CN110671260A - Nonlinear generalized predictive control method for regulating system of hydroelectric generating set - Google Patents

Nonlinear generalized predictive control method for regulating system of hydroelectric generating set Download PDF

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CN110671260A
CN110671260A CN201910875716.9A CN201910875716A CN110671260A CN 110671260 A CN110671260 A CN 110671260A CN 201910875716 A CN201910875716 A CN 201910875716A CN 110671260 A CN110671260 A CN 110671260A
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control
generating set
hydroelectric generating
regulating system
generalized predictive
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鄢波
李超顺
蒙淑平
侯进皎
赖昕杰
何钧
李永刚
陈学志
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Huazhong University of Science and Technology
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jiangxi Electric Power Co Ltd
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Huazhong University of Science and Technology
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jiangxi Electric Power Co Ltd
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B15/00—Controlling
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2270/00—Control
    • F05B2270/10—Purpose of the control system
    • F05B2270/101—Purpose of the control system to control rotational speed (n)
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/20—Hydro energy

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Abstract

The invention discloses a nonlinear generalized predictive control method of a water-turbine generator set adjusting system, which is used for effectively controlling the water-turbine generator set adjusting system. The method specifically comprises the following steps: identifying the initial parameters of the CARIMA model of the water turbine generator set adjusting system by adopting a forgetting factor recursion amplification least square method according to the historical operation data of the set; linearizing the CARIMA model of the water turbine generator set adjusting system at each sampling point by using an instantaneous linearization method; designing a nonlinear generalized prediction controller based on an instantaneous linearized CARIMA model, and updating parameters of the model on line by adopting a forgetting factor recursive augmented least square method; the control method designed by the invention can effectively inhibit the rotation speed oscillation caused by starting under different water head working conditions, has stronger robustness and stability and higher calculation efficiency, and better meets the real-time requirement of an industrial field.

Description

Nonlinear generalized predictive control method for regulating system of hydroelectric generating set
Technical Field
The invention belongs to the technical field of hydroelectric power generation, and particularly relates to a nonlinear generalized predictive control method for a water-turbine generator set adjusting system, which is used for effectively controlling the water-turbine generator set adjusting system.
Background
The hydroelectric generating set control system is a complex time-varying and non-minimum phase system, and system parameters of the system change along with changes of working points, so that the difficulty of unit control is high. In addition, when the regulating system of the water-turbine generator set is greatly interfered, for example, a large fluctuation transition process causes great change of some parameters of the regulating system, and some parameters exceed the linear range of the regulating system, at the moment, the system is a time-varying-strength nonlinear system, and the control difficulty of the regulating system of the water-turbine generator set is further increased. However, the existing linear control strategy can not meet the requirement of the control quality of the water-turbine generator set, and the problem of adaptation between strong nonlinearity, time-varying property and linear control law of a control object of the water-turbine generator set is difficult to solve fundamentally. In order to solve the problems, the control quality of the hydroelectric generating set is improved, the reliability of the system is guaranteed, and the research of a more advanced control strategy becomes the driving force for the scientific and technical development of hydroelectric generation.
The predictive control is an adaptive control algorithm, can update a control object model on line, has a rolling optimization mechanism, can correct uncertainty caused by model mismatch, time variation, interference and the like in time, and is suitable for solving the scientific and technical problems of the control of the hydroelectric generating set. In recent years, a traditional generalized predictive control algorithm is applied to the design of a pumped storage unit controller, the rotating speed overshoot is quickly inhibited under different working conditions, and the unstable characteristic of a system in the reverse S region can be eliminated. However, the traditional generalized predictive control algorithm is too complex, so that the online calculation amount is large, and real-time control is inconvenient. Therefore, a novel predictive control algorithm needs to be further researched, so that the requirement of the control quality of the regulating system of the water-turbine generator set is met, and the requirement of the real-time performance of the industrial field operation is met.
