Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Ordinary Differential Equations -- 1.1 Introduction -- 1.2 Homogeneous ODE with Constant Coefficients -- 1.2.1 General Solution -- CASE 1: REAL AND NONREPEATED ROOTS -- CASE 2: COMPLEX ROOTS -- CASE 3: REPEATED REAL ROOTS -- CASE 4: REPEATED COMPLEX ROOTS -- 1.2.2 Multiple Roots of… -- 1.2.3 Determination of Coefficients -- 1.3 Nonhomogeneous ODE with Constant Coefficients -- 1.3.1 General Solution -- 1.3.2 Particular Solution -- 1.4 Coupled Ordinary Differential Equations -- 1.5 Concluding Remarks -- 1.6 Problems -- BIBLIOGRAPHY -- 2 Elementary Matrix Algebra -- 2.1 Introduction -- 2.2 Vectors and Matrices -- 2.3 Basic Matrix Operations -- MATRIX ADDITION -- MATRIX MULTIPLICATION -- MATRIX TRANSPOSE -- MATRIX COMPLEX-CONJUGATE TRANSPOSE -- MATRIX TRACE -- INNER PRODUCT -- OUTER PRODUCT -- 2.4 Special Matrices -- 2.5 Determinants and Matrix Inverse -- MATRIX INVERSION LEMMA -- 2.6 Subspaces and Rank -- 2.7 Quadratic Form of a Matrix -- 2.8 Matrix Functions -- 2.9 Solving Linear Algebraic Equations -- 2.10 Eigenvalues and Eigenvectors -- 2.11 Diagonalization of a Matrix -- 2.12 Singular-Value Decomposition -- 2.12.1 Basic Equations -- 2.12.2 Some Areas of Application -- EFFECTIVE RANK AND CONDITIONED NUMBER -- FOUR FUNDAMENTAL SUBSPACES -- LEAST SQUARES AND PSEUDOINVERSE -- 2.13 Homogeneous First-Order Matrix Differential Equations -- REAL AND DISTINCT EIGENVALUES -- COMPLEX-CONJUGATE PAIRS OF EIGENVALUES -- REPEATED EIGENVALUES -- 2.14 Matrix Exponential -- 2.15 Nonhomogeneous First-Order Matrix Differential Equations -- METHOD OF UNDETERMINED COEFFICIENTS -- METHOD OF UNCOUPLING THE VARIABLES BY DIAGONALIZATION -- METHOD OF MATRIX EXPONENTIAL -- 2.16 Concluding Remarks -- 2.17 Problems -- BIBLIOGRAPHY -- 3 Modeling Techniques -- 3.1 Introduction.

3.2 Newton's Three Fundamental Laws -- FIRST LAW -- SECOND LAW -- THIRD LAW -- 3.3 D'Alembert's Principle -- 3.4 Principle of Virtual Work -- 3.5 Hamilton's Principle -- 3.6 Lagrange's Equations -- 3.6.1 Rayleigh's Dissipation Function -- 3.6.2 Constraint Equations -- 3.7 Gibbs-Appell Equations -- 3.8 Kane's Equations -- 3.9 Concluding Remarks -- 3.10 Problems -- BIBLIOGRAPHY -- 4 Finite-Element Method -- 4.1 Introduction -- 4.2 Uniform Beam Element -- 4.2.1 Interpolation Functions -- 4.2.2 Matrix Equation of Motion for an Element -- 4.2.3 Boundary Conditions -- 4.3 Element Assembly -- 4.3.1 Combined Matrix Equations of Motion -- 4.3.2 Constraint Equations -- 4.3.3 Assembled Matrix Equations of Motion -- 4.4 Truss Structures -- 4.4.1 Truss Element: Longitudinal Motion -- 4.4.2 Truss Element: Rigid-Body Motion -- 4.4.3 Coordinate Transformation -- 4.5 Energy Method for Element Assembly -- 4.6 Concluding Remarks -- 4.7 Problems -- BIBLIOGRAPHY -- 5 Response of Dynamic Systems -- 5.1 Introduction -- 5.2 Single Degree of Freedom -- 5.2.1 First-Order Systems -- COMPLEX-VARIABLE APPROACH -- FREQUENCY-RESPONSE FUNCTION -- 5.2.2 Second-Order Systems -- 5.3 Two-Degrees-of-Freedom Systems -- RESPONSE TO HARMONIC EXCITATION -- 5.4 Multiple-Degrees-of-Freedom Systems -- 5.5 Bending Vibration of Beams -- FREQUENCY EQUATION -- NATURAL MODES (MODE SHAPES) -- MODAL COORDINATES -- FORCED BENDING RESPONSE OF UNIFORM BEAMS -- 5.6 Concluding Remarks -- 5.7 Problems -- BIBLIOGRAPHY -- 6 Virtual Passive Controllers -- 6.1 Introduction -- 6.2 Direct Feedback -- 6.3 Controller with Second-Order Dynamics -- 6.3.1 Displacement Feedback -- PHYSICAL INTERPRETATION -- CASE 1: -- CASE 2: -- CASE 3: -- 6.3.2 Acceleration Feedback -- 6.3.3 Frequency-Matched Virtual Passive Controller -- 6.4 Concluding Remarks -- 6.5 Problems -- BIBLIOGRAPHY -- SUGGESTED READING.

