Q7Control System
Question
Q.7. What is the need of compensation in control system? Compare lag-lead and lead-lag network in detail.
Answer
Compensation is added to reshape a system's frequency/root-locus response to meet performance specs (steady-state accuracy, transient response, stability margins) that the uncompensated plant cannot satisfy on its own; lag-lead and lead-lag networks are two orderings of combining phase-lag and phase-lead stages to achieve both accuracy and speed simultaneously.
A control system designed only with a simple proportional gain often cannot simultaneously satisfy all desired specifications — e.g. increasing gain K to reduce steady-state error may reduce the phase margin and cause excessive overshoot or instability, while a gain chosen for good transient response may leave unacceptably large steady-state error. Compensation networks are additional elements (electrical, in cascade with the forward path, or as feedback elements) introduced specifically to reshape the open-loop frequency response or root-locus so that both transient (speed, damping, overshoot) and steady-state (error constants) requirements are met together, without redesigning the plant itself.
Lead compensator
A lead network has transfer function Gc(s) = (1+aTs)/(1+Ts), a > 1, adding positive (leading) phase near the gain crossover frequency. It increases phase margin and bandwidth, thereby speeding up transient response and improving stability margins, at the cost of increased high-frequency gain (more sensitivity to noise).
Lag compensator
A lag network has transfer function Gc(s) = (1+bTs)/(1+Ts), b > 1 with the pole closer to the origin than the zero, and mainly increases low-frequency gain (hence steady-state accuracy/error constants) while attenuating high-frequency gain, at the cost of reduced phase margin/bandwidth if not designed carefully, generally slowing the system.
Lag-Lead compensator
A lag-lead network places a lag section (acting at low frequency to raise the error constant) in cascade before a lead section (acting near crossover to restore/boost phase margin and speed). This ordering is chosen when both the DC/steady-state accuracy and the transient response of the original (uncompensated) plant need substantial correction — the lag stage handles accuracy first, and the lead stage subsequently restores adequate phase margin lost to the lag stage's phase lag near crossover.
Lead-Lag comparison
- Design intent: Lag-lead (lag then lead) is the standard industrial ordering used when both steady-state error and transient response must be improved; a pure lead-only design cannot fix steady-state error, and a pure lag-only design cannot fix a poor transient response/damping.
- Frequency action: the lag section operates below the original gain-crossover frequency (raises low-frequency gain), the lead section operates around/above the new crossover frequency (adds phase to restore margin).
- Effect on bandwidth: lag reduces bandwidth (slower), lead increases bandwidth (faster); combined, the lag-lead network is tuned so the net crossover frequency and phase margin land at the design target while low-frequency gain is boosted for accuracy.
- Circuit realization: both are typically realized by a single RC bridge network (or op-amp active network) whose transfer function simultaneously contains one pole-zero pair providing lag action and another pair providing lead action.