Disclosure of Invention
Aiming at the defects of the traditional method, the invention designs the nonlinear generalized predictive control method of the water-turbine generator set regulating system, the control method can effectively inhibit the rotation speed oscillation under the starting working condition, has stronger robustness and stability and higher calculation efficiency, and better meets the real-time requirement of an industrial field.
In order to achieve the aim, the invention designs a nonlinear generalized predictive control method of a water turbine generator set adjusting system, which comprises the following steps:
(1) the method is provided with a hydroelectric generating set adjusting system and a parameter n for setting the hydroelectric generating set adjusting systema、nb、ncD, selecting a prediction length N, controlling a weighting matrix Г, outputting a softening coefficient alpha and a forgetting factor lambda, wherein N isa，nb，ncRespectively the order of polynomials A, B and C in the CARIMA model;
(2) establishing a CARIMA model of an adjusting object in a water turbine generator set adjusting system; the input of the CARIMA model is a control increment signal, and the output of the CARIMA model is a unit rotating speed signal;
(3) collecting actual input and output sequences of a group of hydroelectric generating set adjusting systems as learning data, and identifying initial values of CARIMA model parameters of adjusting objects in hydroelectric generating set adjusting systems
Figure BDA0002204275690000021
And P (0);
(4) determining a reference track and an objective function; selecting a first-order smooth model as a reference track; the variance of the target function for the rotating speed of the unit to track a certain expected track is minimum, and meanwhile, the energy of a control signal is required to be minimum;
(5) and solving the control quantity output by the controller in the water-turbine generator set regulating system.
Further, a CARIMA model is established for the adjusting object in the water turbine generator set adjusting system by adopting a transient linearization method in the step (2).
Further, the identification in the step (3) adopts a recursive augmented least square method with forgetting factors to carry out parameter estimation.
And further, calculating to obtain a control increment by adopting an improved generalized predictive control algorithm in the step (5), and adding the control increment and the control quantity at the previous moment to obtain the control quantity at the current moment.
Further, the CARIMA model of the subject is described as follows:
A(z-1)y(k)＝z-dB(z-1)Δu(k)+C(z-1)ξ(k)
wherein y (k), delta u (k) and xi (k) respectively represent the unit rotation speed, control increment and white noise, d is pure time delay, and
Figure BDA0002204275690000022
further, the forgetting factor recursive augmented least squares method is described as follows:
in the formula
Figure BDA0002204275690000031
Further, the reference trajectory is described as follows:
Figure BDA0002204275690000032
in the formula, ym(k + d-1) is the constructed intermediate variable, w (k) is the expected output at time k, α is the output softening coefficient, YrIs a reference trajectory vector.
Further, the objective function is described as follows:
Figure BDA0002204275690000033
wherein y (k + j) and yr(k + j) is the actual and expected speed output, N, respectively, at the future time k + j of the system1Is a minimum output length, N2Called prediction length, NuTo control the length, γjTo control the weighting coefficients.
Further, the improved generalized predictive control algorithm employed in step (5) includes the steps of:
step 1: setting iteration times T, and setting the current iteration times k as 1;
step 2: sampling the actual rotating speed output y (k) of the current hydroelectric generating set regulating system;
step 3: on-line real-time estimation of controlled object parameters by forgetting factor recursive augmented least square method
Figure BDA0002204275690000034
Step 4: calculating a control matrix G;
Figure BDA0002204275690000035
wherein the elements in the control matrix G can be represented by formula
Figure BDA0002204275690000041
j 2,3, N-d +1 recursion, j1＝min{j-1,naWhen j is reached-1＞nbWhen b is greater than1,j-1＝0；
Step 5: calculating and constructing a vector YmAnd Yr，ym(k + j) is determined entirely by past control inputs and outputs and can be derived from:
in the formula (I), the compound is shown in the specification,
ym(k+j)＝y(k+i),i≤0
step 6: calculating a control amount u (k) of Y*＝YmSubstituting + G Δ U into the target function formula, and solving
Figure BDA0002204275690000045
The control increment is as follows:
ΔU＝(GTG+Γ)-1GT(Yr-Ym)
the control amount u (k-1) and the control increment Δ u (k) at the previous time are added to the control amount u (k) at the current time by the following equation:
u(k)＝u(k-1)+Δu(k)＝u(k-1)+[1,0,...,0](GTG+Γ)-1GT(Yr-Ym)
step 7: k → k +1, if k is less than or equal to T, returning to Step2, otherwise, ending the operation.
