# Introduction to the Control of Electric Drives

Timetable

Day 1

 Time Topic Description 09:00 1. Review of DC motor model. (5s)  (4.3 min/slide) A review of the DC motor and its components is given. This is followed by a derivation of its model in the form of interconnected linear differential equations. 2. Review of Background Theory, Dynamical Systems, Linearity and Laplace transforms (6s)  (4.3 min/slide) First some common control system terminology is reviewed. Then the properties of dynamical systems relevant to control system design are discussed. The Laplace transform is reviewed. 3. Review of Transfer Function and Block Diagram Models (10s) (4.3 min/slide) The application of the Laplace transform to form transfer function and block diagram models of linear, time invariant plants is reviewed, exemplified using the DC motor model of Topic 1. This is used to derive transfer functions between the variables. These transfer functions are then used to form a block diagram model of the DC motor. 10:30 Simulation 1 (30 min) DC Motor Models 11:00 Coffee break. 11:15 4. Review of Background Theory: Dynamic Character and Modes (8s) (4.4 min/slide) Analysis of the dynamic character of a system in terms of its modes and pole locations is reviewed. 5. Model Order Reduction (16s) (4.4 min/slide) Three methods are presented for obtaining simpler plant models for control system design, exemplified using the DC motor model of Topic 1. The first method entails analysis of the modes via partial fraction expansion of the transfer function to determine modes that can be ignored due to fast decay of their impulse responses. The second method entails comparison of the intrinsic dynamics of the physical components of a plant, illustrated by ignoring the electrical time constant of the DC motor. The third method is specific to electric drives, consisting of the introduction of a hysteresis current control loop using power electronics to eliminate the dynamic lag associated with inductive circuits. 13:00 Buffet lunch Opportunity for informal discussion and feedback. Time Topic Description 14:00 Simulation 2 (60 min) a)   Model order reduction by elimination of Fast Component Dynamics b)  Model Order Reduction by Cascade Control 15:00 6. Traditional Controllers: Model Based Design: General (7s) (4.3 min/slide) First the traditional PID controller and the purposes of the three terms are reviewed. Then a proportional controller is applied to the reduced order model of the DC motor for speed control and the closed loop transfer function derived. This is used to demonstrate the design of first order linear control systems to achieve a specified settling time, in contrast to gain adjustment by trial and error. Then the steady state error limitations with a constant external load torque are demonstrated, leading to the introduction of an integral term. At this juncture, Mason’s formula for transfer function derivation is presented for use directly with linear time invariant (LTI) control system block diagrams to avoid having to convert them to signal flow graphs. Then this is used to attain prescribed undamped natural frequency and damping ratio for the second order speed control system resulting from use of the PI controller.  Then a short derivation of the Dodds settling time formula for LTI systems of arbitrary order with coincident closed loop poles is given in preparation for the design of control systems of third and higher order. 15:30 Coffee break 15:45 6. Traditional Controllers: Model Based Design: Speed Control Part 1 (17s) (4.4 min/slide) The settling time formula for second order underdamped linear systems is applied to the speed control system using the PI controller. The zero introduced by the PI controller and its potential effect of causing a single overshoot of the step response, despite real closed loop poles, are demonstrated. The related IP controller that eliminates the zero is then introduced and designed. 17:00 End of day one.

Day 2

Day 3

Delivery Methods

The lectures will be supported by an animated PowerPoint presentation designed for easy assimilation of the concepts. The attendees will be stimulated throughout the course by being involved through discussion, being encouraged to ask questions at any point and also to answer questions posed to them as a group. Most topics will be followed by simulation sessions in which the attendees carry out Matlab-Simulink simulations to reinforce their understanding. Individual attention will be available to provide guidance needed by any attendee as and when necessary while working through the simulations.

The attendees will also be provided with an electronic copy of the tutor’s textbook ‘Feedback Control: Linear, Nonlinear and Robust Techniques and Design with Industrial Applications’, Springer 2015, ISBN 978-1-4471-6674-0’ that serves as a course handbook and may subsequently be used as a reference aiding project development.