critically analyze the impact of disturbance on the system to ensure the stability and obtain the responses in mathematical evaluation.

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A paint industry in Oman for its operation, a central load controller with a second/any higher order model is to be designed. The control systems should be equipped with a motor constant and a suitable amplifier gain to balance the operation. The controller should be designed to operate with unity feedback H(s)=1. The system is expected to perform on unit step/ramp input. Obtain the response for such system if the amplifier gain is varying within the rage of 20 to 55, using mathematical evaluation.

The system is also expected to be dealt in noisy environments. In such a case, if a disturbance is acting on the system with a unit step phase, determine the steady state error component for the system for the same amplifier gains. Also critically analyze the impact of disturbance on the system to ensure the stability and obtain the responses in mathematical evaluation.