The invention has the beneficial effects that: according to the nonlinear generalized predictive control method for the hydroelectric generating set, parameters of the linear model are identified on line by adopting a forgetting factor recursion amplification least square method at each sampling time point, the real-time operation efficiency of a controller adopting the control method is considered, and the problem that a generalized predictive control algorithm needs to be designed based on a linear system CARIMA model is solved.
Compared with the traditional generalized predictive control algorithm, the improved generalized predictive control algorithm has higher operation efficiency and better meets the real-time requirement of an industrial field.
The nonlinear generalized predictive control method for the water turbine generator set regulating system can effectively inhibit the rotation speed oscillation under the starting working condition, has stronger robustness and stability and higher calculation efficiency, and better meets the real-time requirement of an industrial field.
Drawings
FIG. 1 is a block diagram of a pumped storage group conditioning system according to the present invention;
FIG. 2 is a block diagram of the basic structure of the predictive control algorithm of the present invention
FIG. 3 is a diagram showing the simulation comparison result of the process of the rotation speed variation according to the present invention;
FIG. 4 is a graph showing the comparison result of the flow variation process simulation according to the present invention;
FIG. 5 is a graph showing simulation comparison results of the water hammer change process according to the present invention;
FIG. 6 is a diagram showing the simulation comparison result of the torque variation process according to 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 below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention relates to a nonlinear generalized predictive control method of a water-turbine generator set adjusting system, wherein the researched water-turbine generator set adjusting system can be regarded as two parts: a governor and an adjustment target, as shown in fig. 1. The nonlinear generalized predictive control method for the water-turbine generator set adjusting system can improve the control quality of the water-turbine generator set adjusting system under different working conditions and meet the requirement of safe and stable operation.
In order to illustrate the effect of the invention, the method of the invention is described in detail below by taking a pumped storage power station as an implementation object of the invention:
example 1
And establishing a refined simulation model of the water turbine generator set adjusting system.
In this embodiment, a pumped storage unit adjustment system is taken as an example, and a refined simulation model of the pumped storage unit adjustment system is established to replace an actual system to verify the control effect of a designed controller. The structural block diagram of the pumped-storage group regulating system is shown in figure 1. As can be seen from fig. 1, the regulating system of the hydroelectric generating set under consideration can be regarded as two parts: the speed regulator comprises a speed regulator and an adjusting object, wherein the speed regulator can be divided into a controller and a mechanical hydraulic actuating mechanism, and the adjusting object can be divided into a pressure water passing system, a water pump turbine, a generator and a load. The controller is a Nonlinear Generalized Predictive Controller (NGPC) designed by the present invention, which will be described later, and only the adjustment object and the mechanical hydraulic actuator model are described in this step.
1) Pressure water passing system model
For a pressure water diversion pipeline, the compressibility and the elasticity of the water flow of the pressure water diversion pipeline are considered, and the dynamic characteristic of a water diversion system is described by adopting a water hammer characteristic line equation. For any point P in the pipeline, the positive and negative characteristic line equations are established by the left and right points A, B as shown in the following two equations.
C+:Qp＝Cp-CaHp
C-:Qp＝Cn+CaHp
Wherein, Cp＝QA+CaHA-CfQA|QA|，Cn＝QB-CaHB-CfQB|QB|，
Figure BDA0002204275690000061
In the formula, Qi(i ═ P, a, B) is the flow at the pipe node, Hi(i is P, A and B) is the water head of the pipeline node, g is the gravity acceleration, F is the cross-sectional area of the pipeline, a is the water hammer wave speed, F is the hydraulic friction coefficient of the pipeline, and delta t is the calculation step length.
