DC Motor Speed Control using a PI Controller in Simulink

A MATLAB/Simulink implementation of a closed-loop velocity control system using a Proportional-Integral (PI) controller to regulate the speed of a first-order dynamic plant (representing a simplified DC motor model).

System Architecture

The simulation models a standard negative feedback control loop configured as follows:

1. Input Signal: A step input acting as the reference target speed command (setpoint step to 100 at $t = 1\text{ s}$).
2. Error Detection: A summing junction calculating the error signal: $e(t) = \text{Setpoint} - \text{Actual Speed}$.
3. PI Controller: Processes the error signal through parallel controller paths:
   • Proportional Path: Multiplies the error signal by a static proportional gain ($K_p = 10$) to provide immediate corrective action.
   • Integral Path: Integrates the error ($\frac{1}{s}$) to eliminate steady-state tracking error under constant load conditions, scaled by an integral gain ($K_i = 15$).
   • Derivative Path: The derivative gain is set to $K_d = 0$, reducing the controller architecture to a robust PI configuration to prevent high-frequency noise amplification.
4. Plant Dynamics: A first-order system representing the mechanical/electrical time constants of a motor, defined by the transfer function: $$G(s) = \frac{100}{0.5s + 1}$$
5. Visualization: A multi-port Scope capturing both the reference speed command (blue) and the actual motor speed output (yellow) for transient response analysis.

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Technical Specifications

Parameter / Block	Value / Configuration
Plant Transfer Function	$\frac{100}{0.5s + 1}$
Proportional Gain ($K_p$)	10
Integral Gain ($K_i$)	15
Derivative Gain ($K_d$)	0 (Disabled)
Feedback Type	Negative Feedback

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Performance & Results

The plot below shows the closed-loop step response captured by the Scope block.

Transient Response Analysis

• Tracking & Steady-State Error: The system tracks the reference command with zero steady-state error ($\rho_{ss} = 0$). The actual speed settles exactly at the target value of 100, showing that the integral path successfully eliminated systemic offset.
• Overdamped Response: Due to the tuning parameters and the inherent first-order plant dynamics, the system achieves a smooth, overdamped response with 0% overshoot. This is highly desirable in motor applications where speed tracking must avoid mechanical strain or jerking.
• Settling Time ($T_s$): Following the step input command change at $t = 1.0\text{ s}$, the motor speed transitions smoothly and completely settles into the target value within approximately $2.5\text{ seconds}$ ($t \approx 3.5\text{ s}$).

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