fmincon PI-controller of nonlinear System

Hi!

I want to optimize two PI-controllers of my simulink model(high nonlinear). I have several constrains of my nonlinear sytem, but I don't know how to insert these into 'fmincon'.

This is my optimization functinon:

function y = fun(x)
% Set parameter of PI- controller of the force
set_param('Sim_10_01/CF/KpF', 'Gain', 'x(1)');
set_param('Sim_10_01/CF/TiF', 'Gain', 'x(2)');

 % Set parameter of PI-controller of the pressure
set_param('Sim_10_01/Cp/Kpp', 'Gain', 'x(3)');
set_param('Sim_10_01/Cp/Tip', 'Gain', 'x(4)');

 sim('Sim_10_01','SrcWorkspace','current');

 y = [moment force pressure acceleration];

I want to optimize the parameters of both PI-controllers for the same output 'acceleration' in relation of the constrains of the moment, force and pressure.

My issue now: I don't know how to insert those constrains, due they are not dependent on x(well somehow yes, but I don't have any mathematical evidence). In fact those constrains have a scalar min- maximum, such for example. -1kN <= force <= 15kN.

Can fmincon handle a vector returning of my fun.m ?

Any idea's?

Thank you!

Answer 1

[Alan Weiss]

You can include constraints on acceleration as nonlinear constraints. For example, if you want acceleration to be less than 5, your function would be something like

function [c,ceq] = mynlconst(x)
ceq = [];
% Set parameter of PI- controller of the force
set_param('Sim_10_01/CF/KpF', 'Gain', 'x(1)');
set_param('Sim_10_01/CF/TiF', 'Gain', 'x(2)');
 % Set parameter of PI-controller of the pressure
set_param('Sim_10_01/Cp/Kpp', 'Gain', 'x(3)');
set_param('Sim_10_01/Cp/Tip', 'Gain', 'x(4)');
sim('Sim_10_01','SrcWorkspace','current');
c = acceleration - 5;

To put in more than one constraint, just make c a vector:

 c(1) = acceleration - 5;
 c(2) = force - 10;
 c(3) = pressure - 100;

To save time, make sure you use the technique in Objective and Nonlinear Constraints in Same Function.

Alan Weiss

MATLAB mathematical toolbox documentation