Analysis of Control System and Synthesis of Real Compensator
The standard task
Variant 18
Topic: of Control System and Synthesis of Real Compensator.: transfer functions (table 1, 2, 3) and structure diagram (fig. 1, 2, 3) are given. It is necessary to. Analyze uncompensated system:
) calculate the transfer function of the whole uncompensated system :) without MATLAB ;) using MATLAB;
) define zeros and poles of obtained transfer function;
) plot the time responses for obtained transfer function; the responses should be produced in two different windows of one figure graphic object using command subplot ;
) determine settling time and overshoot of the uncompensated system;
) check whether the system is stable or not using Hurwitz criterion;
) check whether the system is stable or not using Nyquist criterion;
) if system is stable, determine the stability margins using Bode diagram;
) do the conversion from the transfer functions to state space;
) calculate the eigenvalues ​​of the uncompensated system;
10) calculate-norm of the uncompensated system .. Synthesize the real PD-compensator () which would guarantee desired phase margin at gain crossover frequency:
) calculate the phase shift of compensator at given frequency;
) determine the gain of proportional part of compensator;
) determine the gain of differential part of compensator;
) plot Bode diagram of the PD-compensator .. Analyze compensated system:
) build in Simulink the compensated system;
) determine settling time and overshoot of the compensated system using transient process received in Simulink;
) calculate the transfer function of the whole compensated system;
) plot the step response for uncompensated and compensated system; the responses should be produced in one window of figure graphic object using command hold on ;
) check whether the system is stable or not using sufficient condition of stability;
) if system is stable, determine the stability margins using Bode diagram;
) do the conversion from the transfer functions to state space;
) calculate the eigenvalues ​​of the compensated system;
) calculate-norm of the compensated system;
) do the conclusions.
Introduction
This term paper represents the analysis of control system and synthesis of real compensator. So here we will examine the uncompensated and compensate...
