# Compensators-Introduction

Compensators are corrective sub systems to compensate the deficiency in the performance of the plant or system, so given a plant and a set of specifications suitable compensators are to be designed so that the overall system will meet given specifications. Proper selection of performance specifications is the most important step in the design of compensators.

i.e, All the control systems are designed to achieve specific objectives that is the requirements are defined for the control system. A good control system has less error, good accuracy, good speed of response, good relative stability, good damping which will not cause unusual Overshoots etc.

For stationary performance of the system, gain is adjusted first but gain adjustment alone can not provide satisfactory results. When gain increases, Steady-state behavior of system improves but results into poor Transient response (or) even instability.

The desired behavior of a system is specified in terms of

• Transient response.
• Steady-state error($e_{ss}$).

$e_{ss}$ →is usually specified in terms of constants $k_{a},k_{v}$ and $k_{p}$ for $u(t),r(t)$ and $p(t)$ as inputs.

Transient response → it measures relative stability and speed of response which are specified in time or frequency domain.

In time domain the measure of relative stability is in terms of $\xi$ or $M_{p}$, while the speed response is measured in terms of rise time $t_{r}$ , settling time $t_{s}$ or natural frequency $\omega&space;_{n}$. Where as in frequency-domain the measure of relative stability is given by Resonant peak $M_{r}$ or Phase margin $\varphi&space;_{pm}$ and the speed response is measured by Resonant frequency $\omega&space;_{r}$ or band width $\omega&space;_{b}$.

Once a set of performance specifications have been selected, the next step is to chose the appropriate compensator. There exists Electrical,hydraulic,pneumatic and mechanical compensators and in this context we prefer Electrical compenators.

An external device which is used to alter the behavior of the system so as to achieve given specifications is called as compensator .

Compensators can be added to the system in series or in parallel or in combination of both.

Series Compensation:-

The flow of signal in series scheme is from lower energy level towards higher energy level. This requires additional amplifiers to increase the gain and also provide necessary isolation. The number of components required in series scheme is more than in parallel scheme.

Parallel Compensation:-

In this compensation technique energy flow is from higher energy level to lower energy level.  As there is no need of any amplifiers additional components required are less.

Series-Parallel Compensation:-

This is a compensation technique which utilizes the advantages of both series and parallel compensation techniques.

## Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.