Please help me solve this problem. I have the equations, but don\'t fully unders
ID: 2081934 • Letter: P
Question
Please help me solve this problem. I have the equations, but don't fully understand the process.
Consider a plant with a transfer function G(s) and a sensor with a transfer function H(s) given by: G(s) = 10/s^3 + 10 s + 29; H(s) = 1 a) Design a Lead Compensator that will have the system operating at a 25%OS, and decrease the settling time by a factor of 5 b) Design a Lag-compensator that will have the system operating at a 25%OS, and decrease the steady state error by a factor of 10. c) Design a Lead-Lag compensator the will have the system operating at a 20%OS, decrease the settling time by a factor of 5, and decrease the steady state error by a factor of 10.Explanation / Answer
A compensating network is one which makes some adjustments in input in order to make up for deficiencies in the system. Compensating devices are may be in the form of electrical, mechanical, hydraulic etc. eg; RC filter.
Compensation is generally used to minimize overshoot.Compensating networks increase the steady state accuracy of the system which brings instability to the system.Compensating networks also introduces poles and zeros in the system thereby causes changes in the transfer function of the system and therefore the performance specifications of the system changes.
Connecting a compensating circuit between error detector and input is SERIES COMPENSATION.
When compensator added in a feedback manner, is feedback compensation.
Another type is load compensation; a combination of series and feedback compensation.
Lead Compensation: One pole & One dominating zero(zero closer to origin is a dominating zero); Used to add a dominating zero for compensation hence a lead network introduces positive phase angle to the system when connected in series. Although, all poles and zeros of the network must lie on the -ve real axis. It doesn't improve steady state error. It only makes the response of the system faster and overshoot decreses.
Lag compensation: One zero and one dominating pole. To add a dominant pole, use lag compensation.Lag network introduces negative phase angle to the system when connected in series.Although, all poles and zeros of the network must lie on the -ve real axis.Steady state accuracy increses if you use lag compensation but, slower speed of the system.
For an unstable uncompensated system, lead compensation provides fast response but does not provide enough phase margin whereas lag compensation stabilize the system but does not provide enough bandwidth. So multiple compensators in cascade known as lag lead compensators are used.