**3.4.3 Systems with 1st order integrator**

By testing the sine-wave method on benchmark systems with 1st order integrator, the B-parabolas in Fig. 14 – 16 were obtained (for Cartesian product Mj×nk of sets (31) and (32), j=1...8, k=1...6 and three various ratios Ti/Td: =4, 8 and 12).

PID Controller Design for Specified Performance 25

Dependencies max=f(M,n), for systems with integrator, =4 Dependencies τs=f(M,n), for systems with integrator, =4

Fig. 14. B-parabolas: a) ηmax=f(M,n); b) τs=cts=f(M,n) for systems with integrator, =4

Fig. 15. B-parabolas: a) ηmax=f(M,n); b) τs=cts=f(M,n) for systems with integrator, =8

n =0,2<sup>c</sup> n =0,35<sup>c</sup> n =0,5<sup>c</sup> n =0,65<sup>c</sup> n =0,8<sup>c</sup> n =0,95<sup>c</sup>


n =0,2<sup>c</sup> n =0,35<sup>c</sup> n =0,5<sup>c</sup> n =0,65<sup>c</sup> n =0,8<sup>c</sup> n =0,95<sup>c</sup>

n =0,2<sup>c</sup> n =0,35<sup>c</sup> n =0,5<sup>c</sup> n =0,65<sup>c</sup> n =0,8<sup>c</sup> n =0,95<sup>c</sup>

<sup>45</sup> <sup>g</sup>

n =0,2<sup>c</sup> n =0,35<sup>c</sup> n =0,5<sup>c</sup> n =0,65<sup>c</sup> n =0,8<sup>c</sup> n =0,95<sup>c</sup>

Závislost reg=f(M) pre rôzne <sup>n</sup>

<sup>45</sup> reg <sup>M</sup> <sup>n</sup>

n =0,2<sup>c</sup> n =0,35<sup>c</sup> n =0,5<sup>c</sup> n =0,65<sup>c</sup> n =0,8<sup>c</sup> n =0,95<sup>c</sup>

<sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>5</sup>

Phase margin M [°]

n =0,2<sup>c</sup> n =0,35<sup>c</sup> n =0,5<sup>c</sup> n =0,65<sup>c</sup> n =0,8<sup>c</sup> n =0,95<sup>c</sup> - astatické systémy, =8

<sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>5</sup>

Phase margin M [°]

Fig. 16. B-parabolas: a) ηmax=f(M,n); b) τs=cts=f(M,n) for systems with integrator, =12

<sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>0</sup>

<sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>0</sup>

Phase margin M [°]

Závislost max=f(M) pre rôzne <sup>n</sup>

<sup>90</sup> max <sup>M</sup> <sup>n</sup>

<sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>0</sup>

Phase margin M [°]

Phase margin M [°]

Maximum overshoot max [%]

Maximum overshoot max [%]

Maximum overshoot max [%]

Relative settling time s=ct

s [-]

Dependencies max=f(M,n), for systems with integrator, =12 Dependencies τs=f(M,n), for systems with integrator, =12

Relative settling time s=ct

s [-]

Dependencies max=f(M,n), for systems with integrator, =8 Dependencies τs=f(M,n), for systems with integrator, =8

Relative settling time s=ct

s [-]

<sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>5</sup>

Phase margin M [°]
