Analysis of Control System and Synthesis of Real Compensator
Курсовой проект - Компьютеры, программирование
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disp (Coefficient of proportional unit )=cos(theta)/mag% task 2.2
Results of the program:
Coefficient of proportional unit=
.2558
3) determine the gain of differential part of compensator ;
Program code:
disp (Coefficient of differentiated unit )=sin(theta)/(w*mag)% task 2.3
Results of the program:
Coefficient of differentiated unit=
.0133
4) plot Bode diagram of the PD-compensator.
Program code:
disp (Tf of compensation unit)=tf([Kp*t1+Kd Kp], [t1 1])% tf of compensation unit
(Tf of compensator)=Wc% tf of compensator(5)(Wcomp), grid on,(Compensator)% task 2.4
Results of the program:
Tf of compensation unitfunction:
.01323 s + 0.2558
.0001 s + 1of compensatorfunction:
.01323 s + 0.2558
.0001 s + 1
. 7
III. Analysis of compensated system:
)build in Simulink the compensated system;
Fig. 8
2)determine settling time and overshoot of the compensated system using transient process received in Simulink;
Fig. 9
time - 2.4; overshoot - 23.4%.
3) calculate the transfer function of the whole compensated system;
Program code:
disp (Tf of open-loop compensated system)= series (Wolun, Wcomp)(Tf of closed-loop compensated system)=feedback (Wolcomp, W5, - 1)% task 3.3
Results of the program:
Tf of open-loop compensated systemfunction:
.8334 s + 16.12
.0001 s^3 + 1.001 s^2 + 6 sof closed-loop compensated systemfunction:
.08334 s^2 + 0.7781 s + 16.12
e-005 s^4 + 0.1002 s^3 + 1.601 s^2 + 5.167 s + 16.12
4) 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;
Program code:
figure(7)(Wclcomp), grid on,on, step(Wclun),(Closed-loop compensated, Closed-loop uncompensated)% task 3.4
Results of the program:
. 10
5) check whether the system is stable or not using sufficient condition of stability;
Program code:
disp (Poles of closed-loop compensated system)(Wclcomp),(8)(Wclcomp), grid on% task 3.5
Results of the program:
Poles of closed-loop copmensated system=
.0e+003 *
.0000
.0130
.0015 + 0.0032i
.0015 - 0.0032i
. 11
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:
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=
.0e+006 *
.0100 -0.1601 -0.5167 -1.6115
.0000 0 0 0
0.0000 0 0
0 0.0000 0=
=
.0e+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 =
.0e+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.
References
uncompensated system phase
1.Dorf R.C., Bishop R.H. Modern Control Systems. - Pearson Education, Inc., Pearson Prentice Hall, 2008. - 1046 p.
2.Бессекерский В.А., Попов Е.П. Теория систем автоматического управления. - СПб.: Профессия, 2003. - 752 с.