2) Water pump and turbine model
The original full characteristic curve is transformed by adopting an improved Suter method, the transformed full characteristic curve basically eliminates an S area of the characteristic curve, and an accurate interpolation result can be obtained. The improved Suter transformation formula is as follows:
Figure BDA0002204275690000062
Figure BDA0002204275690000063
Figure BDA0002204275690000064
in the formula, WH (x, y) and WM (x, y) are respectively the description of dimensionless similarity parameters to the full characteristic curve after transformation, and the parameters
Figure BDA0002204275690000065
M11max、M11rMaximum unit torque and rated unit torque, k2＝0.5～1.2，Cy＝0.1～0.3，ChAnd n, q, h, m and y are relative values of the unit rotating speed, the flow, the water head, the torque and the opening degree respectively, and are 0.4-0.6.
3) Generator and load model
The rotational motion of the pump turbine can be described by the equation of motion of the rotating rigid body:
Figure BDA0002204275690000071
wherein J is the moment of inertia of the rotating part of the unit, n is the rotating speed of the unit, MtIs waterMain driving moment of pump turbine, MgIs the moment of resistance.
4) Mechanical hydraulic actuator model
(1) The mechanical hydraulic mechanism consists of a main servomotor and an auxiliary servomotor, and a transfer function equation of the servomotor is described as follows:
Figure BDA0002204275690000072
wherein, TyIs the servomotor response time constant.
(2) Setting a system parameter na＝5，nb＝3，n c1, d 1, 10, and the weighting control matrix Г is a unit matrix I10*10The output softening coefficient α is 0.7, and the forgetting factor λ is 0.9985, where n isa，nb，ncThe order of the polynomials a, B, C in the CARIMA model, respectively.
(3) Establishing a CARIMA model of a pumped storage unit regulation object:
A(z-1)y(k)＝z-dB(z-1)Δu(k)+C(z-1)ξ(k)
where y (k), Δ u (k), and ξ (k) represent output, control increment, and white noise, respectively, d is pure delay, and
Figure BDA0002204275690000073
the system parameters of the adjusting object need to be obtained by adopting a parameter identification method, and parameter estimation is carried out by adopting a recursive and augmented least square method with forgetting factors.
Figure BDA0002204275690000081
In the formula
Figure BDA0002204275690000082
(4) Collecting actual input of a group of pumped storage unit adjusting systemsOutput sequence as learning data for identifying initial value of CARIMA model parameter of hydroelectric generating set regulating object
Figure BDA0002204275690000083
And P (0), the identification method is the forgetting factor recursion augmentation least square method.
(5) And determining a reference track and an objective function.
Since the pure delay of the hydroelectric generating set regulating system is d, namely u (k) has no control capability on y (k +1), y (k +2), and y (k + d-1), the pure delay has control capability on y (k + d +1) and the output behind the same. Therefore, the design reference trajectory is as follows.
Figure BDA0002204275690000084
In the formula, ym(k + d-1) is the constructed intermediate variable, w (k) is the expected output at time k, α is the output softening coefficient, YrIs a reference trajectory vector.
The target function takes the minimum variance of the output of an object to track a certain expected track, and simultaneously the control energy is required to be minimum.
Figure BDA0002204275690000085
Wherein y (k + j) and yr(k + j) are the actual and expected outputs, N, respectively, at the future time k + j of the system1Is a minimum output length, N2Called prediction length, NuTo control the length, γjTo control the weighting coefficients.
(6) And solving the control quantity output by the controller.
