Control Engineering

Lectures: 

1. Basic concepts of control engineering (2 hours lecture): The concept of control, the sense-think-act paradigm. The principle of regulation and control, their comparison. Scheme of operation, block diagram, elements of the control loops, external and internal signals. Control loop performance: reference tracking, disturbance and noise rejection properties. Static and dynamic characteristics of control loops and error integrals. Classification of control loops. Modelling of some processes by applying physical laws (through examples). Setpoint linearization of nonlinear continuous-time state equations.

2. Analysis of continuous-time linear control loops in the frequency domain (4 hours lecture): Elementary connections, open loop, feedback loop, transfer functions between external and internal variables of the control loop. The loop gain and loop type, the steady state properties of the closed-loop. Approximation of transients with a dominant pole pair. Plotting the asymptotic amplitude characteristic of an open loop transfer function, determining the crossover frequency, and the bandwidth of the closed-loop system. Stability of control loops, zero-state and zero-input stability. Stability criteria: Nyquist criterion, Bode criterion, phase and gain crossover frequencies, stability margins.

3. Design of continuous-time linear controllers in the frequency domain (4 hours lecture): PID regulators: proportional, integral and ideal/approximated derivative terms and their combinations. Antiwindup solutions to prevent integrator saturation. Features of P/PI/PD/PID regulators. Tuning of PID controllers for required accuracy and specified phase margin using pole-zero cancellation strategies that maximize bandwidth and also consider the actuator signal limitation. Control of systems with time delay: characteristics and integrator-based compensation.

4. Analysis of discrete-time linear control loops (2 hours lecture): Shannon’s sampling law. The use of hold elements instead of an ideal low-pass filter, consequences on the stability (phase margin) of the control loop. The discrete-time equivalent of the plant and PID regulators in the case of the application of a zero-order hold element. Sampled implementation of analog compensators (PID controllers): approximations of differentiating and integrating operators, step response equivalence.

5. Design of discrete-time linear controls (4 hours lecture): Implementation of sampled PID controller. Control of systems with large time delay using the Smith predictor. The principle of deadbeat control, the properties of the transfer functions of the closed loop, and calulations using a correction polynomial. Design of two-degree freedom (2DOF) controller: the need to obtain good performance for reference tracking and disturbance rejection at the same time, the 2DOF controller structure, choice of the reference model and observation polynomial, design by solving diophantine equation, effect of parameter changes.

6. Analysis and synthesis of continuous-time control systems in state space (4 hours lecture): Controllability and observability in a continuous-time linear system, criteria for complete controllability and observability. Pole placement with state feedback, Ackermann formula. Design of a full-order state observer, algebraic similarity to the pole placement task. Dynamic extensions of state feedback: load estimation and integrating effect.

7. Analysis and synthesis of discrete-time control loops in state space (4 hours lecture): Availability, controllability, observability and reconstructionability of discrete-time systems. Algebraic similarities and differences compared to the continuous-time case. Pole placement and actual state observer design in discrete-time systems, integrating control and load estimation in discrete-time systems. Implementation issues of actual observers (prediction and correction phases).

8. On-off controllers (2 hours lecture): principle of operation of on-off or bang-bang controllers, switching strategies, boundary cycle, combining on-off controllers and linear regulators. 

9. Summary and outlook (2 hours lecture): systematic overview of concepts, design methods and their relationships presented during the semester. Some modern trends and recent achievements of control technology (based on examples, with illustrations that change from year to year). 

Practice sessions (each item listed is presented during two practice sessions):

1. Review of concepts of signals and systems, description of SISO LTI systems (state equation and transfer function), characteristics of first order and second order underdamped systems. Frequency and time domain responses (Nyquist curve, Bode diagram, step response, impulse response). Basic features and use of the Matlab development environment, tools to study SISO LTI systems with Control System Toolbox services, use of LTI viewer. Setpoint linearization.

2. Transfer functions and analysis of a control loop in the frequency domain. Calculation of transfer functions between external and internal signals in a closed loop. Parameterization of the open loop transfer function, loop gain and loop type, calculation of steady-state values. Application of stability criteria, determination of crossover frequency and phase margin. (Option: Hurwitz criterion with examples.)

3. Design of PID controllers for a given phase margin in continuous time. Manual PID design for simple (second order) plants. Set the required phase margin using the Bode diagram of the open loop. Calculation of the controller parameters by numerical solution (supported by Matlab) of a system of equations. 

4. Design of discrete-time controllers. Calculation of sampling times and difference equations of PID controllers designed in continuous time. Tuning of a two degrees of freedom controller (with and without integrator), calculations of the differential equations, simulation of a closed-loop circuit.

5. Controllability and observability criteria for continuous-time systems. Controller design in state space. Specification of the eigenvalues of the closed loop system based on the eigenvalues. Calculation of the gains of controller components: state feedback, observer, reference, load estimator and integrator. State-space control of unstable plant, study of the relationship between eigenvalues and the magnitude of actuator signals.

6. Using controllability and observability criteria for discrete-time systems. Design of state-space controllers in discrete time. Calculation of gains for controller components: state feedback, actual state observer, setpoint gains, load estimation and integral effect. 

7. Identification of the transfer function of the plant from measurements (with Matlab support) and model based controller design using a selected controller type. A systematic summary of Matlab features.