the question is clear .Use approximation methods to get K variables.

2 Use the disturbance-observer based approach to design a PID controller for the following system: G(S) (s - 1)(8+1) 1. (5 marks) Choose the desired closed-loop characteristic polynomial for the proportional plus derivative controller as s2 +2u.s+u, where $ = 0.707 and n = 3, while the pole for the estimator is -4. What are the values of K1, K2 and Kg? 2. (8 marks) Simulate the closed-loop step response and input distur- bance rejection where the derivative filter time constant Tj = 0.Imp. In the simulation, the reference signal r = 1 and the input disturbance has an amplitude of -3 entering the simulation at half of the simula- tion time. The sampling interval At = 0.001 and the simulation time 3. What are the maximum and minimum values of the control signal? 3. (7 marks)Evaluate the effect of constraints on the control signal where the constraint parameters u mat and mini are chosen to be 90 percent of the control signal's maximum and minimum amplitude from the previous step. Submit your MATLAB/Simulink programs together with your solutions, simulation results control signal and output plots) and discussions. Tsim 2 Use the disturbance-observer based approach to design a PID controller for the following system: G(S) (s - 1)(8+1) 1. (5 marks) Choose the desired closed-loop characteristic polynomial for the proportional plus derivative controller as s2 +2u.s+u, where $ = 0.707 and n = 3, while the pole for the estimator is -4. What are the values of K1, K2 and Kg? 2. (8 marks) Simulate the closed-loop step response and input distur- bance rejection where the derivative filter time constant Tj = 0.Imp. In the simulation, the reference signal r = 1 and the input disturbance has an amplitude of -3 entering the simulation at half of the simula- tion time. The sampling interval At = 0.001 and the simulation time 3. What are the maximum and minimum values of the control signal? 3. (7 marks)Evaluate the effect of constraints on the control signal where the constraint parameters u mat and mini are chosen to be 90 percent of the control signal's maximum and minimum amplitude from the previous step. Submit your MATLAB/Simulink programs together with your solutions, simulation results control signal and output plots) and discussions. Tsim