Step 1: the simulation time is 100s, the simulation step length is 0.02s, the iteration time T is 5000, and the current iteration time k is set to 1;
step 2: sampling the rotating speed output y (k) of a refined simulation model of the current pumped storage unit adjusting system;
step 3: on-line real-time estimation of controlled object parameters by forgetting factor recursive augmented least square method
Figure BDA0002204275690000091
Step 4: calculating a control matrix G;
Figure BDA0002204275690000092
wherein the elements in the control matrix G can be represented by formula
Figure BDA0002204275690000093
j 2,3, N-d +1 recursion, j1＝min{j-1,naWhen j-1 is larger than nbWhen b is greater than1,j-1＝0；
Step 5: calculating and constructing a vector YmAnd Yr，ym(k + j) is determined entirely by past control inputs and outputs and can be derived from:
Figure BDA0002204275690000094
in the formula
Figure BDA0002204275690000095
Figure BDA0002204275690000096
ym(k+j)＝y(k+i),i≤0
Step 6: calculating a control amount u (k) of Y*＝YmSubstituting + G Δ U into the target function formula, and solving
Figure BDA0002204275690000097
The control increment is as follows:
ΔU＝(GTG+Γ)-1GT(Yr-Ym)
the control amount u (k-1) and the control increment Δ u (k) at the previous time are added to the control amount u (k) at the current time by the following equation:
u(k)＝u(k-1)+Δu(k)＝u(k-1)+[1,0,...,0](GTG+Γ)-1GT(Yr-Ym)
step 7: k → k +1, if k is less than or equal to T, returning to Step2, otherwise, ending the operation.
In order to compare the performance of the method described by the invention, the nonlinear generalized predictive controller of the water-turbine generator set designed by the invention is compared with the traditional parallel PID controller, the PID controller is a proportional-integral-derivative controller, and the transfer function equation of the parallel PID controller is described as follows:
Figure BDA0002204275690000101
wherein, Kp＝2.08，Ki＝1.08，KdThe proportional, derivative and integral element gains of the controller are 5.02.
The adjusting object and the mechanical hydraulic actuating mechanism of the parallel PID controller are the same as the fine simulation model of the pumped storage unit adjusting system established by the invention.
And under the working conditions of the upstream reservoir water level 735.45m and the downstream reservoir water level 181m, performing a unit startup comparison experiment, and comparing the two controllers by taking the unit rotation speed, flow, water hammer and moment variation process as reference objects. Fig. 2-5 are graphs showing simulation comparison results of the variation processes of the rotating speed, the flow rate, the water hammer and the moment of the unit in sequence.
According to the simulation result, the rotating speed overshoot x can be obtained1And revolution speed rise time x2The quality of the two controllers is measured by two indexes, and the indexes are compared as shown in table 1.
TABLE 1 comparison of the indices of two controllers
Figure BDA0002204275690000102
Under the above working conditions, after the unit is started, the unit rapidly enters the start transition process, and as can be seen from fig. 3, the NGPC controller has a better control effect. The rise time of the rotating speed of the unit under the control of the two controllers is similar, but the rotating speed overshoot of the NGPC is small, and the rotating speed curve of the unit rapidly and stably enters a steady state, namely the rotating speed adjusting time is also short. In addition, as can be seen from fig. 4-6, the peak values of the unit flow, the water hammer and the torque curve under the control of the NGPC controller are smaller, the oscillation times are fewer, and the steady state can be rapidly reached. Thus, from the fleet transition process indicators, it can be derived that NGPC controllers have superior control quality compared to PID controllers.
Comparing the two controllers according to the specific indexes in Table 1, the rotational speed overshoot of NGPC is 0.025, and the rotational speed overshoot of PID is 0.041, which is almost twice that of NGPC; the rise time of the NGPC is 30.84s, the rise time of the PID is 30.74s, and the difference between the two is only 0.1 s. Therefore, the nonlinear generalized predictive controller designed by the invention is better than a traditional PID controller.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A nonlinear generalized predictive control method for a hydroelectric generating set regulating system is characterized in that: the method comprises the following steps:
(1) the method is provided with a hydroelectric generating set adjusting system and a parameter n for setting the hydroelectric generating set adjusting systema、nb、ncD, selecting a prediction length N, controlling a weighting matrix Г, outputting a softening coefficient alpha and a forgetting factor lambda, wherein N isa，nb，ncRespectively the order of polynomials A, B and C in the CARIMA model;
(2) establishing a CARIMA model of an adjusting object in a water turbine generator set adjusting system; the input of the CARIMA model is a control increment signal, and the output of the CARIMA model is a unit rotating speed signal;
(3) collecting actual input and output sequences of a group of hydroelectric generating set adjusting systems as learning data, and identifying initial values of CARIMA model parameters of adjusting objects in hydroelectric generating set adjusting systems
Figure FDA0002204275680000011
And P (0);
(4) determining a reference track and an objective function; selecting a first-order smooth model as a reference track; the variance of the target function for the rotating speed of the unit to track a certain expected track is minimum, and meanwhile, the energy of a control signal is required to be minimum;
(5) and solving the control quantity output by the controller in the water-turbine generator set regulating system.
