如何 plot 零点多于极点的系统的阶跃响应（不改变原始传递函数）

Question

I am trying to plot step response of an electronic circuit(differentiator) using MATLAB but I get an error:

Error using DynamicSystem/step (line 95)
Cannot simulate the time response of models with more
zeros than poles.

My code is below:

R=47*10^3%resistance value
C=1*10^-6% capacitor value
den=[-1]%denominator of transfer function
num=[R*C 0]%numerator of transfer function
sys=tf(num,den)%transfer function expression of model/system
step(sys)%step response

How can I plot my graph without changing my original transfer function? Because if I change the original transfer function, it will become a new system. However, I want to analyze original system.

Answer 1

I would try adding poles with very fast dynamic (going to -inf for continuous system, close to 0 for discrete). This will make the system to meet the criteria and will have minimal impact on the system dynamic. But as for the step response you will probably have some spikes and maybe some nan will pollute your results.

What is a system with more zeros than poles? You must have some derivatives in the response. What is the step response? Is the response of the system to a step input, and the step infput is not differentiable at t = 0 . So, I would try to compute the response to another (differentiable) input.