CAPS-Simulink.zip

%% Anti-Windup Control Using PID Controller Block % % This example shows how to use anti-windup schemes to prevent integration % wind-up in PID controllers when the actuators are saturated. The PID % Controller block in Simulink(R) features two built-in anti-windup % methods, |back-calculation| and |clamping|, as well as a tracking mode to % handle more complex industrial scenarios. The PID Controller block % supports several features that allow it to handle controller windup % issues under commonly encountered industrial scenarios. % Copyright 2009-2022 The MathWorks, Inc. %% % The plant to be controlled is a saturated first-order process with % dead-time. open_system('sldemo_antiwindup') %% % The PID Controller block has been tuned with saturation ignored using the % Simulink(R) Control Design(TM) PID tuner. %% % The controlled plant is a first-order process with dead-time described % by % % $$P(s)=\frac{1}{10s+1}e^{-2s}$. % % The plant has known input saturation limits of |[-10, 10]|, which are % accounted for in the Saturation block labeled |Plant Actuator|. The PID % Controller block in Simulink features two built-in anti-windup methods % that allow it to account for the available information about the plant % input saturation. %% Performance Without Using Anti-Windup % First, examine the effect of saturation on the closed-loop when the % saturation model is not considered by the PID Controller block. % Simulating the model generates these results. The figure shows the setpoint % versus measured output with no anti-windup. open_system('sldemo_antiwindup/Scope'); open_system('sldemo_antiwindup/Scope1'); % This ensures legends get displayed simout1= sim('sldemo_antiwindup','ReturnWorkspaceOutputs','on'); close_system('sldemo_antiwindup/Scope1'); %% % The figure shows the controller output and saturated input with no % anti-windup. close_system('sldemo_antiwindup/Scope'); open_system('sldemo_antiwindup/Scope1'); %% % These figures highlight two problems with controlling a system with input % saturation: % % # When the setpoint value is |10|, the PID control signal reaches a % steady-state at about |36.29|, outside the range of the actuator. The % controller is therefore operating in a nonlinear region where increasing % the control signal has no effect on the system output, a condition known % as _winding up_. Note that the DC-gain of the plant is unity. Therefore, % the controller output does not need to have a steady-state value outside % the range of the actuator. % # When the setpoint value becomes |5|, there is a considerable delay before % the PID controller output returns to within the actuator range. % % Designing the PID controller to account for the effect of saturation % improves its performance by allowing it to operate in the linear region % most of the time and recover quickly from nonlinearity. You can use anti-windup % mechanism to achieve this. %% Configure Block for Anti-Windup Based on Back-Calculation % The back-calculation anti-windup method uses a feedback loop to unwind % the PID Controller block internal integrator when the controller hits % specified saturation limits and enters nonlinear operation. To enable % anti-windup, go to the *Output Saturation* tab in the block dialog. % Select *Limit output* and enter the saturation limits for the plant. % Next, from the *Anti-windup method* list, select % |back-calculation|. Then, specify the % *Back-calculation coefficient (Kb)*. The inverse of this gain is the time % constant of the anti-windup loop. In this example, the back-calculation % gain is chosen to be |1|. For more information on how to choose this value, % see [1]. % % <<../blkDlgAntiWindup.png>> % set_param('sldemo_antiwindup/PID Controller','LimitOutput','on',... 'UpperSaturationLimit','10','LowerSaturationLimit','-10',... 'AntiWindupMode','back-calculation'); %% % Once back-calculation is enabled, the block has an internal tracking loop % that unwinds the Integrator output. This figure shows the under-mask % view of the PID Controller block with back-calculation. open_system('sldemo_antiwindup/PID Controller','force'); %% % Note how quickly the PID control signal returns to the linear region and % how fast the loop recovers from saturation. close_system('sldemo_antiwindup/PID Controller'); close_system('sldemo_antiwindup/Scope1'); open_system('sldemo_antiwindup/Scope'); % To force data to plot on scope simout2= sim('sldemo_antiwindup','ReturnWorkspaceOutputs','on'); close_system('sldemo_antiwindup/Scope1'); %% % The controller output |u(t)| and the saturated input |SAT(u)| coincide with % each other because *Limit output* is enabled. %% close_system('sldemo_antiwindup/Scope'); open_system('sldemo_antiwindup/Scope1'); %% % To better visualize the effect of anti-windup, this figure illustrates the % plant measured output |y(t)| with and without anti-windup. close_system('sldemo_antiwindup/Scope1'); t1 = get(simout1,'tout'); y1 = get(simout1,'yout'); t2 = get(simout2,'tout'); y2 = get(simout2,'yout'); figure('Tag','sldemo_antiwindup'); plot(t1,y1,t2,y2);axis([0 t1(end) round(min([y1;y2])-2) round(max([y1;y2])+2)]); title('Measured output'); legend('Without anti-windup','With anti-windup'); grid on; %% Configure Block for Anti-Windup Based on Integrator Clamping % Another common anti-windup strategy is based on conditional integration. % To enable anti-windup, in the Block Parameters dialog box, select the % *Saturation* tab. Select *Limit output* and enter the saturation limits % for the plant. Then, from the *Anti-windup method* list, select % *clamping*. % % This figure shows setpoint versus measured output with clamping. open_system('sldemo_antiwindup/Scope'); open_system('sldemo_antiwindup/Scope1'); % To force data to plot on scope set_param('sldemo_antiwindup/PID Controller','AntiWindupMode','clamping'); sim('sldemo_antiwindup'); close_system('sldemo_antiwindup/Scope1'); %% % This figure shows that the controller output |u(t)| and the saturated % input |SAT(u)| coincide with each other because *Limit output* is % enabled. close_system('sldemo_antiwindup/Scope'); open_system('sldemo_antiwindup/Scope1'); %% bdclose('sldemo_antiwindup') close(findobj('Type','figure','Tag','sldemo_antiwindup')) %% % For more information on when to use clamping, see [1]. %% Use Tracking Mode to Handle Complex Anti-Windup Scenarios % The anti-windup strategies discussed so far rely on built-in methods to % process the saturation information provided to the block via its dialog. % For those built-in techniques to work as intended, two conditions must be % met: % % # The saturation limits of the plant are known and can be entered into the % dialog of the block. % # The PID Controller block output signal is the only signal feeding the % actuator. % % These conditions may be restrictive when handling general anti-windup % scenarios. The PID Controller block features a tracking mode that allows % you to set up a back-calculation anti-windup loop externally. The next % two examples show the use of tracking mode for % anti-windup purposes: % % # Anti-windup for saturated actuators with cascaded dynamics % # Anti-windup for PID control with feedforward %% Construct Anti-Windup Scheme for Saturated Actuators with Cascaded Dynamics % The actuator in |sldemo_antiwindupactuator| has complex dynamics. Complex % dynamics are common when an actuator has its own closed-loop dynamics. % The PID controller is in an outer loop and sees the actuator dynamics as % an inner loop, which is also called cascaded saturated dynamics. open_system('sldemo_antiwindupactuator'); %% % A successful anti-windup strategy requires feeding back the actuator % output to the tracking port of the PID Controller block. To configure the % |tracking mode| of the PID Controller block, in the block Parameters % dialog box, click the *Initialization* tab. Select % *Enable tracking mode* and specify the gain |Kt|. The inverse of this % gain