Combine two controllers in ODE45 environment

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Telema Harry
Telema Harry 2022-6-7
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
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
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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Sam Chak
Sam Chak 2022-6-8
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
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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