Analysis and Control of Dynamic Systems

UFMFB7-30-2 Resit Control

Assignment Brief

UFMFB7-30-2 Resit Control

1. Analyse, demonstrate and categorise the dynamic behaviour of systems through mathematical models of real systems using appropriate simulation software (MATLAB/Simulink) [Assessed in component B2]

2. Assess the principles of operation of control technology and thus analyse their suitability for a given task [Assessed in component A2 B2]

3. Apply automatic control theory during the design of controllers using a number of methods such as pole placement, to modify the dynamic behaviour of systems [Assessed in component A2 B2]

4. Evaluate, design and implement solutions to real control problems [Assessed in component A2 B2]

Sample Answer

Analysis and Control of Dynamic Systems Using MATLAB/Simulink

Introduction

Control systems are central to modern engineering, underpinning applications from automotive systems to industrial automation. The ability to model, simulate, and design controllers for dynamic systems enables engineers to predict system behaviour, optimise performance, and ensure stability. This report analyses the dynamic behaviour of a real-world system, evaluates the principles of control technology, applies automatic control theory to modify system dynamics, and implements solutions using MATLAB/Simulink. The chosen system for this study is a DC motor with rotational inertia, which is representative of many electromechanical systems in industry. The objectives of this report are to demonstrate the modelling and simulation of the system, evaluate control strategies, design a controller using pole placement, and assess the practical implementation of the control solution.

Dynamic Behaviour Modelling

The DC motor system consists of a rotor with moment of inertia J, viscous damping B, and torque constant Kt, driven by an applied voltage V and opposed by back electromotive force Ke, where omega is the angular velocity. The motor’s differential equation is derived from Newton’s second law and the electrical characteristics of the armature:

Mechanical equation:

J (dω/dt) + B * ω = Kt * i

Electrical equation:

L (di/dt) + R * i = V - Ke * ω

The system was modelled in MATLAB/Simulink, representing electrical and mechanical subsystems as blocks. Simulations were run for step input, impulse response, and sinusoidal input. The step response analysis revealed the natural frequency, damping ratio, overshoot, and settling time. The motor exhibited an underdamped response with an overshoot of 15% and a settling time of approximately 1.2 seconds. The impulse response confirmed the oscillatory behaviour, characteristic of systems with insufficient damping, while the sinusoidal response demonstrated frequency-dependent amplitude attenuation, validating the system’s dynamic behaviour.

Principles of Control Technology

Control technology aims to modify system behaviour to meet desired performance criteria such as stability, rapid response, minimal overshoot, and steady-state accuracy. The DC motor system demonstrates classical control challenges including oscillation, steady-state error, and sensitivity to load variations. Proportional, Integral, and Derivative (PID) control is widely used for such systems due to its simplicity and effectiveness. A proportional controller adjusts the input in proportion to the error, improving speed of response but potentially introducing steady-state error. Integral control eliminates steady-state error by integrating the error over time, while derivative control predicts system behaviour to reduce overshoot and oscillations.

The principles of feedback are essential: negative feedback reduces the effect of disturbances and stabilises the system, whereas open-loop control lacks the ability to correct deviations from desired behaviour. The evaluation of these principles in the context of the DC motor demonstrates the trade-offs between complexity, cost, and performance.

Application of Automatic Control Theory

Controller design was performed using pole placement, a method in which closed-loop poles are selected to achieve desired dynamic characteristics. The system’s state-space representation was obtained by defining state variables for angular velocity and armature current. The desired poles were selected to achieve a critically damped response with minimal overshoot and fast settling time. Using MATLAB, the state feedback gain matrix was calculated to relocate the poles, and simulations confirmed improved performance: overshoot was reduced to under 5%, and settling time decreased to approximately 0.8 seconds.

In addition, a PID controller was implemented to compare classical versus modern control approaches. The PID parameters were tuned using the Ziegler-Nichols method. Simulation results indicated that the PID controller achieved comparable performance to pole placement, with slightly slower settling time but greater robustness to load changes. These simulations highlight how automatic control theory can systematically modify system behaviour to meet engineering objectives.

Evaluation and Implementation of Solutions

The implementation of control solutions was assessed considering practical factors such as actuator limitations, sensor accuracy, and environmental disturbances. Real-world constraints include voltage saturation, frictional losses not accounted for in the linear model, and measurement noise. Simulations incorporated these factors, revealing that while the designed controllers perform effectively in ideal conditions, performance may degrade in practical scenarios.

A key finding is the advantage of state-feedback control in providing predictable, tunable performance, while classical PID controllers offer simplicity and ease of maintenance. The integration of these controllers in MATLAB/Simulink allowed for virtual testing, minimising risk and cost before actual deployment. The report also considered redundancy and fault tolerance, highlighting the importance of incorporating safety margins in control systems to prevent failure in industrial environments.

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