How do I obtain the step response of this PID controller in Matlab?

Question

I'm relatively new to Control systems. I'm trying to obtain a graph for the step response of a PID controller of the form

Is this possible to plot in mat lab because I get the error that the function cannot plot the step response of a system with more poles than zeros. Is there any way to plot this system without the whole infinity issue so that I can observe the characteristics of its step response? I'm sorry if I'm asking a dumb question that may seem obvious but any help or explanation would be greatly appreciated.

This is my mat lab code for my PID controller:

%3.PID Control,Td=0.001, 0.01, 0.05, 0.1
a=tf([0 0 -10],[0 1 10]);
b=tf([0 -1 -5],[1 3.5 6]);
kc=5;
Ti=1;
Td=0.001;
k1=tf([0 Td 0],[0 0 1]);       %derivative control
k2=tf([0 1],[Ti 0]);            %integral control
G=kc*(k1+k2+1);                % the controller
G1=series(a,b);
y=feedback(G,G1,-1);
subplot(2,2,1),stepplot(y),title('kc=5,Ti=1,Td=0.001');

Answer 1

As thewaywewalk mentioned, MATLAB can only deal with proper systems, and a pure derivative isn't proper, so you need to use an approximate derivative in your transfer function. It's never a good practice to use pure derivatives as they tend to amplify noise.

Look at the documentation on the PID Controller block in Simulink to see how to implement a PID controller with approximate derivative. In short, you need to replace Kd*s by Kd*s/(1+a*s) where a is small compared to the dominant time constant of the system.

EDIT: The best way to create your PID is to use the actual pid function from the Control System Toolbox. It implements a first-order derivative filter on the derivative term.