模型预测控制4-MIMO-Example

1、第七章 模型预测控制算法之二5-状态方程模型,杨根科 上海交通大学自动化系 2011年3月,内容提要,概述 动态矩阵控制-状态方程模型 动态矩阵控制的进一步讨论 模型算法控制 应用,动态矩阵控制-状态方程模型,Matlab6.5-参考MPC.pdf Matlab7.1-在线,动态矩阵控制-参数设置对性能作用,MPC Control of a DC Servomotor,动态矩阵控制-未建模动态对性能作用,A position servomechanism consists of a DC motor, gearbox, elastic shaft, and a load, 参数含义,动态矩阵控

2、制-参数设置对性能作用,参数含义,动态矩阵控制-参数设置对性能作用,参数含义 The controller must set the loads angular position qL at a desired value by adjusting the applied voltage, V. measurement available for feedback is qL. From an input/output viewpoint, the plant has a single input, V, which is manipulated by the controller. It h

3、as two outputs, one measured and fead back to the controller, qL, and one unmeasured, T,动态矩阵控制-参数设置对性能作用,A single input, V, one measured and fead back to the controller, qL, and one unmeasured, T,动态矩阵控制-参数设置对性能作用,MPC Control of a DC Servomotor-Simulink Design,MPC Control of a DC Servomotor-SIMO模型描述,

4、参数与模型设计 MpcMotorModel.m,MPC Control of a DC Servomotor-模型描述,SYS = SS(A,B,C,D) creates a SS object SYS representing the continuous-time state-space model dx/dt = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t,MPC Control of a DC Servomotor-模型描述,sys a = x1 x2 x3 x4 x1 0 1 0 0 x2 -51.21 -1 2.56 0 x3 0 0 0 1 x4 128

5、0 -6.401 -10.2 b = u1 x1 0 x2 0 x3 0 x4 1 c = x1 x2 x3 x4 y1 1 0 0 0 y2 1280 0 -64.01 0 d = u1 y1 0 y2 0,MPC Control of a DC Servomotor-模型描述,umin=-220; umax=220; % 控制约束 dumin=-Inf; dumax=Inf; %控制增量约束 ymin= -ymax; ymax=Inf Vmax; %输出约束 % Vmax=tauam*pi*dshaft3/16=78.5; %Maximum admissible torque Ts=0.1

6、;Tstop=200*Ts; uweight=0; duweight=.05; yweight=10*1 0; % y2转矩没有权系数,MPC Control of a DC Servomotor-模型描述,备注：下面文件单独键入运行界面 ManipulatedVariables=struct(Min,umin,Max,umax,Units,V); OutputVariables(1)=struct(Min,-Inf,Max,Inf,Units,rad); OutputVariables(2)=struct(Min,Vmin,Max,Vmax,Units,Nm); Weights=struct

7、(Input,uweight,InputRate,duweight,Output,yweight); clear Model Model.Plant=sys; Model.Plant.OutputGroup=1 Measured;2 Unmeasured; PredictionHorizon=10; ControlHorizon=2,MPC Control of a DC Servomotor-模型描述,Create MPC object in workspace ServoMPC=mpc(Model,Ts,PredictionHorizon,ControlHorizon); ServoMPC

8、.Weights=Weights; ServoMPC.ManipulatedVariables=ManipulatedVariables; ServoMPC.OutputVariables=OutputVariables,MPC Control of a DC Servomotor-参数设置对性能作用,仿真运行 Simulink仿真 mpc_motor.m,MPC Control of a DC Servomotor-Simulink仿真,MPC Control of a DC Servomotor-Analysis,仿真运行 Simulink仿真 mpc_motor.m,动态矩阵控制-扰动情

9、形,扰动情形分析 MPC Control of a Multi-Input Single-Output system mpc_misonoise,动态矩阵控制-例子2,状态方程模型 sys=ss(tf(1,1,1,1 .5 1,1 1,.7 .5 1),min); tf(1,1,1,1 .5 1,1 1,.7 .5 1),动态矩阵控制-例子,离散）状态方程模型 Ts=.2; % sampling time model=c2d(sys,Ts); % prediction model,动态矩阵控制-例子,与阶跃响应模型关系 step(model,动态矩阵控制-例子,阶跃响应模型 S=step(mo

10、del) ？ S=S(:,:,1),S(:,:,2),S(:,:,3) ？ S(k,j,i), 时间k，输出j，输入i,动态矩阵控制-可测/不可测系统输入,Define type of input signals: the first signal is a manipulated variable, the second signal is a measured disturbance, the third one is an unmeasured disturbance model=setmpcsignals(model,MV,1,MD,2,UD,3,动态矩阵控制-可测/不可测系统输入,D

11、efine the structure of models used by the MPC controller Model=; % reset structure Model Model.Plant=model,动态矩阵控制-例子, Disturbance model: Integrator driven by white noise with variance=1000 Model.Disturbance=tf(sqrt(1000),1 0); p=40; m=3; MPCobj=mpc(Model,Ts,p,m); MPCobj.MV=struct(Min,0,Max,1,RateMin

12、,-10,RateMax,10,动态矩阵控制-例子,The continuous-time plant to be controlled has the following state-space realization: A,B,C,D=ssdata(sys,动态矩阵控制-例子,Now simulate closed-loop MPC in Simulink Tstop=30; % Simulation time mpc_miso 解释：t=10,20时加入可测/不可测系统输入的动态特性,动态矩阵控制-例子,mpc_miso,动态矩阵控制-可测测量干扰, Lets say we know t

13、hat output measurements are affected by a sinusoidal % measurement noise of frequency 0.1 Hz. We want to inform the MPC object % about this so that state estimates can be improved omega=2*pi/10; MPCobj.Model.Noise=0.5*tf(omega2,1 0 omega2); % % We also revised the MPC design MPCobj.Model.Disturbance

14、=.1; % Model for unmeasured disturbance = white Gaussian noise with zero mean and variance 0.01 MPCobj.weights=struct(MV,0,MVRate,0.1,OV,.005); MPCobj.predictionhorizon=40; MPCobj.controlhorizon=3,动态矩阵控制-可测测量干扰,备注-前1： sys=ss(tf(1,1,1,1 .5 1,1 1,.7 .5 1),min); Ts=.2; % sampling time model=c2d(sys,Ts)

15、; % prediction model model=setmpcsignals(model,MV,1,MD,2,UD,3); Model=; % reset structure Model Model.Plant=model; % Disturbance model: Integrator driven by white noise with variance=1000 Model.Disturbance=tf(sqrt(1000),1 0,动态矩阵控制-可测测量干扰,备注-前2： Model.Disturbance=tf(sqrt(1000),1 0); p=; m=3; MPCobj=mpc(Model,Ts,p,m); MPCobj.MV=struct(Min,0,Max,1,RateMin,-10,RateMax,10); A,B,C,D=ssdata(sys,动态矩阵控制-例子, Open the simulink diagram MPC_MISONOISE.MDL mpc_misonoise Tstop=150; %Simulation time,动态矩阵控制-例子mpc_misonoise,动态