Calculating steady-state errors for control systems (Type 0, Type 1, Type 2; Step Input, Ramp Input, Parabolic Input)
Module 3 Testing
Theoretical questions
1 Main performance criteria of control systems (explain the essence of all criteria)
2 Performance parameters of control systems in the transient process
3 Effects of a third pole and a zero on the second-order system response
4 Assessment of damping ratio
5 The root methods to assess control systems performance indicators
6 Sensitivity of control systems to parameter variations
7 Error signal analysis
8 Steady-state errors of control systems
9 Disturbance rejection
10 Noise attenuation
11 Performance indices of control systems
12 Gain and phase margins of control systems
13 Assessing performance indicators using Bode diagram
14 Assessing stability indicators using Nichols diagrams
15 The oscillation indicator
16 Performance analysis using gain-frequency characteristics
17 System Bandwidth
18 The stability of control systems with time delays
19 THE ROOT LOCUS CONCEPT
20 Step 3: Locating of the poles — 
and zeros — 
on the s-plane
21 Step 4: Locating the segments of the real axis that are root loci.
22 Step 7: Locating asymptotes
23 Step 8: Defining the points where the root locus will cross the imaginary axis
24 Step 9: Defining the breakaway points from real axis
25 Step 10: Determine the angle of departure of the locus from a pole and the angle of arrival of the locus at a zero
26 PARAMETER DESIGN BY THE ROOT LOCUS METHOD
27 APPROACHES TO SYSTEM DESIGN
28 PHASE-LEAD NETWORK
29 PHASE-LAG NETWORK
30 PHASE-LEAD DESIGN USING THE BODE DIAGRAM
31 Compensator design by changing a system gain
32 SYSTEM DESIGN USING INTEGRATION NETWORKS (proportional plus integral (PI) controller)
33 Proportional plus derivative control (PD control)
34 Analytical design of PID controllers
35 System design using the Bode diagram, analytical methods and computer programs.
36 SYSTEMS WITH A PREFILTER
37 DESIGN FOR DEADBEAT RESPONSE
38 PID controller design
39 Phase lead controller design using the root locus method
40 Analytical design of a phase lead controller using the root locus method
41 Phase lag controller design using the root locus method
42 Analytical design of PID controller using the root locus method
Practical questions
1. Constructing Nyquist, Bode and Nichols diagrams and defining stability indicators for the following transfer functions:
1.1 
1.2 
1.3 
1.4 
1.5 
1.6 
1.7 
1.8 
1.9 
1.10 
1.11 
1.12 
1.13 
1.14 
1.15 
2. The construction of asymptotic gain-frequency characteristic for following transfer function:
3. Consider the following control system and define:
- the control system reaction to step input signal at K=20 and K=100
- the control system reaction to step disturbance input signal at K=20 and K=100
- how the change in damping ratio affects control system transient characteristics
4. Define the control system bandwidth
5. Define Impulse response characteristics for 2nd order control systems
6. Control system reaction to linear input (ramp) signal
6.Compare step response for second-order approximation of 3rd order control system
num1=[6]; den1=[1 6 11 6];
sys1=tf(num1,den1) %<— 
num2=[1.6]; den2=[1 2.594 1.6];
sys2=tf(num2,den2) %<— 
Calculating steady-state errors for control systems (Type 0, Type 1, Type 2; Step Input, Ramp Input, Parabolic Input)
8. Meeting steady-state error requirements
9.Analyzing the system sensitivity to the changes in its parameters.
10. Analyzing the system sensitivity to the changes in its parameters.
|
11.
Define steady-state error at unit step function and for 
and 
Draw graphically the system reaction to unit disturbance for various values of 
.
=0;10;100
; 
; 
|
12.Researching the properties of a control system with Transport Delay link depending on Controller gains:
13. Researching the behavior of this control system depending on the time delays of Transport Delay link.
13. Researching the behaviour of the following control system with input delay:
14.Researching the behaviour of the following control system with output delay:
14. Construct the root locus for the following transfer function
15. Construct the root locus for the following transfer function G(s)=K/[s(s^2+4s+13)]
16.Construct the root locus for the following transfer function G(s)=K(s+2)/[s(s+2)(s+5)]
17. Construct the root locus for the following transfer function
G(s)=K(s+2)(s^2+4s+8)/[s(s+1)(s ^2+0.7s+2)]
18. Controller design procedure for the rotor winder control system
19. Compensator design by changing gain constant
20.Researching control system’s step response characteristics depending on the change in the frequency which provides for the set Phase Margin value.
21. Researching phase lead and lag compensators
22. Researching the behavior of a control system with various gain values of P-controller
(K = 5, 10, 15)
23. Researching reference and disturbance behaviour of control systems with various controller types
