Answer Happy

9) Analytically calculate the steady state error due to the disturbance and the reference signal. What can you infer from the values obtained? [7 marks] 10) Prove that the output y(t) will only track steady-state targets if there is an integrator in either a feedforward controller C(s) or the plant G(s). What other condition is required? In addition, using a mathematical derivation, specify the requirement for disturbance signals to be totally rejected, that is to have no steady- state impact on the output? [12 marks] 11) Use MATLAB to investigate how offset and performance varies as you change the scalar controller gain Kp. Give some generic conclusions based upon what you observe. [7 marks]

7 Oēc g = ((G) T+CG 7S+1 V = (G 7s+1 1+ CG 75+1 ū 1 1+ CG J + G H 75+1 JH Ts+1 H a) Gry(s) b) Gdy (s) = 75+1 1+ CG₁₂ Is+1 c) Gre(s) = d) Gde = HCG Ts+1 TS+1 1+ Ca Tstl 9) Analytically calculate the steady state error due to the disturbance and the reference signal. What can you infer from the values obtained? [7 marks] 10) Prove that the output y(t) will only track steady-state targets if there is an integrator in either a feedforward controller C(s) or the plant G(s). What other condition is required? In addition, using a mathematical derivation, specify the requirement for disturbance signals to be totally rejected, that is to have no steady- state impact on the output? [12 marks] 11) Use MATLAB to investigate how offset and performance varies as you change the scalar controller gain Kp. Give some generic conclusions based upon what you observe. [7 marks] + Ts+1 y(s)