Introduction to Cascade Control

串级控制主要用于实现快速的球员ection of disturbance before it propagates to the other parts of the plant. The simplest cascade control system involves two control loops (inner and outer) as shown in the block diagram below.

ControllerC1in the outer loop is the primary controller that regulates the primary controlled variabley1by setting the set-point of the inner loop. ControllerC2内循环是次要的控制器rejects disturbanced2locally before it propagates toP1. For a cascade control system to function properly, the inner loop must respond much faster than the outer loop.

In this example, you will design a single loop control system with a PI controller and a cascade control system with two PI controllers. The responses of the two control systems are compared for both reference tracking and disturbance rejection.

Plant

In this example, the inner loop plant P2 is

The outer loop plant P1 is

P2 = zpk([],-2,3); P1 = zpk([],[-1 -1 -1],10);

Designing a Single Loop Control System with a PI Controller

Usepidtunecommand to design a PI controller in standard form for the whole plant model P = P1 * P2.

The desired open loop bandwidth is 0.2 rad/s, which roughly corresponds to the response time of 10 seconds.

% The plant model is P = P1*P2P = P1*P2;% Use a PID or PIDSTD object to define the desired controller structureC = pidstd(1,1);% Tune PI controller for target bandwidth is 0.2 rad/sC = pidtune(P,C,0.2); C

C = 1 1 Kp * (1 + ---- * ---) Ti s with Kp = 0.0119, Ti = 0.849 Continuous-time PI controller in standard form

Designing a Cascade Control System with Two PI Controllers

The best practice is to design the inner loop controllerC2first and then design the outer loop controllerC1with the inner loop closed. In this example, the inner loop bandwidth is selected as 2 rad/s, which is ten times higher than the desired outer loop bandwidth. In order to have an effective cascade control system, it is essential that the inner loop responds much faster than the outer loop.

Tune inner-loop controller C2 with open-loop bandwidth at 2 rad/s.

C2 = pidtune(P2,pidstd(1,1),2); C2

C2 = 1 1 Kp * (1 + ---- * ---) Ti s with Kp = 0.244, Ti = 0.134 Continuous-time PI controller in standard form

Tune outer-loop controller C1 with the same bandwidth as the single loop system.

% Inner loop system when the control loop is closed firstclsys = feedback(P2*C2,1);% Plant seen by the outer loop controller C1 is clsys*P1C1 = pidtune(clsys*P1,pidstd(1,1),0.2); C1

C1 = 1 1 Kp * (1 + ---- * ---) Ti s with Kp = 0.015, Ti = 0.716 Continuous-time PI controller in standard form

Performance Comparison

First, plot the step reference tracking responses for both control systems.

% single loop system for reference trackingsys1 = feedback(P*C,1); sys1.Name ='Single Loop';% cascade system for reference trackingsys2 = feedback(clsys*P1*C1,1); sys2.Name ='Cascade';% plot step responsefigure; step(sys1,'r',sys2,'b') legend('show','location','southeast') title('Reference Tracking')

Secondly, plot the step disturbance rejection responses of d2 for both control systems.

% single loop system for rejecting d2sysd1 = feedback(P1,P2*C); sysd1.Name ='Single Loop';% cascade system for rejecting d2sysd2 = P1/(1+P2*C2+P2*P1*C1*C2); sysd2.Name ='Cascade';% plot step responsefigure; step(sysd1,'r',sysd2,'b') legend('show') title('Disturbance Rejection')

From the two response plots you can conclude that the cascade control system performs much better in rejecting disturbance d2 while the set-point tracking performances are almost identical.