Design and Simulation of a DC Motor Control System with Feedback: Speed and Torque Control Using MATLAB

Abstract

The control of DC motors has remained a fundamental concern in industrial automation, robotics, and electromechanical systems due to their simple architecture and high performance. This paper presents a comprehensive design and simulation of a DC motor control system incorporating a feedback control strategy. The study focuses on the control of both speed and torque using Proportional-Integral-Derivative (PID) controllers implemented in MATLAB/Simulink. The motor model includes mechanical and electrical dynamics, with a feedback loop for achieving stability, fast response, and minimal steady-state error. Simulation results demonstrate the effectiveness of feedback-based control systems, and the performance of the system is analyzed using standard performance indices. This report also includes detailed design methodology, mathematical modeling, and comparative analysis with different controller settings.

1. Introduction

DC motors play a pivotal role in modern engineering systems due to their advantages in speed control, torque performance, and ease of modeling and implementation [1]. Applications range from electric vehicles and industrial automation to servo mechanisms and robotics [2]. With the increasing need for efficient and stable operation, the integration of feedback control systems in DC motor applications has become essential.

This project deals with a classical control experiment where the objective is to position a ball on a beam by appropriately inclining the beam. Figure 1 shows the ball and beam apparatus that we will be using in this lab. As seen in the figure, a DC motor is used to control a lever arm, which in turn is used to raise or lower the right side of the beam to cause the ball to move. The beam itself consists of two parallel rods, which together with the ball form a potentiometer used to measure the ball’s position. One of the rods has a resistive film glued onto it, while the other rod and the ball form the wiper of the potentiometer. The left side of the beam is pivoted on a support. The input to the ball and beam apparatus is the motor voltage; both the ball position and the motor gear angle are measurable outputs.

Figure 2 shows the main connections between the ball and beam apparatus, control computer (cRIO) and the lab Nexus computer. The cRIO has an FPGA, a real-time processor, an analog-to-digital converter and a dc servo motor drive and amplifier.

Feedback control enables dynamic correction of motor behavior by comparing output parameters (like speed or torque) with reference inputs. PID controllers, the most widely used feedback control method, offer robust and simple solutions for dynamic response improvement and steady-state error minimization [3]. MATLAB/Simulink provides a convenient platform for modeling, simulating, and analyzing control systems, and thus is employed in this study.

This paper presents a detailed design, implementation, and simulation of a DC motor control system with a feedback mechanism, primarily focusing on speed and torque regulation using PID controllers.

2. Design Methodology

An application written in LabVIEW, GWiz, is used to access the measured signals and to set the desired motor voltage. The main user interaction with GWiz is through a virtual instrument (vi) named cRIO-9076_RT.vi, shown in Figure 3. This vi is customizable; you can add or modify controls and indicators to suit your needs. Files giving users a tutorial on LabVIEW, an overview of GWiz, and how to get started, are provided on LEARN.

2.1. Mathematical Modeling of DC Motor

The performance of a DC motor is governed by both electrical and mechanical equations. The equivalent circuit and free-body diagram help derive the following standard equations:

Electrical Equation:

V(t) = L di(t)/dt + Ri(t) + e_b(t)

Mechanical Equation:

T(t) = J dω(t)/dt + Bω(t)

Where:
– V(t): Applied voltage (V)
– i(t): Armature current (A)
– R: Armature resistance (Ohm)
– L: Armature inductance (H)
– e_b(t): Back EMF (V), e_b = K_e ω
– T(t): Torque (Nm), T = K_t i(t)
– ω(t): Angular velocity (rad/s)
– J: Moment of inertia (kg.m^2)
– B: Viscous friction constant (Nm.s)
– K_e, K_t: Motor constants

2.2. Block Diagram of Feedback Control System

The feedback control system consists of:
– DC Motor Plant
– PID Controller
– Speed/Torque Reference Input
– Feedback from the output (speed or torque)
– Comparator (Error computation)

This classic closed-loop system ensures that the output tracks the reference by minimizing the error signal.

