Dynamic Systems and Control

The course is devoted to basics of automatic control, including modeling and understanding dynamics of systems. Main topics covered: logical control and PLC controller, structure of the feedback loop, building mathematical models of dynamic systems, linearization, analysis of dynamic systems in (continuous) time domain and in complex variable domain, transfer functions, static errors in feedback systems, Hurwitz stability criterion, Nyquist and Bode plots, Nyquist stability criterion, stability margins, linear compensator design in feedback loops, PID tuning rules, digital implementation of continuous-time control algorithms.

Lecture contents

• Introduction (2h): Role and goals of automatic control. Basic
  control structures, fundamental role of feedback, examples. Logical
  open-loop control, continuous control, regulatory feedback control. An
  example of a decision support system. Brief history.


• Controllers, types of industrial feedback control (4h):
  Industrial control hardware. Programmable logical controller (PLC):
  architecture, principle of operation. Basic structure of feedback
  control. Continuous control, on-off control, three-positions relay
  control, examples.


• Modeling of dynamical objects (4h): Theoretical and empirical
  models, modeling by differential and difference equations, examples,
  role of identification. Equilibrium points, static characteristics,
  linearization of nonlinear models.


• Analysis of linear dynamic models in time domain (3h): Impulse
  and step responses, convolution, general solution to linear dynamic
  state equations, stability of dynamic systems.


• Analysis of linear dynamic models in complex variable domain
  (3h): Laplace transform, transfer function. Basic linear dynamic
  models. Transformation of block structures, transfer functions of
  structured systems. Hurwitz stability criterion.


• Static errors in feedback systems (3h): Static errors for static
  (type zero) systems, influence of feedback on tracking accuracy and
  disturbance attenuation. Static errors in type I and type II feedback
  systems with integrators, influence of integration in the plant and in
  the controller.


• Analysis and correction of feedback systems in frequency domain
  (6h): Nyquist plot, Bode plots, plots for basic linear dynamic systems.
  Nyquist stability criterion, amplitude and phase margins. Design of a
  servomechanism-type feedback system.


• PID control (3h): Goals of process control. Structures and
  properties of PID controllers. Process modeling for PID control, PID
  tuning methods. Cascade and feedback-feedforward control structures.
  Model-based predictive control.


• Digital implementation of control algorithms (2h): Design methods
  for control loops with digital controllers. Discrete (Z) transform.
  Emulation method, discretization of continuous algorithms. Discrete PID
  algorithm. Choice of sampling interval.

• Modeling of dynamic systems. Equilibrium points. Static
  characteristics.


• Static errors in feedback systems, stability (Hurwitz criterion).


• Test 1.


• Nyquist and Bode plots. Nyquist stability criterion, gain and
  phase margins.


• Design of compensators for feedback control (servomechanism
  design).


• PID tuning. Digital implementation of continuous controllers.


• Test 2.

1. Digital Open-loop Control


2. PLC Control


3. PID feedback Control


4. Servomechanism Control


5. Human-Machine Interface (SCADA)

Maximum score for the lab exercises is 40 points.

Maximum score for each of the tests is 30 points.

The final result is based on the following pattern:

A: 87-100 points

B+: 78-86 points

B: 69-77 points

C+: 50-68 points

C: 51-59 points

D: 0 -50 points