preparation exercises, pt.2, 2017
collected: Jakub Mo˙zaryn, PhD, Eng.
June 16, 2017
Exercise 1
For the block diagram shown in Fig. 1, determine the gain of the proportional controller to meet the following static accuracy requirements:
1. calculate gain value of the proportional controller to meet ewst.(s) <
10%wst for z(s) = const,
2. which values of the gain value of the proportional controller ensure stabil- ity of the system?
3. draw static characteristics of the system.
In the the input of the element described with the following transfer function
G(s) = 0.1s + 1
0.5s(0.2s + 2)2(0.001s + 0.1) (1) there is given signal
x(t) = sin t (2)
1. sketch by hand Bode plots of the system,
2. determine approximate values of gain and phase margins, 3. sketch by hand static characteristics,
4. sketch by hand Nyquist plot.
Exercise 4
Chect the stability of the system given in Fig. 2. If the system is stable, determine gain and phase margins - give approximate values.
Figure 2: Block diagram for Ex. 3.
2
For the system in Fig. 3 determine the value of the proportional gain k of the PI controller(, when (Ti= 5[s]), to meet the following requirements:
1. z = const, 2. ewst.≤ 5%wst.
Additionally sketch static characteristics for all system inputs.
Figure 3: Block diagram for Ex. 5.
For the system in Fig. 4 determine the value of the proportional gain k of the PD controller (Td= 5[s]), to meet the following requirements:
1. w = const, 2. ezst.≤ 3%zst.
Additionally sketch static characteristics for all inputs of the system.
Figure 4: Block diagram for Ex. 6.
4
Calculate the values of the proportional gain kp of the PD controller in single loop control system given in Fig. 5, to meet the following requirements:
1. ∆L = 6dB, 2. ∆φ = 45◦.
Time constant of the differential part of the controller is equal to Td = 2[s].
Additionally sketch static characteristics for all inputs of the system.
Figure 5: Block diagram for Ex. 7.
