1Introduction to Control Systems
102Solved Example:: Practice Problem:
21.1 What is a Control System?
1035.3 Routh-Hurwitz Criterion
3Solved Example:: Practice Problem:
104Solved Example:
41.2 Types of Control Systems
105Practice Problem:: Solving Examples and Practice Problems:
5Solved Example:: Practice Problem:
1065.4 Stable, Unstable, and Marginally Stable Systems
61.3 Importance of Control Systems
1071. Stable Systems:
7Solved Example:: Practice Problem:
108Properties of Stable Systems:
81.4 Open-Loop and Closed-Loop Control Systems
1092. Unstable Systems:: Properties of Unstable Systems:
9Open-Loop Control Systems:
1103. Marginally Stable Systems:
10Closed-Loop Control Systems:
111Properties of Marginally Stable Systems:
11Solved Example:: Practice Problem:
112Solved Example:: Practice Problem:
121.5 Examples of Control Systems
1135.5 Stability of Time-Varying Systems
131.6 Mathematical Modeling of Control Systems
1141. Lyapunov Stability Theory for Time-Varying Systems:
14Differential Equation Modeling:
1152. Floquet Theory:
15Transfer Function Modeling:
1163. Theory of Linear Periodic Systems:
16State-Space Modeling:
117Solved Example:: Practice Problem:
17Linearization of Nonlinear Systems:
1185.6 Stability in the State-Space
18Solved Example:: Practice Problem:
1191. Stability Conditions in the State-Space:
191.7 Linearization of Nonlinear Systems
1202. Lyapunov Equation:
20Introducing the following notation:
1213. Controllability and Observability:
21Solved Example:
122Solved Example:: Practice Problem:
22Practice Problem Solutions:: Conclusion
1235.7 Describing Function Analysis
23Mathematical Preliminaries
124Solved Example:
242.1 Matrices and Matrix Operations
125Practice Problem:
25Definition of a Matrix:
126Solving Examples and Practice Problems:: Conclusion
26Types of Matrices:
127Linear Feedback Control Systems
27Matrix Operations:
1286.1 Introduction to Feedback Control
28Properties of Matrix Operations:: Practice Problems:
129Solved Example:: Practice Problem:
292.2 Determinants
1306.2 State Feedback Control
30Definition of a Determinant:
131Solved Example:: Practice Problem:
31Properties of Determinants:
1326.3 Pole Placement
32Inverse of a Matrix:
133Pole placement offers several advantages, including:: Practice Problem:
33Solved Example:: Practice Problems:
1346.4 Ackermann’s Formula
342.3 Eigenvalues and Eigenvectors
135Solved Example:: Practice Problem:
35Properties of Eigenvalues and Eigenvectors:
1366.5 Output Feedback Control
36Solved Example:: Practice Problems:
137Solved Example:: Practice Problem:
372.4 Vector Spaces
1386.6 Observers
38Definition of a Vector Space:
139Solved Example:: Practice Problem:
39Subspaces:
1406.7 Separation Principle
40Linear Independence and Basis:
141Solved Example:
41Dimension of a Vector Space:
142Practice Problem:: Conclusion
42Solved Example:: Practice Problem:
143Transfer Function Representation
432.5 Linear Transformations
1447.1 Introduction to Transfer Functions: Practice Problems:
44Definition of a Linear Transformation:
1457.2 Transfer Functions of Linear Time-Invariant (LTI) Systems: Practice Problems:
45Matrix Representation of Linear Transformations:
1467.3 Poles and Zeros
46Properties of Linear Transformations:
147Poles:
47Kernel and Range of a Linear Transformation:
148Zeros:: Practice Problems:
48Eigenvalues and Eigenvectors of Linear Transformations:
1497.4 Block Diagram Algebra
49Solved Example:: Practice Problems:
150Series Connection:
502.6 Quadratic Forms
151Parallel Connection:
51Definition of a Quadratic Form:
152Feedback Connection:
52Properties of Quadratic Forms:
153Solved Example:: Practice Problem:
53Applications of Quadratic Forms:
1547.5 Signal Flow Graphs
54Solved Example:: Practice Problems:
