Combine two controllers in ODE45 environment

Question

Telema Harry 2022-6-7

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评论： Telema Harry 2022-6-8

Hi,

Please I need idea on how to implement the following problem on MATLAB.

My aim is to stabilize a plant using two dynamic controllers. Only one controller is implemented at a time. The controller to be implemented is depended on a logic variable q = 1 or q = 0.

If q = 0, controller 1 is implemented and if q = 1, controller 2 is implemented.

The controller output is given by:

u = q* K2(x) + (1 - q) * K1(x).

K1 and K2 are dynamic controllers. so they are solved using ODE45.

By default controller 1 will be triggered at the start of the program until output variable is less than 5. and the second controller is triggered.

The main challenge:

The last output of controller 1 (The output just before controller 2 is triggered) should be used as the initial condition of controller 2 when controller 2 is triggered.

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Sam Chak 2022-6-7

编辑：Sam Chak 2022-6-7

Yes @Telema Harry

Thanks for clarifying the matter. I think I understand that the dynamics is something like

, where

, in order to preserve the continuity of the control action. Actually, I'm thinking, "if this is a state-space, where do I put

?"

Telema Harry 2022-6-7

@Sam Chak. Sorry, that I did not write the controller dynamics. Please see below a simplified version of the problem. Please let me know if it is not clear.

I am currently trying to code the problem using Euler's numerical technique. In the past, I used if statement in the ODE environment. But it did not work as intended.

Controller 2:

when q = 1,

when q = 0

u = K1

State Space Representation:

Assuming a linear system

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Answer 1

Sam Chak 2022-6-8

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在 MATLAB Online 中打开

Hi @Telema Harry

Since you are unable to provide more info, here is a very simple example, which I'm not sure if this is what you want.

System:

, where

is a sinusoidal disturbance.

function dxdt = odefcn(t, x)

dxdt = zeros(2, 1);

h = 0.2; % activation if x < |h|

q = (sign(x(1) + h) - sign(x(1) - h))/2; % trigger condition for K2

u1 = sign(x(1)); % K1

u2 = x(1)/h; % K2

u = (1 - q)*u1 + q*u2;

d = 0.75*cos(t*2*pi/10) + 0.5*sin(t*2*pi/5); % disturbance

dxdt(1) = d + x(2);

dxdt(2) = (- u - x(2))/0.01;

end

Solving ODE

tspan = linspace(0, 20, 2001)';
x0 = [1 -1];
[t, x] = ode45(@odefcn, tspan, x0);

Plotting the results

plot(t, x, 'linewidth', 1.5)

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Telema Harry 2022-6-8

@Sam Chak Thank you so much for your help. Though I did not provide enough information (model) of my problem as it is my graduate school research project. You still managed to provide great help. I will say, your solution gave me another insight.

Thank you.

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