Module 15 Bode Diagrams Plot Bode Diagrams of elemental TFs Draw Bode diagram of a open loop TF Bode diagrams
Modulusfrequency plot Phase angle plot
ζ＜-1 Amplitude
1.5 1 0.5 0 0
0＜ζ＜1
10
ζ=0
20
0.5
Time (sec.) ζ=1
1
5 ζ ＞1
10
15
2 Amplitude
1 Amplitude
1 Amplitude
1
0.5
0.5
0 0
10
20
30
0 0
5
10
15
0 0 5 1015202530354045
Time (sec.)
• 具有可控标准形的系统，一定是状态完全可控。 • 当A阵为对角阵且元素各异时，B阵不存在全零行，系统状态完全可控。
3. Determine the observability of system
• The system is observable if the rank of OT is n, the order of the system. • 具有可观测标准形的系统，一定是状态完全可观测。
Automatic Control Theory Review
Exam time: January, 2011 Exam place: C12
2010
本课程的两大基本内容
z
已知系统结构、参数， 对系统进行分析。

系统分析
z
已知系统性能要求，求系统 结构、参数，系统校正。
系统设计
分析系统的
¾ 稳定性 ¾ 稳态性能 ¾ 动态性能
Structure of the Textbook
Automatic control theory
Concepts, Principle Module 1 Maths base Module 2 Methods Module 3-25 Modern control theory Module 22-25 State-space Module 22-25 Models Module 22 Analysis Module 23 Design Module 24-25
Establish the state-space model Sketch the state-variable block diagram
Calculate the eigenvalues
M23. State space system response: Controllability and Observability 1. System stability 2. Determine the controllability of system • The system is controllable if the rank of CT is n, the order of the system.
Module 10-11 Rules for Plotting the Root Locus Apply these rules plot root locus analyze System performance
− 10
K = 0, 10, 25, 50, 100
Im
5i
Re
−5
Stability The range of K Transient response Steady state response
− 5i
Module 12-14 Frequency response Nyquist Diagrams, Nyquist Stability Criterion, and Nyquist Analysis Draw Nyquist diagram of a given TF system stability Nyquist stability criterion Concept of gain margin and phase margin The number of closedloop poles in righthand half s-plane
Module 6 Disturbance rejection, Velocity feedback Closed-loop feedback control velocity feedback reject disturbances improve the transient response ζ ↑⇒ σ % ↓, t s ↓ ωn
Knowing the desired poles Knowing the time-domain performance specifications
3. Plot the state-variable block diagram with state variable feedback.
M25. State-Space Observer Design
Module 4-5 Time domain response of second order systems Calculate time responses step response Time-domain performance specifications %Overshoot, rise time, peak time, settling time, steady state error.
¾ The Concept of the observer ¾ Observer design 1. Check the system observability Æ whether an observer may be used to estimate the state. 2. Calculate the observer gain vector K Æ locate the eigenvalues of the observer with respect to the desired poles of the system.
System poles ~ transient response
-1＜ζ＜0
ζ＜-1
0＜ζ＜1
ζ=0
ζ=1
ζ ＞1
ω n2 G ( s) = 2 2 s + 2ζω n s + ω n
Step Response
100 Amplitude 0 -100 -200 0
-1＜ζ＜0
6 Amplitude 4 2 0 0
the openloop transfer function
Nyquist diagram
(For minimum-phase system, the red arrow is right.)
Module 16 Bode Analysis, Stability, and Gain and Phase Margins Gain margin Bode plots phase margin
Module 7 Higher order systems
Root locus
Dominant poles
Poles placement in state space form
Module 8 System type and Steady-state errors Identify system type Calculate steadystate errors Determine the stability of systems
− 60 dB / dec
M22. State space system description: MIMO systems
Knowing Selecting State variables
the differential equation
the transfer function
the block diagram
e ss ( t ) = lim sE ( s ) s→ 0
error constant Kp, Kv, Ka ess including the input and disturbance
Module 9 Routh Method the concept of stability the stability condition of LTI systems
Analyze the system stability
Analyze the system time response
Module 19 & 20 Phase Lead, Phase Lag and Lead-lag Compensation gain compensation phase lead compensation phase lag compensation lead-lag compensation
Module 1 Introduction to Feedback Control draw a block diagram representation identify elements
the plant, controller, transducer(s), differencing junction, input, output, and forward and feedback paths.
被控对象 被控量
传感器(测量装置)
Module 2 Transfer Functions and Block Diagram Algebra Develop dynamic models Derive transfer function Module 3 First order systems First-order systems Poles and zeros Dominant poles Block diagram Simplify complex block diagrams