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1、第七章 模型预测控制算法之一5杨根科杨根科上海交通大学自动化系上海交通大学自动化系2005年年9月月内容提要n概述n动态矩阵控制n动态矩阵控制的进一步讨论n模型算法控制n应用思想nZ域设计（直接设计）n时域设计n现代控制理论（基于状态空间）：如最优控制、极点配置等n应用航空航天（理想环境）n工业过程控制（基于模型预测）：预测控制！n石油、化工、发电等n先进控制算法工业过程特点n数学模型的非精确性n不确定性、随机性、参数时变性n material, energy balancesn flow dynamicsn physical properties (often unknown)n therm
2、odynamicsn多变量系统n控制算法的可实施性n历史，。n脉冲响应与阶跃响应；滚动模型预测控制, 动态复杂性nFigure: Two processes exhibiting unusual dynamic behavior. (a) change in base level due to a step change in feed rate to a distillation column(分裂蒸馏塔). (b) steam temperature change due to switching on soot blower (吹灰器) in a boiler.模型预测控制, 方法nMo
3、del Predictive Control (MPC) regulatory controls that use an explicit dynamic model of the response of process variables to changes in manipulated variables to calculate control “moves”. nControl moves are intended to force the process variables to follow a pre-specified trajectory from the current
4、operating point to the target.nBase control action on current measurements and future模型预测控制,优点nOptimal controller is based on minimizing error from set pointnBasic version uses linear model, but there are many possible modelsnCorrections for unmeasured disturbances, model errors are includednSingle
5、step and multi-step versions Treats multivariable control, feedforward control模型预测控制,优点/特点nProcesses are difficult to control with standard PID algorithm long time constants, substantial time delays, inverse response, etc.nThere is substantial dynamic interaction among controls, i.e., more than one
6、manipulated variable has a significant effect on an important process variable.nConstraints (limits) on process variables and manipulated variables are important for normal control.模型预测控制nTechniques developed by industry:1.Dynamic Matrix Control (DMC)-Shell Development Co.,Cutler and Ramaker (1980),
7、-Cutler later formed DMC, Inc.-DMC acquired by Aspentechin 1997.2.Model Algorithmic Control (MAC) ADERSA/GERBIOS, Richaletet al (1978)Over 4000 applications of MPC since 1980 (Qin and Badgwell, 1998 and 2003).模型预测控制, 优点/特点nTime-delay compensation techniques predict process output one time delay ahea
8、d.nHere we are concerned with predictive control techniques that predict the process output over a longer time horizon. (e.g., open-loop response time).模型预测控制, ideaBasic concept for Model Predictive Control模型预测控制, 优点/特点General Characteristics Targets (set points) selected by real-time optimization s
9、oftware based on current operating and economic conditionsMinimize square of deviations between predicted future outputs and specific reference trajectory to new targets Discrete step response modelFramework handles multiple input, multiple output (MIMO) control problems.模型预测控制, 优点/特点nCan include eq
10、uality and inequality constraints on controlled and manipulated variablesSolves a quadratic programming problem at each sampling instantDisturbance is estimated by comparing the actual controlled variable with the model predictionUsually implements the first move out of M calculated moves1 动态矩阵控制 (2
