Is there an example of a technical system model in Simscape with a PID controller and an LQR controller?

The question is: is there a ready model of some technical system, in simscape, which is controlled by a classical sub-controller and a linear quadratic-controller, so that it is possible to compare the simulation results? For example, I have model of cooling system https://www.mathworks.com/help/hydro/ug/refrigeration-system-level.html In this model system controlled by thermostat and pid regulator with transfer function 1/(2s+1l... Is it possible to integrate a ready-made block for control with the help of the lqr regulator into this model? Or is there another example of a model in simscape?

Answer 1

[Ashok]

Hi @Alex Milns,

The‘lqr’command in the Control System Toolbox is used to design a linear quadratic controller in MATLAB. However, as noted in this MATLAB Answer, there isn't a Simulink block for the LQR controller that can be directly used:

https://www.mathworks.com/matlabcentral/answers/87237.

An alternative approach is to design the LQR gain in a MATLAB script using a linearized state-space model. The calculated LQR gain can then be accessed inside Simulink to implement the controller. Here's an example of designing and implementing an LQR controller for a spring-mass-damper system modelled in Simscape.

In the attached files, thelqr_design_R2023a.mscript contains the LQR design for the linearized state-space model. The corresponding Simscape model is in themodel_R2023a.slxfile. The LQR gain,‘K’, is designed in the MATLAB script and accessed by the gain block from the MATLAB workspace.

The state-cost and input-cost weights, ‘Q’ and ‘R’, can be adjusted in the MATLAB script to achieve the desired response. Here's the response for the current weights.

A similar approach can be used for a pole placement controller, which can be designed using the‘place’command. Here are some relevant documentation links:

• 'place' command: https://www.mathworks.com/help/releases/R2023a/control/ref/place.html
• Linearizing a Simscape model: https://www.mathworks.com/help/releases/R2023a/slcontrol/ug/linearize-simscape-networks.html