The course offers undergraduate students a rather broad view on Automatic Control methodologies and techniques for feedback linear systems.
It starts from the modeling problem using Laplace domain transfer functions and time domain State Variables, then shows the techniques to gain an inside view to the system structure (Kalman decomposition) and stability and to analyze the system performances both at steady state and during transients. Basic design technics are then introduced and finally the methodologies for the implementation of a control devices by a computer (i.e. as a discrete-time system) is presented.
Representation of Linear Time Invariant (LTI) systems
State-variable description of linear dynamic systems; state-transition matrix and equation; characteristic equation and eigenvalues.
Analysis in the time domain for discrete time and continuous time systems: free modes, eccitability and observability; free modes in the unforced evolution; free modes in the forced evolution.
Analysis in the complex domain for discrete time and continuous time systems: computation of the mathematical model; computation of the forced response.
The steady state response: existence conditions for periodic inputs and polynomial inputs. Computation of the state response for periodic/polynomial inputs.
Realization theory: minimal realizations; canonical realizations; Gilbert method.
Structural properties of linear time invariant systems : definitions of reachability and observability. Reachability and observability decompositions; Kalman decomposition.
Eigenvalues assignment and state reconstruction.
Decomposition of transfer functions. Impulse response and transfer functions of linear systems.
Mathematical modeling of physical systems
Electric networks, mechanical systems, thermal systems, hydraulic systems. DC motors and operational amplifiers in control systems.
Polar plots; bode plot; Nyquist plot; magnitude-versus-phase plot; gain and phase crossover points; minimum-phase and nonminimum-phase functions.
Stability of linear control systems
Bounded-input bounded-output stability and zero-input stability of continuous-data systems; methods of determining stability of linear continuous-data systems.
Frequency-domain analysis of control systems
Resonant peak, frequency peak and bandwidth of the prototype 2n order system; Nyquist stability criterion; relative stability: gain margin and phase margin; stability analysis with the Bode plot and with the gain-phase plot; the Nichols chart; attenuation and rejection of sinusoidal disturbances; sensitivity studies in the frequency domain.
Note: The students that have already passed the exam of "Control System Design" in the previous academic years have to study only the underlined subjects to complete this exam.
Ahmed El Garhy
- Helwan University (Helwan, Cairo - Egypt)
- Politecnico di Torino (Torino - Italy)