Symbols in a transfer function:

Im trying to get a step response for a transfer function but having trouble implementing it in matlab.

H(s)=K/(t*s+1)

Code:

sym k
sym t
sys = tf(k,[t 1])
step(sys)

Answer 1

[Star Strider]

The Control System Toolbox functions require numerical values.

It is possible to create an anonymous function with your code, and you can then use numerical values for ‘k’ and ‘t’ with it —

sys = @(k,t) tf(k,[t 1]);

k = 0.5;
t = 2;

figure
step(sys(k,t))
grid

The Symbolic Math Toolbox can be used to derive transfer functions. The sym2poly and double functions are helpful in that situation.

EDIT — Corrected typographical error.

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[Zain Ali]

Thank you!

[Star Strider]

As always, my pleasure!

Answer 2

[Walter Roberson]

tf() is part of the Control System Toolbox, which is not designed at all to be able to use symbolic expressions.

The Control System Toolbox has no capacity to draw a family of plots -- the plots for all of the different shapes that can be generated by using different K and t values. K might be negative. K might be 0. t might be negative. K or t might be complex.

You can work symbolically, such as

syms k t s
sys = k/(t*s + 1)

sys = 

isys = ilaplace(sys, s)

isys = 

but the symbolic toolbox has no way to draw families of plots either.

[Paul]

The Control System Toolbox has some capacity to draw a family plots where the user defines a parametric model and the values to use in the parametric model. For example, see this doc page.

Mixing t and s in an expression for a Laplace transform as in this Question is asking for nothing but trouble.

[Walter Roberson]

The Control System Toolbox has very limited capacity to work with systems with parameters in them. There is some capacity; see https://www.mathworks.com/matlabcentral/answers/305339-how-to-create-a-transfer-function-with-gain-k#answer_236890 . In each case, at any time the parameter is considered to have a specific value; the facilities that exist are there to make it easier to change the value of the parameter, potentially using automatic tuning.

[Zain Ali]

Thank You!