# Engineering

## ECM2105 - Control Engineering (2010)

MODULE TITLE CREDIT VALUE Control Engineering 15 ECM2105 Dr Mustafa Aziz (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS
DESCRIPTION - summary of the module content
AIMS - intentions of the module
To introduce students to the basic concepts of dynamics and supporting computational techniques. To introduce students to the concepts of feedback and stability. To expose students to standard control concepts and calculations by a detailed analysis of proportional, integral and derivative controls for first and second order systems models.
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
Note: List A comprises core outcomes that will be covered fully in lectures and must be achieved by all students to meet the minimum university requirement for progression. List B comprises outcomes that are EITHER more difficult to achieve OR are to be achieved by private study (or both). All outcomes will be assessed, and coverage of List B outcomes is essential for both BEng and MEng students. A: THRESHOLD LEVEL Review of concepts of Laplace transform; Laplace transform theorem; Inverse Laplace transformation; partial-fraction expansion; and solving linear, time-invariant differential equations. Derive differential equations of the simple physical systems, eg mechanical systems, electrical systems, and electromechanical systems. Obtain a small-signal linear approximation for non-linear control systems/components using a Taylor series expansion; derive the transfer function of the linear differential equation using Laplace transformation; develop block diagram models of systems of interconnected components using transfer function; given a block diagram, find the transfer function. Determine the unit-step time response, unit-ramp time response, and unit-impulse response of a first-order system and a second-order system, respectively: sketch their response diagrams. For the response of a second-order system, describe the three different cases: the underdamped, critically damped, and overdamped cases. Familiarise the performance index of a second-order system: e.g., Rise time, Peak time, Maximum overshoot, Settling time, etc; explain the relationship between poles and the responses. Compare open- and closed-loop systems; explain the advantages and disadvantages of a closed-loop system; discuss the effect of parameter variations; determine and analysis the transient response of a system; determine the steady-state error and the response to the disturbance and noise signals for the system; explain the improvement in the rejection of the disturbance and reduction of the steady-state error of the closed-loop system. Case Study - Speed control of a DC motor. Derive the differential equations using the physical laws. Derive the transfer function. Determine the step response of the system using open and close loop arrangements. Explain the stability and unstability of a physical system; discuss the relationship between the stability and the pole locations and the system; determine the system stability using Routh-Hurwitz stability criterion. Design a proportional (P) controller for a first-order and a second-order system respectively; discuss the problems of a high gain controller; explain the need of an integral (I) term to further improve the system performance; design a PI controller for a first-order system. Discuss the need of a derivative (D) controller to further improve the system performance; explain the functions of each term of a PID controller; design a PID controller for a first-order system. B: GOOD TO EXCELLENT Prove final value and initial value theorems. Derive the state variable equations of the physical systems. Discuss the difference between the linear and non-linear systems; explain the difficulty of solving the non-linear differential equations. Explain effects of zeros and additional poles; discuss the system type with respect to disturbance inputs. Determine the system sensitivity; discuss the extra cost of feedback control. Analyse the effect of introducing a proportional gain on the step response of the system. Discuss the stability versus parameter range; deal with the special cases when the standard Routh array cannot be formed. Design a PI controller of a second-order system. Discuss the difficulties to implement a D controller.
SYLLABUS PLAN - summary of the structure and academic content of the module
Mathematical Foundation - Complex Variable Concepts - Laplace Transform: Definition and Notation - Properties and Theorems of Laplace Transform - Inverse Laplace Transform and Partial Fraction Expansion - Using Laplace Transforms to Solve Differential Equations System Dynamics - Mechanical Systems - Electrical Systems - Electrical and Mechanical Systems - Linearisation of Nonlinear Systems Transfer Functions and Block Diagrams - Transfer Functions of Linear Systems - Block Diagrams - Multiple Inputs System Response - Response Analysis of First-Order Systems - Second-Order Systems - Sinusoidal Response of the System - Polar (Nyquist) Plot - Bode Diagrams Feedback Control Systems - Open and Closed-Loop Control Systems - Sensitivity of Control Systems to Parameter Variation - Disturbance Rejection - Transient Response - Steady-State Error - Case Study: Speed Control of a DC Motor - The Stability of Linear Feedback Systems - Three-Term PID Controller - Control of First-Order Systems - Proportional (P) Control of First-Order Systems - Integral (I) Control of First-Order Systems - PI Control of First-Order Systems - Derivative (D) Control - PD Control of Second-Order Systems - PID Control
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 30 70
DETAILS OF SUMMATIVE ASSESSMENT
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
RE-ASSESSMENT NOTES
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener