n="justify"> So the system is stable as all poles are negative.
6) if system is stable, determine the stability margins using Bode diagram;
Program code:
figure (9) (Wolcomp), grid on, ('Compensated system')% task 3.6
Results of the program:
В
Fig. 12
So gain margin is 17.1 dB and phase margin - 60 deg.
7) do the conversion from the transfer functions to state space;
Program code:
[n1, d1] = tfdata (Wclcomp, 'v'),
[A1, B1, C1, D1] = tf2ss (n1, d1)% task 3.7
Results of the program:
n1 =
0 -0.0833 0.7781 16.1154 =
.0000 0.1002 1.6006 5.1666 16.1154 =
.0 e +006 *
.0100 -0.1601 -0.5167 -1.6115
.0000 0 0 0
0.0000 0 0
0 0.0000 0 =
=
.0 e +006 *
-0.0083 0.0778 1.6115 =
8) calculate the eigenvalues ​​of the compensated system;
Program code:
cl_loop_eigen = eig (A1)% task 3.8
Results of the program:
cl_loop_eigen =
.0 e +003 *
.0000
.0130
.0015 + 0.0032i
.0015 - 0.0032i
9) calculate -norm of the compensated system;
Program code:
H2cl_loop = normh2 (A1, B1, C1, D1)% task 3.9
Results of the program:
H2cl_loop =
.4874
Conclusion
In this term paper we estimated properties of uncompensated dynamic system, synthesized real PD-compensator and as a result of including it in our system is changed. Also we estimated properties of compensated system and compared them with corresponding properties of uncompensated system. So we can say that overshoot is less and settling time of compensated system is more than in uncompensated system. br/>
References
uncompensated system phase
1. Dorf RC, Bishop RH Modern Control Systems. - Pearson Education, Inc., Pearson Prentice Hall, 2008. - 1046 p.
2. Бессекерскій В.А., Попов О.П. Теорія систем автоматичного керування. - СПб.: Професія, 2003. - 752 с.
