Why two different responses are produced when a same step signal is used to excite a First order transfer function block and a Subsystem that has a numerical model of the time domain equivalent of the same?

Hi,

Let me give a brief explanation of the scenario:

The Step response of a First order System, is being analyzed in two different scenarios.

1. With First order transfer function of the System &
2. With time-domain equivalent of the same.

Here i am getting Different Output responses, for the same step input as shown in screen capture and in the model attached.

Explanation

With System transfer function as: 1/(s+β); (note: here β is set to 0.01), And with input step as: α/s; (note: here α is the magnitude of the Step, and is set to 20 from time t=0 to t=500, and then to 10 from time t=500 to t=100, where total simulation time is 1000.)

We get the output as: α/(s*(s+β));

Which when converted to time domain results in a following expression: y(t)= (α/β)*(1-e^(-βt)) Where “α” denotes step magnitude, and the above expression describes the change in output for a step input.

Problem:

In my Simulink Model, I designed a Sub-System as per the above time-domain equation with all the available mathematical blocks; please verify my attached model (Sub-System in Pink). As per my understanding it should be the same as the step response of the 1st order transfer function (in green), right????

Now my problem is when both the Systems are excited by the same step Signal of same magnitude I get different responses as shown in the Graph image attached:

The response graph in Yellow indicates the response of the transfer function, and the response in green indicates response of the Sub-system designed.

I am unable to understand this disparity. I would be grateful to you people, if you can clarify / help me on this

Thanks & regards

Balaji