indicates that AoThere are different characteristic values, all AoCan be diagonalized, i.e. there is an invertible real matrix ToSo that:
Figure BDA0002215200420000102
therefore, the first and second electrodes are formed on the substrate,
Figure BDA0002215200420000103
for all the values of t > 0, the values of,
Figure BDA0002215200420000104
wherein
Figure BDA0002215200420000105
For a given lambdao1，λo2，λo3Then βoIs a constant that is determined, therefore,
Figure BDA0002215200420000106
and the solution of equation (17) is:
Figure BDA0002215200420000107
then the process of the first step is carried out,
Figure BDA0002215200420000108
therefore, the temperature of the molten metal is controlled,
Figure BDA0002215200420000109
4.2. nonlinear state error feedback controller (NLSEF)
To make x realized1And x2Tracking x separately1dAnd x2dAn error feedback controller is designed for the system (14). Therefore, the nonlinear error feedback controller is designed as follows:
Figure BDA00022152004200001010
namely:
u＝x3d-xo3-kc1(xo1-x1d)-kc2(xo2-x2d)；
wherein u is0Tracking error, x, output by error feedback controllero1、xo2And xo3Are the three observed state quantities output by the extended state observer,x1d、x2dand x3dRespectively, are observed state quantities xo1、xo2And xo3A corresponding state quantity expected value; k is a radical ofc1、kc2Are design parameters of the error feedback controller and are all positive values.
FIG. 2 shows a block schematic diagram of the active disturbance rejection control system of the dielectric elastomer actuator of the present invention.
And (3) convergence derivation:
substituting (20) into (14):
Figure BDA0002215200420000111
let ec＝[ec1,ec2]T＝[x1-x1d,x2-x2d]TAccording to the formulae (21) and (13), there are:
Figure BDA0002215200420000112
as a result of this, it is possible to,
Figure BDA00022152004200001112
according to the formula (23), (22) can be converted into:
Figure BDA0002215200420000113
order to
Figure BDA0002215200420000114
And
Figure BDA0002215200420000115
then (24) can be expressed as:
Figure BDA0002215200420000116
due to the fact that
Figure BDA0002215200420000117
By selecting the appropriate kci(i ═ 1,2), there is a normal number λc1＜λc2Such that:
Figure BDA0002215200420000118
this indicates that AcThere are different characteristic values, all AcCan be diagonalized, i.e. there is an invertible real matrix TcSo that:
Figure BDA0002215200420000119
therefore, the first and second electrodes are formed on the substrate,
Figure BDA00022152004200001110
for all the values of t > 0, the values of,
Figure BDA00022152004200001111
wherein
Figure BDA0002215200420000121
For a given lambdac1And λc2，βcIs a definite constant, so there are:
Figure BDA0002215200420000122
by similar analysis, there are:
||exp(Ac(t-τ))||≤βcexp(-λc1(t-τ))，t≥τ
according to formula (19), eoThere is an supremum of α, and for any given normality η > 0, there is a normality t0So that | eo(t) | ≦ η, thus:
Figure BDA0002215200420000123
due to t0Is a normal number, there is exp (-lambda) with t → ∞c1t) → 0 and exp (-lambda)c1(t-t0) Arbitrary → 0, and η, there are:
Figure BDA0002215200420000124
(25) the solution of formula (la) is:
Figure BDA0002215200420000125
then there are:
Figure BDA0002215200420000126
according to (26) and (27),
Figure BDA0002215200420000127
therefore, based on the above analysis, the following conclusions can be drawn.
Theorem 1: for systems (14), (17) and (25), an extended state observer (15) and a nonlinear error feedback controller (20) are utilized and appropriate observation parameters k are selectedoi(i ═ 1,2,3) and control parameter kcj(j ═ 1,2), the observation error e of the closed-loop control system can be madeoAnd a tracking error ecConverging to 0.
Note that 2: from the conclusion of theorem 1, the control task (11) can be successfully implemented. Thus, x can be successfully made1And x2Tracking x separately1dAnd x2d。
5. Simulation experiment
To verify the correctness and validity of the control strategy proposed herein, this section has conducted simulation experimental studies using Matlab. Simulation experiment in the bookIn the method, the model parameters of the dielectric elastomer actuator are selected as follows: l is 0.02m, L3＝0.01m，ρ＝960kg/m3，μ(T)＝0.097MPa，Jm＝70，c＝1.2。
The results obtained according to the document "J.J.Sheng, H.L.Chen, L.Liu, et al.dynamic electrochemical performance of visco-electronic two-electronic elastomers, Journal of Applied Physics, vol.114, No.13, pp.134101-1-134101-8, 2013":
Figure BDA0002215200420000131
Figure BDA0002215200420000132
wherein
Figure BDA0002215200420000133
T＝300K，aw＝-0.1658，bw＝-0.04086，cw＝-0.003027。
The initial state of the dielectric elastomer actuator is set as: lambda [ alpha ]0＝1.5，
Figure BDA0002215200420000134
Therefore, the pulling force is:
Figure BDA0002215200420000135
the target trajectory is: x is the number of1d＝-0.5cos t+2，x2d＝0.5sin t，x3d＝0.5cos t。
The simulation results are shown in fig. 3 to 5, wherein the observation error e of the extended observer is shown in fig. 3oA convergence curve; the control error e of the non-linear error feedback controller is shown in fig. 4cA convergence curve; the control input u is shown in fig. 5. As can be seen from fig. 3 and 4, the errors of both the extended state observer and the nonlinear feedback controller converge to zero rapidly, with a convergence time of about 1 second, which means that the control objective is achieved.As can be seen from fig. 5, the control input is always smooth and stable throughout the control process, which implies that it is easy to implement and apply in practical applications.
