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Mathematical foundations: Laplace transform and application to the solution of linear ordinary differential equations; elementary matrix theory; vector-matrix form of state equations. Zeta transform. |
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The aim of this course is to provide the students the main methodologies for the analysis and control of linear time invariant dynamical systems, either in the time or in the complex domain |
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Representation of Linear Time Invariant (LTI) systems
State-variable description of linear dynamic systems; state-transition matrix and equation; characteristic equation and eigenvalues; 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.
Frequency-domain plots
Polar plots; Bode plot; Nyquist plot; magnitude-versus-phase plot; gain and phase crossover points; minimum-phase and nonminimum-phase functions.
Structural analysis of control systems
Reachability and observability. Structural decompositions. Kalman decomposition
Stability of linear control systems
Internal stability and asymptotic stability; 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.
Time-domain analysis of control systems
Typical test signals for the time response of control systems; time-domain performance of continuous-data control systems: the steady-state response of a linear control system; the steady state error characterization; time-domain performance of control systems: transient response; transient response of a prototype second-order system. Attenuation and/or rejection of polynomial disturbances.
Eigenvalues assignment through state feedback and through output feedback
Frequency-domain design of control systems
design with the phase-lead controller; design with the phase-lag controller; design with lead-lag lag-lead controllers
Digital control system design
through discrete approximation of analog controller. |
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Richard C. Dorf and Robert H. Bishop
Modern Control Systems (eleventh edition) 2007 Prentice Hall |