7 State--Space Models -- 7.1 Introduction -- 7.2 Continuous-Time State-Space Model -- 7.2.1 Direct-Transmission Term -- 7.2.2 Coordinate Transformation -- 7.2.3 Dynamic Response to General Input -- 7.3 Discrete-Time State-Space Model -- 7.3.1 A Zero-Order Hold (or Sample and Hold) -- 7.3.2 Continuous-Time to Discrete-Time Conversion -- 7.3.3 Coordinate Transformation -- 7.3.4 Dynamic Response of a Discrete-Time Model -- 7.4 Sampling and Aliasing -- 7.5 System Eigenvalues -- 7.6 Concluding Remarks -- 7.7 Problems -- BIBLIOGRAPHY -- 8 State-Feedback Control -- 8.1 Introduction -- 8.2 Controllability and Observability -- 8.2.1 Controllability in the Discrete-Time Domain -- 8.2.2 Observability in the Discrete-Time Domain -- 8.3 Continuous-Time State Feedback -- 8.4 Discrete-Time State Feedback -- 8.5 Placement of Closed-Loop Eigenvalues -- 8.5.1 Null-Space Technique -- 8.5.2 Gain Minimization -- 8.6 Optimal Control -- 8.6.1 Continuous-Time Technique -- 8.6.2 Discrete-Time Technique -- 8.6.3 Realistic Discrete-Time Implementation -- 8.7 Concluding Remarks -- 8.8 Problems -- BIBLIOGRAPHY -- 9 Dynamic Feedback Controller -- 9.1 Introduction -- 9.2 Continuous-Time State Estimation -- 9.3 Discrete-Time State Estimation -- 9.4 Placement of Observer Eigenvalues -- 9.4.1 Definition Based on the First-Order Model -- 9.4.2 Second-Order Formulation -- 9.5 Continuous-Time Observer-Based State Feedback -- 9.6 Discrete-Time Observer-Based State Feedback -- 9.7 Static Output Feedback -- 9.8 Dynamic Output Feedback -- CONTINUOUS-TIME DYNAMIC OUTPUT FEEDBACK -- DISCRETE-TIME DYNAMIC OUTPUT FEEDBACK -- A SPECIAL CASE: OBSERVER-BASED STATE-FEEDBACK CONTROL -- 9.9 Concluding Remarks -- 9.10 Problems -- BIBLIOGRAPHY -- 10 System Identification -- 10.1 Introduction -- 10.2 Finite-Difference Model -- 10.3 Multistep Output Prediction -- 10.4 System Markov Parameters.

10.5 Eigensystem Realization Algorithm -- 10.6 Observable Canonical-Form Realization -- 10.7 Relationship with an Observer Model -- 10.7.1 State-Space Observer Model -- 10.7.2 Relationship with State-Space System Matrices -- 10.7.3 Computation of Observer Gain -- 10.8 Concluding Remarks -- 10.9 Problems -- 10.10 Appendix: Efficient Computation of Data Correlation Matrix -- BIBLIOGRAPHY -- 11 Predictive Control -- 11.1 Introduction -- 11.2 Generalized Predictive Control -- COMPUTATIONAL STEPS -- 11.3 Deadbeat Predictive Control -- COMPUTATIONAL STEPS -- 11.4 Direct Algorithm for GPC and DPC -- 11.4.1 Direct GPC Algorithm -- 11.4.2 Direct DPC Algorithm -- GPC Controller -- DPC Controller -- COMPUTATIONAL STEPS -- 11.5 State-Space Representation -- 11.5.1 Observable Canonical-Form Realization -- 11.5.2 GPC Controller -- 11.5.3 DPC Controller -- GPC Controller -- DPC Controller -- 11.6 Concluding Remarks -- 11.7 Problems -- BIBLIOGRAPHY -- SUGGESTED READING -- Index.