Composite Controllers

 

Composite Controllers

Composite controllers combine basic control actions (P, I, D) to improve performance and overcome the limitations of individual modes. The most common are PI, PD, and PID controllers.

1. PI Controller (Proportional + Integral)

• Operation: Combines proportional control with integral action to eliminate steady-state error.

• Output Equation:

$$u(t)=K_{p}e(t)+K_i\int e(t)dt$$

• Response Graph: Faster than pure I, slower than pure P; smooth correction with no steady-state error.

• Characteristics:

  • Eliminates steady-state error.

  • May cause overshoot.

• Applications: Speed control of motors, temperature control systems.

2. PD Controller (Proportional + Derivative)

• Operation: Combines proportional control with derivative action to predict future error and improve stability.

• Output Equation:

$$u(t)=K_{p}e(t)+K_d\frac{de(t)}{dt}$$

• Response Graph: Faster response, reduced overshoot, but steady-state error remains.

• Characteristics:

  • Improves transient response.

  • Cannot eliminate steady-state error.

• Applications: Robotics, aerospace systems, where fast response is critical.

3. PID Controller (Proportional + Integral + Derivative)

• Operation: Combines all three actions for precise and stable control.

• Output Equation:

$$u(t)=K_{p}e(t)+K_i\int e(t)dt+K_d\frac{de(t)}{dt}$$

• Response Graph: Balanced response—fast, stable, and no steady-state error.

• Characteristics:

  • Eliminates steady-state error.

  • Improves transient response.

  • Most versatile and widely used.

• Applications: Industrial process control, motor drives, chemical reactors, power systems.

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