Final answer:
The student is asking how to apply a PID controller with given parameters to a system when the inputs are a 1-unit step and a unit ramp function, with an emphasis on checking the steady-state error for each case.
Step-by-step explanation:
The question is about applying a PID controller to a system (denoted here as Ex1) with specific gains for the proportional (Kp), integral (Ki), and derivative (Kd) elements. The gains are given as Kp = 1, Ki = 1, Kd = 2. The question also asks to check the steady-state error (ess) when the input (i/p) is a 1-unit step and a unit ramp function.
The PID controller is a widely used feedback controller in control systems that adjusts the control input based on the proportional, integral, and derivative terms, aiming to minimize the error between the desired output and the actual output of a system. The proportional term (Kp) produces an output that is proportional to the current error. The integral term (Ki) computes the cumulative sum of past errors and helps eliminate the steady-state error. The derivative term (Kd) predicts future errors based on the rate of change of the error, adding a corrective action that is proportional to it.
For a 1-unit step input, a PID controller will react to minimize the difference between the actual output and the step input. In the case of a unit ramp input, which increases linearly over time, the PID controller will attempt to track this changing input and reduce the error over time. However, the integral component of the PID is key in reducing the steady-state error, which is especially relevant for inputs like a ramp function where the error could accumulate over time.