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Theoretical information:
There are two formulations of Nyquist criterion of stability depending on whether the open-loop system is stable or not stable.the open-loop system is stable, the closed loop system would be stable if the Nyquist plot of the open-loop system does not encircle the point with coordinates (-1, 0) at the complex plane.
If the open-loop system is unstable, the closed loop system would be stable if the Nyquist plot of the open-loop system encircles the point with coordinates (-1, 0) at the complex plane times, where is the number of roots in RHP, in the counter-clockwise direction when frequency changes from zero to infinity.
Operator nyquist (sys) plots the Nyquist response of an arbitrary LTI model sys.
Program code:
figure (3), nyquist (Wolun), grid on% task 1.6
Results of the program:
. 5
System is stable because Nyquist plot for the open-loop system doesn `t encircle point (-1; 0).
7) if system is stable, determine the stability margins using Bode diagram;
Theoretical information:
Stability margins
There is a special operator margin for calculating the stability margins in MatLab. Its syntax is
[Gm, Pm, Wcg, Wcp] = margin (sys) ,
where is gain margin, is phase margin, is frequency under which, is frequency under which. and are crossover frequencies.invoked without left-hand arguments, margin (sys) plots the open-loop Bode response with the gain and phase margins marked by vertical lines.
Program code:
figure (4), margin (Wolun), grid on, legend ('Uncompensated system')% task 1.7
Results of the program:
. 6
So, gain margin is equal to infinity and phase margin - 41.1 deg.
8) do the conversion from the transfer functions to state space;
Theoretical information:
State space description
Complete state space description of a continuous system with constant coefficients is the following:
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where is the input vector; is the output vector; is the state vector characterizing the system dynamics.
To create the conti...
