Question

only Q 1 please

is is the last homework. 1. Compare and contrast designing via gain versus designing via compensation (what's the same? what's different? advantages? disadvantages? etc.). Also, discuss the effects of adding a zero or a pole. Solution: 2. What kind of compensation improves steady state error? List all and indicate whether they are active or passive. Solution: 3. Cascade compensation to improve transient response is based upon what pole-zero placement of the compensator? Also, state the reasons for this placement. Solution: 4. Why is there more improvement in steady state error if a PI controller is used instead of a lag network Solution: 5. A lag compensator with the zero 25 times as far from the imaginary axis as the compensator pole will yield approximately how mnch improvement in steady state error? Solution: 6. Consider a unity-feedback control system with the following feed forward transfer function: If the value of gain K is set equal to 2. where are the closed-loop poles located? Solution: The closed loop transfer fiunction is Cis)

Answer 1

Compensation via Gain: Controllers

1. Used to improve time response characteristics of the system

e.g. PID (Proportinal Integral Derivative) Controller has

PD part which

Improves transient response of system bcz of increses damping ratio of system which keeping natural frequency fo oscillation constant hence increasing speed of response.

PI part which

Increase type of the system due to which steady state error decreases which makes system more stable

Hence PID Controller is better than PI and PD controller alone respectively.

Compensation via Compensation: Compensators

1. Used to improve frequency response characteristics of the system

e.g. lead lag compensator

Lead Compensator

Increase w_g where w_g is the frequency at which gain = 0dB of system .This in turn increase BW of the system which increases speed of the system also PM (Phase Margin) of system also increase making it more stable. But because BW is increased Noise effect also increases.

Lag Compensator

This compensator makes sure that noise effect ans steady state error remains constant as compensated system when lead compensator is applied to the system in conjunction with lag compensator

Hence Lead Lag compensator is better than Lead and lag alone respectively.

Addition of poles increase the order of the system and hence steady state error of the system decreases .It corresponds to lag compensator and hence above given facts are valid.

Addition of zeros correspond to lead compensator hence above facts do apply for this also.