Change value of parameters in simulink over time

I am simulating a complex system and have a trouble. However, I will explain my problems by similar case.

Assuming I have a following system:

with a1, a2, a4, a5 are functions depending on u, v. For example, a1 = u*v; a2 = u+v; a4 = u-v; a5 = u/v (in fact, they are more bulky).

I want to change values u, v in a certain domain over time, it leads to a1, a2, a3, a4 are changed values. But, I don't know how to do.

Please help me. Thank you.

[Sam Chak]

Try modeling the nonlinear system using @Deep's approach (MATLAB function block) based on the proposed mathematical model in my Answer.

Answer 1

[Deep]

You can use a 'clock' and model your u,v signals as functions of the simulation time. For modeling complex and bulky math functions, a 'MATLAB function' block can help you write big functions as MATLAB code.

You can double click on the MATLAB function blocks to edit your functions.

Answer 2

[Sam Chak]

Hi @Hoang Vu Huy

If the parameters in the transfer function vary over time, then it is a nonlinear system. Nonlinear systems need to be modeled in the equivalent continuous-time state differential equations. In your case, the system output is .

Equivalent state differential equations and system output:

.

Substituting the parameters for as the time-varying functions of auxiliary inputs and

.

Since the system input is given, then the overall model becomes

.

In Simulink, if you are using basic blocks, then the system needs to be expressed in the Integral form. In other words, you need to construct the integrands (right-hand side of the ODEs) and then feed them into the input ports of the Integrator blocks.

The outputs of the Integrator blocks are the states , and they can be fed back into the integrands.

Example:

The following example assumes that the parameters are constants. But I think that you should get the idea.

% Parameters
a1     = 7;
a2     = 5;
a4     = 3;
a5     = 2;
params = [a1 a2 a4 a5];

% Transfer function of the Plant
G      = tf([a1 a2], [1 a4 a5])

G =
 
     7 s + 5
  -------------
  s^2 + 3 s + 2
 
Continuous-time transfer function.

tspan  = linspace(0, 6, 60001);
x0     = [0 0];
[t, x] = ode45(@(t, x) odefcn(t, x, params), tspan, x0);

% Solution Plot
subplot(2, 1, 1)
plot(t, x(:,1), 'color', 'r'), grid on, ylabel('Amplitude')
title('Time response of Output, y(t)')
subplot(2, 1, 2)
step(G), grid on

function xdot = odefcn(t, x, params)
    xdot    = zeros(2, 1);
    a1      = params(1);
    a2      = params(2);
    a4      = params(3);
    a5      = params(4);
    w       = heaviside(t);     % step input
    xdot(1) = x(2) + a1*w;
    xdot(2) = - a5*x(1) - a4*x(2) + (a2 - (a1*a4))*w;
end