Control Systems Compensation Techniques

Compensation in Control Systems

• The primary purpose of compensation is to stabilize a system and enhance its performance.

Feed-Forward Compensation

• Feed-forward compensation uses changes made to the output before external factors disturb it.

Active Compensation

• A PID (Proportional-Integral-Derivative) controller is a type of active compensation.

Proportional-Derivative (PD) Controller

• A key feature of a PD controller is that it does not affect system type.

Steady-State Performance

• The phase-lag controller improves steady-state performance by increasing the system type.

Passive Compensation Controllers

• Phase-lead configurations improve transient response without affecting steady-state performance.

Phase-Lag Controller

• Employing a phase-lag controller eliminates steady-state error in first-order systems.

Active vs. Passive Compensators

• Active compensators provide greater control over system dynamics compared to passive compensators.

Root-Locus Design

• The primary purpose of using root-locus design is to adjust system gain for satisfactory closed-loop behavior.

PI Controller

• The PI (Proportional-Integral) controller combines proportional gain with the integral of the error.

Phase-Lead Compensator

• In a phase-lead compensator, the zero is greater than the pole.

PD Compensator Design

• A typical goal when designing a PD compensator is to improve the transient response of the system.

Phase-Lag Compensators

• Phase-lag compensators primarily shift the root-locus to the right.

PID Controller Characteristics

• A key characteristic of a PID controller is that it combines proportional, integral, and derivative actions.

MATLAB Command for Root Locus

• The rlocus() command in MATLAB is used to plot the root locus of a system.

Compensator Design: Angular Criterion

• In compensator design, the angular criterion helps determine the positions of zeros and poles in the s-plane.

Root-Locus: Breakaway Point

• The "breakaway point" refers to the location on the root locus where multiple trajectories diverge.

Effect of Increasing Gain in P-Controller

• Increasing the controller gain in a P-controller improves transient response at the risk of overshoot.

Compensator Function in Root-Locus Design

• The function of a compensator is to reshape the root-locus plot for desired performance.

PD Controller Effect on Overshoot

• A PD controller can reduce overshoot in transient response.

PID Controller: Eliminating Steady-State Error

• For a control system using a PID controller, integral action is responsible for eliminating steady-state error.

Phase-Lead Compensator Pole Placement

• When designing a phase-lead compensator, the pole should satisfy the angle criterion.

Graphical Root-Locus Design

• The purpose of the graphical root-locus design method is to select points in the s-plane for closed-loop poles.

Root-Locus: Dominant Poles

• "Dominant poles" refer to poles that contribute most significantly to the system's behavior.

System Behavior with High Gain

• A system with a gain that is too high can cause instability.

PID Controller: Quick Response Adjustment

• Adjusting proportional gain (K_P) first is recommended to achieve quick response in a PID controller.

PID Controller: Integral Action

• The integral action of a PID controller primarily addresses steady-state error.

Root-Locus: Angle Criterion

• The angle criterion in root-locus design is used to establish the phase contribution of poles and zeros.

Filtering Capacity of Compensators

• With regard to filtering capacity, the lead compensator and lag compensator are high pass and low pass filters, respectively.

Phase Lag Compensation Effects

• Phase lag compensation increases the velocity constant for a given relative stability in a servo system.

Composite R-C Network Transfer Function

• A composite R-C network with the transfer function T(s) = (1+21s+20s^2)/(1+11s+10s^2) can be used as a phase-lag compensator

Open Loop Transfer Function Stabilization

• For a plant with an open loop transfer function G(s) = 1/(s^2-1) operated in unity feedback, the lead compensator 10(s-1)/(s+2) can stabilize the control system.

Bode Plot Representation

• A Bode plot represents the frequency response of a system.

Bode Plot Axes

• The axes used in a Bode plot are log scale for both magnitude and frequency.

Gain to Decibels Conversion

• The formula to convert gain G into decibels (dB) is dB = 20log10G.

Phase Margin in Bode Plot

• The phase margin in a Bode plot is the distance from -180 degrees to the phase at the gain crossover frequency.

Bode Plots for High-Order Transfer Functions

• High-order transfer functions can be effectively plotted using Bode plots by plotting each term separately and adding them graphically.

Bode Plot Response Analysis

• A Bode plot analyzes the frequency response of a system.

Bode Plots and Time Constants

• A Bode plot does not directly provide information about the time constant.

Bode Plots: First-Order System Slope

• In Bode plots, a first-order system is represented by a slope of 20 dB/decade on the magnitude plot.

Bode Plot Stability Indication

• A Bode plot indicates a stable system when the phase margin is positive.

Corner Frequency in Bode Plot

• The corner frequency in a Bode plot is the frequency at which the slope of the magnitude plot changes.

Bode Plot: Zero at Origin

• Adding a zero at the origin in a Bode plot increases the slope by 20 dB/decade on the magnitude plot.

Log-Scales Principle

• According to the principle of log-scales, if the ratio between two points is the same, then the two points get separated equally.

Gain Margin

• The term "gain margin" refers to the maximum gain that a system can tolerate before becoming unstable in a Bode plot

Second-Order System on Bode Plot

• A second-order system appears on a Bode plot with a slope that changes at two distinct frequencies.

Bode Magnitude Plot: 4th Order All-Pole System

• In a Bode magnitude plot, a 4th order all-pole system exhibits a slope of -80dB/decade at high frequencies.

Bode Plot: Magnitude Slope

• In a Bode plot, the slope of the magnitude plot indicates system order.

Stable Systems: Gain Margin

• A system is marginally stable when the gain margin is +∞.

Magnitude and Frequency

• The magnitude of a system becomes zero dB at the gain crossover frequency.