how to make input to the system time variable?

I would like to make an input that is time varying.

I have attached a photo that describe the time varying input I want.

Im a beginner. I hope someone can help me with this. Thank you

Im open to all suggestions or references that can help me learn.

[Rik]

I have some difficulty understanding what you actually want to achieve in terms of Matlab code. It seems like there are a few steps missing.

Have a read here and here. It will greatly improve your chances of getting an answer.

Answer 1

[Sam Chak]

Okay @Min Khant, the problem is incomplete. However, you can learn by yourself using this example for tracking the desired trajectory . Change the tau number as you wish to observe the time response of .

tspan  = linspace(0, 20, 3001);     % can set tspan from 0 to π 
y0     = [0; 0];                    % initial values
[t, y] = ode45(@odefcn, tspan, y0);
yd     = pi/2 - pi/4*cos(t);        % desired trajectory

% Plots
plot(t, yd),     hold on
plot(t, y(:,1)), grid on
title('Time response of \theta(t) in tracking \theta_{d}', 'fontsize', 10)
xlabel('t', 'fontsize', 10), ylabel('\theta', 'fontsize', 10)
legend('\theta_{d}', '\theta(t)', 'location', 'best', 'fontsize', 10)

% Simplified Robt dynamics
function dydt = odefcn(t, y)
    dydt    = zeros(2, 1);
    
    % parameters
    M       = 1;
    b       = 1;
    m       = 1;
    g       = 1;
    r       = 0.16;     % true value
    rmeas   = 0.08;     % measured
    kp      = 1;
    kd      = 2;
    
    % desired trajectory
    yd      = pi/2 - pi/4*cos(t);
    dyd     = 1/4*pi*sin(t);
    ddyd    = 1/4*pi*cos(t);
    
    % tau input (3 variants)
    tau1    = M*ddyd + b*dyd + m*g*rmeas*cos(yd);   % so-called feedforward control
    tau2    = M*ddyd + M*kd*dyd + M*kp*yd - M*kd*y(2) - M*kp*y(1) + b*y(2) + m*g*r*cos(y(1));       % perfect r
    tau3    = M*ddyd + M*kd*dyd + M*kp*yd - M*kd*y(2) - M*kp*y(1) + b*y(2) + m*g*rmeas*cos(y(1));   % imperfect r
    dydt(1) = y(2);
    dydt(2) = (- b*y(2) - m*g*r*cos(y(1)) + tau3)/M;    % <-- change the tau number
end

[Min Khant]

thank you for generously answering my question even though I was bad at making a question. sir

as I am a beginner, I found simulink easier than coding in Matlab and thus I tried to finish my midterm project building blocks in simulink. i have alrdy finished problem 2(in attached file) by building blocks for feedback control. Now in problem 3 I have to create blocks for feedforward control which including a time-varying desired theta value. I wanted to ask how I can create a simulink block that can defines the desired time varying input.

[Min Khant]

I was willing to create an input that defines time-varying desired theta and differentiate it twice and build other necessary blocks to complete the feedforward tau which will lated be fed into the plant.

if there are better ideas than mine , I am willing to hear it sir

[Sam Chak]

Hi @Min Khant

Good to hear that you like Simulink. This following approach is generally more accurate than applying the differentiation block twice to get . If you find the solution helpful, please consider clicking 'Accept' ✔ on the answer and voting 👍 for it.

[Min Khant]

May I know how to use derivative block consecutively? sir

as i tried , it does not function properly

Answer 2

[Aquatris]

You can create your own numeric integration to solve the equation and provide the desired input in each time step.

Here is an example (the accepted answer) which you can modify for your need.