Control Actions in Control Systems

 

Control Actions in Control Systems

Control actions define how a controller responds to the error signal (difference between setpoint and actual value). They are broadly classified into Discontinuous Mode and Continuous Mode.

i. Discontinuous Mode: ON–OFF Controllers

Concept

• Controller output switches fully ON or fully OFF depending on the error.

• Common in simple systems like thermostats, refrigerators, and water level controllers.

Equation

$$u(t)=\{\begin{array}{cc}{U}_{max},& e(t)>\text{Neutral Zone}\\ 0,& e(t)<\text{Neutral Zone}\end{array}$$

Neutral Zone (Dead Band)

• A small range around the setpoint where the controller does not act.

• Prevents frequent switching (chattering).

• Example: Thermostat set at 25°C with ±1°C neutral zone → heater ON below 24°C, OFF above 26°C.

ii. Continuous Mode Controllers

1. Proportional (P) Controller

• Output proportional to error.

• Equation:

$$u(t)=K_p\cdot e(t)$$

• Response: Reduces steady-state error but cannot eliminate it completely.

• Characteristic: Faster response, but large $K_p$ may cause oscillations.

2. Integral (I) Controller

• Output proportional to the integral of error.

• Equation:

$$u(t)=K_i\int e(t)dt$$

• Response: Eliminates steady-state error.

• Characteristic: Slower response, may cause overshoot.

3. Derivative (D) Controller

• Output proportional to the rate of change of error.

• Equation:

$$u(t)=K_d\frac{de(t)}{dt}$$

• Response: Predicts future error, improves stability.

• Characteristic: Reduces overshoot, but sensitive to noise.

Combined Controllers (PID)

• Proportional–Integral–Derivative (PID) combines all three actions:

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

• Most widely used in industry for precise and stable control.