Before attempting to control the ball and beam system, it is important to consider the control structure; that is, decide if a single control loop or an inner/outer-loop control structure is best, and considers what type of compensation is reasonable. As we will show later, the essential linearized ball and beam dynamics are summarized as follows:

where signals V(t) ,q(t) , f(t) , and y(t) (and some key geometric variables) are shown in Figure 4. Notice, among other details, the direction of measurement for the motor gear angle and for the ball position on the beam.

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The simplest control topology is a single feedback control loop shown in Figure 5, where the plant is treated as the cascade connection of (1), (2) and (3). Although it is possible to design the compensator C(s) such that the closed-loop system is stable, the triple integrator in the plant contributes o 270 phase lag to the loop gain making it difficult to obtain “good” closed-loop performance. Another practical difficulty with this setup is that it is not clear how one can ensure that the motor does not rotate so much as to damage the lever arm mechanism. To avoid damage, you must ensure that

An alternative control arrangement is shown in Figure 6. In this setup, two feedback loops are used. The purpose of the inner-loop is to control the motor gear angle position; controller ( ) 1 C s should be designed so that q(t) tracks the reference signal (t) qref . The outer-loop uses the inner feedback loop to control the ball position. From the point of view of controller ( ) 2 C s , the “plant” is composed of everything enclosed by the dotted box in Figure 6. Clearly the inner-loop must be designed before the outer-loop. We will also see that the inner/outer-loop control setup in Figure 6 avoids the two problems associated with the single loop control configuration in Figure 5.

2.3. Controller Design

PID controllers are used due to their robustness and ease of implementation:

u(t) = Kp e(t) + Ki ∫e(t)dt + Kd de(t)/dt

Where Kp, Ki, and Kd are proportional, integral, and derivative gains respectively.

The controller is tuned for optimal performance using trial-and-error or methods like Ziegler-Nichols [4].

3. MATLAB Simulation Design Work

3.1. Simulation Environment

The entire system is implemented in MATLAB Simulink. Components used include:
– Transfer Function blocks (for DC motor modeling)
– PID Controller block
– Scope (to monitor speed and torque)
– Step Input (as reference)

3.2. Modeling of DC Motor in Simulink

Parameters used:
– R = 1 Ohm
– L = 0.5 H
– Ke = Kt = 0.01
– J = 0.01
– B = 0.1

The electrical and mechanical equations are modeled as transfer functions in the s-domain:
G(s) = K / [(Js + B)(Ls + R) + K^2]

3.3. Speed Control Simulation

– A step input of 100 rad/s is applied.
– PID controller tuned to Kp = 1, Ki = 10, Kd = 0.01
– Simulation time: 5 seconds

Result: The motor speed reaches the reference in 1.2 seconds with negligible overshoot and steady-state error.

3.4. Torque Control Simulation

Torque control is implemented by regulating the current:
T = Kt i(t)

– A current controller is implemented using another PID loop.
– Reference current is derived from desired torque.

Result: The torque tracks the reference accurately, with a rise time of ~0.5 seconds.

3.5. Performance Metrics Evaluated:
– Rise Time
– Settling Time
– Overshoot
– Steady-state error

The feedback controller improves all metrics significantly compared to open-loop.

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4. Results and Discussion

The simulation results validate the efficiency of feedback control in enhancing the dynamic and steady-state response of the DC motor system. Key findings:
– Speed control achieved <2% steady-state error.
– Torque control had a rapid and stable response.
– PID tuning plays a critical role in system stability [5].

The feedback control system offers robustness against load disturbances and parameter variations [6].

