8. Synopsis
**Lectures**

__1. Basic notions of control theory (2 hours of lectures)__: The principle of control and description of control structures. Principles and differences of open and closed loop control. Functional diagrams, dataflow diagrams, conventions and standard signals and their nomenclature in a control loop. Static and dynamic characteristics of control loops, integrals of the error function. Classification of control systems.

__2. Modeling of dynamical systems (2 hours of lectures)__: Dynamical systems. State, and state space. Solution of the state equation of a continuous time, linear, time invariant (LTI) system, the exponential matrix, the transfer function, poles, and zeros. The consequences of a (invertible linear) coordinate transformation in the state space. Linearization around a setpoint. Models of some classes of physical systems including mechanical and thermal processes using energy preservation laws of physics.

__3. Analysis of continuous time linear control systems (4 hours of lectures)__: Description of single variable (SISO) linear transfers: ordinary differential equation, transfer function, Bode-plot, impulse response, step response, state equation. Transformations between descriptions. Fundamental interconnections of elements, open and closed loops. Elementary transfers; first and second order prototype systems: characteristics in the time and frequency domains. Relation between the dominant pole(s) and the dynamical characteristics of a transfer. Properties of the amplitude and phase plots of a general open loop transfer function, the calculation of the crossover frequency. Steady-state in linear control loops steady-state properties of reference tracking and disturbance rejection. Stability of control loops: BIBO stability definition, Hurwitz criterion, Nyquist criterion, Bode criterion, phase margin and crossover frequency.

__4. Synthesis of continuous time linear control systems in frequency domain (4 hours of lectures)__: The class of PID compensators, the filtered D term, Bode plots and pole-zero distribution of the compensators. Properties of the compensators. Setting the compensator parameters for a desired phase margin and steady-state behavior. Prototype examples of compensation with P, PD, PI, and PID controllers. Feedback compensation. Controller design for minimal error square integral. Root locus methods. Compensation of plants with time lag: compensation of an ideal time lag with an integrator.

__5. Analysis of discrete time linear control systems (2 hours of lectures)__: The Shannon law of sampling. Properties of hold elements. Signal propagation in a discrete time system in frequency domain and using state space description. Discrete time equivalent of a continuous time plant using a zero-order-hold circuit and an ideal sampler. Discrete time implementation of continuous time compensators: discrete time realization of integral and differential operators (approximations), step response equivalence.

__6. Synthesis of discrete time linear control systems (4 hours of lectures)__: Hardware and software realization of a PID controller using integrator anti-windup techniques. Dead-beat controller design to get finite impulse response in closed loop. The correction polynomial and the calculation of its coefficient. Design of two-degree-of-freedom controllers: the choice of the observer polynomial and the transfer function of the reference model, the steps of the design procedure to arrive to a Diophantine equation. Illustration with an example. Robustness of the two-degree-of-freedom controller scheme against parameter uncertainties.

__7. Continuous time control loop analysis and synthesis in state space (2 hours of lectures)__: Controllability and observability in continuous time linear systems. Conditions of full state controllability and observability. Pole placement using state feedback, the Ackermann formula. Design of full state observers, algebraic equivalence to the pole placement problem. Integral control and load estimator design.

__8. Discrete ____time control loop analysis and synthesis in state space (2 hours of lectures)__: Controllability, reachability, detectability and observability in discrete time linear systems and their conditions. Pole placement using state feedback, the Ackermann formula. Design of full state, actual observers, algebraic equivalence to the pole placement problem. Integral control and load estimator design.

__9. Discrete time system models and parameter identification methods (4 hours of lectures):__ Autoregressive (AR) and moving average (MA) processes, ARX and ARMAX models. Parameter identification of ARX models using LS methods. Parameter identification of the ARMAX model using numerical optimization and the quasi-Newton method. The services of the Identification toolbox of Matlab.

**Practice sessions**

Classroom and computer room practices are paired together. Students use Matlab and Simulink during computer room practices. Topics of the practice session pairs (a classroom and a computer room practice):

1.Introduction to Matlab, Control Systems Toolbox and Simulink. Features of the LTI view tool.

2. Analysis of control loops: simulation, stability, stability criteria, frequency and time domain features, their relations

3. Serial compensators: design with Matlab, features of the SISO design tool. Solution of the parameter equations using fsolve.

4. Discrete time controller design: discrete realization of a PID controller, two degrees of freedom controller design

5. State space controller design in continuous time, state feedback, state observer, load estimation and integral control

6. State space controller design in discrete time

7. identification from measured data using the services of the system identification toolbox