6. Summary of the invention
In summary, the present invention provides a soft robot active disturbance rejection control method based on a dielectric elastomer actuator, which designs a trajectory tracking controller for the dielectric elastomer actuator by using an active disturbance rejection control technique, wherein the active disturbance rejection controller is composed of an extended state observer and a nonlinear error feedback controller. The controller is designed based on a dynamic control model of the dielectric elastomer actuator. For unknown information in the system, an extended state observer is used for acquiring a substitute signal which can be used in the control process, and on the basis, an error feedback controller is designed, so that the track tracking control of the dielectric elastomer actuator is realized, and the control target of the soft robot is achieved. The theoretical analysis derivation and simulation experiment prove that the soft robot active disturbance rejection control method based on the dielectric elastomer actuator can effectively converge the observation error and the tracking error of a closed-loop control system, can control the successful convergence of the control output to a desired value by the dynamic control virtual model of the dielectric elastomer actuator, and realizes the control target of the soft robot. Therefore, the control strategy does not depend on an accurate dynamic control model, the requirement on input signals is reduced, and the robustness and the adaptability of the soft robot control system based on the dielectric elastomer actuator are enhanced.
Finally, it is noted that the above-mentioned embodiments illustrate rather than limit the invention, and that, while the invention has been described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A soft robot active disturbance rejection control method based on a dielectric elastomer actuator is characterized by comprising the following steps:
establishing a dynamic control model of the dielectric elastomer actuator by using a virtual work simulation mode; the dynamic control model of the dielectric elastomer actuator is as follows:
Figure FDA0002511560210000011
wherein u is Φ2Is the control input to the dielectric elastomer actuator, Φ is the control voltage of the dielectric elastomer actuator; y is the output signal of the dielectric elastomer actuator and has:
Figure FDA0002511560210000012
Figure FDA0002511560210000013
wherein x ═ x1,x2]TIs a state quantity of a dielectric elastomer actuator, where x1Is the transverse deformation ratio of the dielectric elastic film in the dielectric elastic body actuator, i.e. the ratio of the transverse length value after the deformation of the dielectric elastic film to the transverse length value before the deformation, x2For the rate of deformation of the dielectric elastomeric film in the dielectric elastomeric actuator,
Figure FDA0002511560210000014
and
Figure FDA0002511560210000015
respectively represent state quantities x1、x2Differentiation of (1); l is a value of a transverse length before deformation of the dielectric elastic film, L3Thickness of the dielectric elastic film before deformation; p is the transverse tension to which the dielectric elastic film is subjected when deformed; t is the temperature of the environment and,
Figure FDA0002511560210000016
is the dielectric constant of the dielectric elastomer actuator and μ (T) is the dielectric elasticityShear modulus of a body actuator dependent on ambient temperature T, JmIs the limit of the transverse deformation ratio of the dielectric elastomer actuator after deformation relative to the actuator before deformation; ρ is the density of the dielectric elastomer actuator, c is the damping coefficient of the dielectric elastomer actuator,
Figure FDA0002511560210000017
is dielectric constant
Figure FDA0002511560210000018
At x1The amount of change in deformation process;
acquiring unknown system dynamic information and state quantity of the dielectric elastomer actuator by using an extended state observer, and using the system dynamic information and the state quantity as substitute quantity in the control process;
and respectively carrying out difference calculation on the state quantity which can be measured in the dielectric elastomer actuator and the observed state quantity obtained by the extended state observer and the designed corresponding expected values to obtain corresponding state tracking error signals, and feeding back the state tracking error signals to the dielectric elastomer actuator by using a designed state error feedback controller, so that the control target of the soft robot is realized when the tracking error converges to zero.
2. The dielectric elastomer actuator based soft robotic active disturbance rejection control method of claim 1, wherein the extended state observer is:
Figure FDA0002511560210000021
wherein x iso1、xo2And xo3Are the three observed state quantities output by the extended state observer,
Figure FDA0002511560210000022
and
Figure FDA0002511560210000023
respectively representObserved state quantity xo1、xo2And xo3Differentiation of (1); k is a radical ofo1、ko2And ko3The method is a design parameter of the extended state observer, and the design parameters are positive values; e.g. of the typeo1＝xo1-x1For expanding the observer pair x1The observation error of (2).
3. The method of claim 1, wherein the error feedback controller is:
Figure FDA0002511560210000024
wherein u is0Tracking error, x, output by error feedback controllero1、xo2And xo3Three observed state quantities, x, output by the extended state observer1d、x2dAnd x3dRespectively, are observed state quantities xo1、xo2And xo3A corresponding state quantity expected value; k is a radical ofc1、kc2Are design parameters of the error feedback controller and are all positive values.
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