Figure 7 presents the complete simulation model built in MATLAB Simulink for the DC motor control system. The model includes key blocks such as the DC motor plant, PID controller, summing junction, and scope output. Each element represents a critical part of the control loop, from reference signal input to error computation and motor actuation. The modular design facilitates real-time adjustments and detailed performance analysis. This model serves as the core environment for both speed and torque control implementations.

Figure 8 illustrates the time-domain output response of the DC motor system operating under closed-loop feedback control. It includes plots of system variables such as speed, torque, and possibly current, showing how the system tracks a desired reference input. The results emphasize the effectiveness of the feedback mechanism in reducing error and maintaining system stability. The graph confirms that the feedback loop quickly compensates for disturbances. Such outputs validate the reliability and robustness of the control strategy used.

Figure 9 displays the motor speed response over time when a step input is applied in a closed-loop system. The curve demonstrates a smooth transition from zero to the reference speed with minimal overshoot and a short rise time. The feedback PID controller adjusts the input voltage to ensure the motor reaches and maintains the desired speed. This figure is a critical proof of the control system’s precision. It highlights the ability of the designed model to stabilize motor dynamics efficiently.

Figure 10 shows the angular position (theta) of the DC motor as a function of time, derived by integrating the speed output. The graph represents the cumulative rotational displacement, essential in position control applications. A steadily increasing theta curve indicates consistent motor operation and speed tracking. The output confirms that the control system accurately follows motion profiles. This result further supports the effectiveness of the feedback-based controller in dynamic motor applications.

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5. Conclusion

A complete DC motor control system with feedback has been successfully designed and simulated in MATLAB/Simulink. The use of PID controllers ensures effective control of both speed and torque. The system achieves stability, rapid response, and low steady-state error, which are essential for industrial and automation applications [7]. The simulation results validate the benefits of implementing closed-loop feedback in improving system accuracy and robustness. The motor speed achieved the reference with minimal overshoot and rapid rise time. Torque control was equally efficient, demonstrating fast response and precision.

The mathematical modeling provided insights into the relationship between electrical and mechanical parameters of the motor, laying a foundation for controller design. The block diagram helped in understanding the feedback loop functionality. PID controller tuning proved to be critical in determining system performance. Proper tuning helped achieve optimal transient and steady-state characteristics. Moreover, performance metrics like rise time, settling time, and overshoot indicate that the feedback control system significantly outperforms an open-loop configuration. The results confirm that a well-tuned feedback control system is vital for maintaining operational reliability.

The project emphasizes the importance of feedback in electromechanical systems and how simulation tools like MATLAB/Simulink can streamline control design. Future work can explore modern control techniques such as fuzzy logic, neural networks, and model predictive control to further improve system adaptability and efficiency.

References

[1] Hughes, A. and Drury, B. “Electric Motors and Drives: Fundamentals, Types and Applications”, Newnes, 2019.

[2] Dorf, R.C. and Bishop, R.H., “Modern Control Systems”, Pearson, 2020.

[3] Ogata, K., “Modern Control Engineering”, Prentice Hall, 2010.

[4] Ziegler, J. G., and Nichols, N. B., “Optimum Settings for Automatic Controllers,” Trans. ASME, 1942.

[5] Nise, N.S., “Control Systems Engineering”, Wiley, 2021.

[6] Bolton, W., “Mechatronics: Electronic Control Systems in Mechanical and Electrical Engineering”, Pearson, 2015.

[7] Liu, J. et al., “Advanced PID Control Techniques: A Survey,” Control Engineering Practice, 2022.

[8] MATLAB Documentation, MathWorks. https://www.mathworks.com/help

[9] Khalil, H.K., “Nonlinear Systems”, Pearson, 2002.

[10] Franklin, G.F., Powell, J.D., and Emami-Naeini, A., “Feedback Control of Dynamic Systems”, Pearson, 2019.

You can download the Project files here: Download files now. (You must be logged in).

Keywords: Proportional-Integral-Derivative (PID), DC Motor Control System, Speed control, Torque Control, MATLAB Simulink

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