MATLAB: Nonlinear plant model in matlab

imcinternal model controlnonlinear plantnonlinear state space modelsimulink

Hi I want to use a nonlinear plant to design IMC. The controller and the inverse model are linear but I have to use the nonlinear plant in the IMC structure. I really don't know how to describe the nonlinear state space model! Should I use Simulink and call it from the Mfile or what? the system is described like xdot=-x^2+(x+1)u and y=x+u … it's a toy plant and I know it's maybe easy but if anyone can, help me please. Thanks

Best Answer

You can use ordinary differential equation (ODE) solvers in MATLAB by specifying the relationship between ydot and y.

See for example: https://www.mathworks.com/help/matlab/ordinary-differential-equations.html or https://www.mathworks.com/videos/series/solving-odes-in-matlab-117658.html

- Sebastian

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MATLAB: How to specify plant while using MPC Toolbox when I don’t have state space equations of the plant

To create a plant model, you can directly specify a linear model (state space equations), linearize a Simulink model, or identify a linear model using measured data. Following documentation explains this in detail:

https://www.mathworks.com/help/releases/R2016b/mpc/plant-specification.html

As described in the above documentation, you can use the MPC Designer App to linearize your plant and obtain the plant model:

https://www.mathworks.com/help/releases/R2016b/mpc/gs/linearize-simulink-models-using-mpc-designer.html

You can also use following method to linearize your Simulink model without using the MPC Designer:

https://www.mathworks.com/help/releases/R2016b/mpc/gs/using-simulink-to-develop-lti-models.html

If your model is strongly nonlinear and you wish to use another control mechanism you can explore Adaptive MPC or Gain-Scheduled MPC (Non-linear MPC is also available starting from R2017a):

https://www.mathworks.com/help/releases/R2016b/mpc/

MATLAB: Adding trajectories to vector fields of a linear system

[x1, x2] = meshgrid(-.5:0.05:0.5, -.5:.05:.5);
x1dot = - x1; 
x2dot = 2*x2;
quiver(x1,x2,x1dot,x2dot)
hold on
starty = -0.5:0.05:0.5;
startx = ones(size(starty))*-0.5; %specify the starting x values- LHS
streamline(x1,x2,x1dot,x2dot, startx,starty)
startx_2 = ones(size(starty))*0.5; %specify the starting x values -RHS
streamline(x1,x2,x1dot,x2dot, startx_2,starty);

Best Answer

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MATLAB: How to specify plant while using MPC Toolbox when I don’t have state space equations of the plant

MATLAB: Adding trajectories to vector fields of a linear system

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