155Solved Example:: Practice Problem:
552.7 Complex Numbers and Functions
1567.6 Mason’s Gain Formula
56Complex Numbers:
157Solved Example:: Practice Problem:
57Complex Functions:
1587.7 Sensitivity and Robustness
58Solved Example:
159Sensitivity Analysis:
59Practice Problems:: Conclusion
160Robustness:
60State–Space Representation
161Solved Example:
613.1 Introduction to State-Space Models
162Practice Problem:: Conclusion
623.2 State Equations
163Time–Domain Analysis
633.2.1 Continuous-Time State Equations
1648.1 Time Response of First-Order Systems
643.2.2 Discrete-Time State Equations: 3.2.3 Properties of State Equations
165Solved Example:: Practice Problem:
653.3 Output Equations
1668.2 Time Response of Second-Order Systems
663.3.1 Continuous-Time Output Equations
167Solved Example:: Practice Problem:
673.3.2 Discrete-Time Output Equations: 3.3.3 Properties of Output Equations
1688.3 Step Response
683.4 State-Space Representation of Linear Time-Invariant (LTI) Systems
169Solved Example:: Practice Problem:
693.4.1 Continuous-Time LTI Systems
1708.4 Ramp Response
703.4.2 Discrete-Time LTI Systems: 3.4.3 Properties of State-Space Representations
171Solved Example:: Practice Problem:
713.5 Controllability and Observability
1728.5 Impulse Response
723.5.1 Controllability: 3.5.2 Observability
173Solved Example:: Practice Problem:
733.6 Canonical Forms
1748.6 Performance Specifications
743.6.1 Controller Canonical Form: 3.6.2 Observer Canonical Form
175Solved Example:: Practice Problem:
753.7 State-Space Realization from Transfer Functions
1768.7 Steady-State Errors
763.7.1 State-Space Realization for SISO Systems
177Solved Example:: Conclusion
773.7.2 State-Space Realization for MIMO Systems: Conclusion
178Frequency–Domain Analysis
78Solution of State Equations
1799.1 Introduction to Frequency Response
794.1 Homogeneous State Equations
1809.2 Bode Plots
804.1.1 Continuous-Time Homogeneous State Equations
181Magnitude Plot:: Phase Plot:
814.1.2 Discrete-Time Homogeneous State Equations: 4.1.3 Properties of Homogeneous State Equations
1829.3 Nyquist Plots
824.2 Non-Homogeneous State Equations
183Solved Examples and Practice Problems:
834.2.1 Continuous-Time Non-Homogeneous State Equations: 4.2.2 Discrete-Time Non-Homogeneous State Equations
184Example 1: Bode Plot Analysis
844.3 Matrix Exponential
185Example 2: Nyquist Plot Analysis
854.3.1 Definition and Properties: 4.3.2 Computation of Matrix Exponential
186Practice Problems:
864.4 Transition Matrix
187Practice Problem 1: Bode Plot Analysis
874.4.1 Continuous-Time Transition Matrix
188Practice Problem 2: Nyquist Plot Analysis: Practice Problem 3: Compensator Design Using Bode Plot Shaping
884.4.2 Discrete-Time Transition Matrix: 4.4.3 Applications of Transition Matrices
1899.4 Gain and Phase Margins
894.5 Impulse Response
190Gain Margin:
904.5.1 Continuous-Time Impulse Response
191Phase Margin:
914.5.2 Discrete-Time Impulse Response: 4.5.3 Properties and Applications of Impulse Response
192Solved Example:: Practice Problem:
924.6 Zero-Input Response
1939.5 Nichols Charts
934.6.1 Continuous-Time Zero-Input Response
194Stability Analysis:
944.6.2 Discrete-Time Zero-Input Response: 4.6.3 Properties and Applications of Zero-Input Response
195Gain and Phase Margins:
954.7 Zero-State Response
196Compensator Design:
964.7.1 Continuous-Time Zero-State Response
197Solved Example:: Practice Problem:
974.7.2 Discrete-Time Zero-State Response: 4.7.3 Properties and Applications of Zero-State Response
1989.6 Frequency Response Shaping
98Stability of Linear Systems
199Solved Example:
995.1 Introduction to Stability
200Practice Problem:: Conclusion
100Solved Example:: Practice Problem:
201Glossary
1015.2 Lyapunov Stability
202Index