11、)n动态矩阵控制原理与算法n控制结构组成n优化策略n反馈校正n算法n设计参数选择n采样周期n优化时域长度n控制时域程度n权矩阵n误差校正向量1 动态矩阵控制 ()n DMC依靠对象的阶跃响应n控制结构组成n预测模型a2a1123N-1Na3aN-1aN模型截断离散的阶跃响应1 动态矩阵控制 ()nStep Response ModelsnStep response models are based on the following idea. Assume that the system is at rest. For a linear time-invariant single-input
12、single-output (SISO) system let the output change for a unit input change be given by n0, a1, a2, . . . , aN, aN, . . .nHere we assume that the system settles exactly after N steps. The step response a1, a2, . . . , aN constitutes a complete model of the system, which allows us to compute the system
13、 output for any input sequence: 可加性1 动态矩阵控制 ()n预测模型对象的动态特性通过动态系数a1, a2, , aN来描述na1, a2, , aN是阶跃响应在采样时刻t=T,2T,NT的值n(ai step response coefficients)n(ai+1-ai impulse response coefficients)nN的选择应该使aias, (jN), as是阶跃响应终止值1 动态矩阵控制 ()For exampleif the discrete system description (sampling time T = 0.1) isy(
14、k) = 0.5y(k 1) + u(k 3)then the transfer function is1 动态矩阵控制 ()nThe following commands generate the step response model for this system and plot it:num = 0 1;den = 1 0.5;delt1 = 0.1;delay = 2; % why dont we choose 3 ?g = poly2tfd(num,den,delt1,delay);% Set up the model in tf formattfinal = 1.6;delt2
15、 = delt1;nout = 1;plant = tfd2step(tfinal,delt2,nout,g);% Calculate the step responseplotstep(plant) % Plot the step response1 动态矩阵控制 ()1 动态矩阵控制 ()nplant =n 0 -a1n 0 -a2n 1.0000-a3n 0.5000n 0.7500n 0.6250n 0.6875n 0.6563n 0.6719n 0.6641n 0.6680n 0.6660n 0.6670n 0.6665n 0.6667n 0.6666-a16n n 1.0000 -
16、 nout(i) = 1 if output i is stable.n 1.0000 - nyn 0.1000 - delt21 动态矩阵控制 ()n预测模型n线性系统的可加性，可以由a=a1, a2, , aNT描述n假设t=kT有一个控制增量u(k),后面控制量不变n在采样时刻t=(k+1)T, (k+2)T, (k+N)T的值1 动态矩阵控制 ()n1 预测模型n假设t=kT,(k+1)T, (k+M-1)T 有控制增量u(k), u(k+1), ,u(k-M+1); 后面控制量不变n在采样时刻t=(k+1)T, (k+2)T, (k+P)T的值 (滚动)1 动态矩阵控制 ()n2 优
17、化策略n权矩阵：n期望轨迹：n优化控制变量:uM(k)n期望指标(无约束问题) ：误差小，控制量小，即1 动态矩阵控制 ()n优化策略n优化控制量:uM(k)1 动态矩阵控制 ()n优化控制n这就是t=kT时刻解的最优控制增量序列n优化控制量: u M(k)=u (k); ; u (k+M-1)nt=kT, u (k)=u (k-1)+ u (k);nt=(k+1)T, u (k+1)=u (k)+ u (k+1);nnt=(k+M-1)T, u (k+M-1)=u (k+M-2)+ u (k+M-1);nt=(k+M)T, u (k+M)=u (k+M-1);nt=(k+M+1)T, u (
18、k+M+1)=u (k+M);1 动态矩阵控制 ()u(k+3)u(k+2)u(k+M-1)u(k+3)u(k+1)u(k+2)u(k)123W(k)t/Twkk+M-1k+Pk+1W(k+1)W(k+2)W(k+3)W(k+M-1)W(k+P)yM(k+1|k)k+2yM(k+2|k)yM(k+3|k)yM(k+P|k)Pt/Tkk+M-1k+Pk+1k+2u(k-1)u(k)u(k+1)u(k+M-1)u(k+P)P189图7-3 DMC的优化策略1 动态矩阵控制 ()1 动态矩阵控制 ()3 反馈校正n原因n模型误差n非线性特性n干扰n方法n动态调整1 动态矩阵控制 ()3 反馈校正n预
19、测误差(一步控制Du(k)后的预测与实际值之差)n校正权系数1 动态矩阵控制 ()3 反馈校正nt=(k+1)T时刻误差校正后的系统在t=(k+i)T, (i=1,2,N)的输出预测nt=(k+1)T时刻误差校正后的系统，在t=(k+1+i)T, (i=1,2,N)的输出预测1 动态矩阵控制 ()3反馈校正nThough m control moves are calculated, only the first one (Du(k) is implemented. At the next sampling interval, new values of the measured output are obtained, the control horizon is shifted forward by one step, and the same computations are repeated.n“moving horizon” or “receding horizon.”1 动态矩阵控制 ()4算法(1) 离线计算N; 阶跃响应系数 a1,a2,aN优化校正参数 h1,h2,hP 优化控制参数 d1,d2,dP(2) 初始化初始值(3) 在线计算Y(k)更新规律;优化控制量u (k)，u M(k)