2. The nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 1, wherein: and (3) establishing a CARIMA model for an adjusting object in the water turbine generator set adjusting system by adopting a transient linearization method in the step (2).
3. The nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 1, wherein: and (3) performing parameter estimation by adopting a recursive augmented least square method with forgetting factors in the identification.
4. The nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 1, wherein: and (5) calculating by adopting an improved generalized predictive control algorithm to obtain a control increment, and adding the control increment and the control quantity at the previous moment to obtain the control quantity at the current moment.
5. The nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 1, wherein: the CARIMA model of the subject is described as follows:
A(z-1)y(k)＝z-dB(z-1)Δu(k)+C(z-1)ξ(k)
wherein y (k), delta u (k) and xi (k) respectively represent the unit rotation speed, control increment and white noise, d is pure time delay, and
Figure FDA0002204275680000021
6. the nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 3, wherein: the forgetting factor recursive augmented least squares method is described as follows:
Figure FDA0002204275680000022
in the formula
Figure FDA0002204275680000023
7. The nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 1, wherein: the reference trajectory is described as follows:
Figure FDA0002204275680000024
in the formula, ym(k + d-1) is the constructed intermediate variable, w (k) is the expected output at time k, α is the output softening coefficient, YrIs a reference trajectory vector.
8. The nonlinear generalized predictive control method of a hydroelectric generating set regulating system of claim 1, wherein: the objective function is described as follows:
Figure FDA0002204275680000025
wherein y (k + j) and yr(k + j) is the actual and expected speed output, N, respectively, at the future time k + j of the system1Is a minimum output length, N2Called prediction length, NuTo controlSystem length, gammajTo control the weighting coefficients.
9. The non-linear generalized predictive control method of a hydroelectric generating set regulating system according to claim 4, characterized in that: the improved generalized predictive control algorithm adopted in the step (5) comprises the following steps:
step 1: setting iteration times T, and setting the current iteration times k as 1;
step 2: sampling the actual rotating speed output y (k) of the current hydroelectric generating set regulating system;
step 3: on-line real-time estimation of controlled object parameters by forgetting factor recursive augmented least square method
Figure FDA0002204275680000031
Step 4: calculating a control matrix G;
Figure FDA0002204275680000032
wherein the elements in the control matrix G can be represented by formula
Figure FDA0002204275680000033
Recursion of j1＝min{j-1,naWhen j-1 is larger than nbWhen b is greater than1,j-1＝0；
Step 5: calculating and constructing a vector YmAnd Yr，ym(k + j) is determined entirely by past control inputs and outputs and can be derived from:
Figure FDA0002204275680000034
in the formula (I), the compound is shown in the specification,
step 6: calculating a control amount u (k) of Y*＝YmSubstituting + G Δ U into the target function formula, and solving
Figure FDA0002204275680000041
The control increment is as follows:
ΔU＝(GTG+Γ)-1GT(Yr-Ym)
the control amount u (k-1) and the control increment Δ u (k) at the previous time are added to the control amount u (k) at the current time by the following equation:
u(k)＝u(k-1)+Δu(k)＝u(k-1)+[1,0,...,0](GTG+Γ)-1GT(Yr-Ym)；
step 7: k → k +1, if k is less than or equal to T, returning to Step2, otherwise, ending the operation.
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