Lyapunov-Based Control of Mechanical Systems

by De Queiroz, Marco S.; Dawson, Darren M.; Nagarkatti, Siddharth P.; Zhang, Fumin

• ISBN13: 9780817640866
• ISBN10: 081764086X
• Format: Hardcover
• Copyright: 2000-05-01
• Publisher: Birkhauser

Summary

This is a new text/reference on advanced nonlinear algorithms for mechanical systems that are based on Lypaunov-type design and stability analysis. The presentation illustrates, in a unified framework, how recent Lyapunov-based techniques can be used to solve a variety of nonlinear control problems for mechanical systems. Starting with part one, the foundations are established in a thorough manner, including necessary math background materials. Part two covers solutions to some tracking problems for rigid mechanical systems, i.e., systems modeled by ordinary differential equations. Part three addresses problems of setpoint/vibration control of flexible mechanical systems, i.e., systems modeled by partial differential equations. By covering theory and applications, the book addresses both ODE-based and PDE-based mechanical systems and presents results for many useful real-time experiments and computer simulations.

Table of Contents

Preface	xi
Introduction	1	(10)
Lyapunov-Based Control	1	(2)
Rigid Mechanical Systems	3	(2)
Flexible Mechanical Systems	5	(2)
Real-Time Control Implementation	7	(4)
References	8	(3)
Control Techniques for Friction Compensation	11	(42)
Introduction	11	(3)
Reduced-Order Friction Model	14	(1)
Control Designs for Reduced-Order Model	15	(19)
Standard Adaptive Control	16	(2)
Modular Adaptive Control	18	(7)
Adaptive Setpoint Control	25	(3)
Experimental Evaluation	28	(6)
Full-Order Friction Model	34	(1)
Control Designs for Full-Order Model	35	(9)
Model-Based Control: Asymptotic Tracking	36	(2)
Model-Based Control: Exponential Tracking	38	(2)
Adaptive Control: Case 1	40	(2)
Adaptive Control: Case 2	42	(1)
Experimental Evaluation	43	(1)
Notes	44	(9)
References	48	(5)
Full-State Feedback Tracking Controllers	53	(34)
Introduction	53	(1)
System Model	54	(1)
Problem Statement	55	(2)
Standard Adaptive Control	57	(2)
Controller Formulation	57	(1)
Stability Result	57	(2)
Desired Trajectory-Based Adaptive Control	59	(13)
Controller Formulation	59	(1)
Stability Results	60	(5)
Experimental Results	65	(1)
Nonadaptive Extensions	66	(6)
Control/Adaptation Law Modularity	72	(10)
Input-to-State Stability Result	73	(2)
Position Tracking Result	75	(3)
Experimental Results	78	(1)
Discussion of Results	79	(3)
Notes	82	(5)
References	84	(3)
Output Feedback Tracking Controllers	87	(42)
Introduction	87	(2)
Problem Statement	89	(1)
Model-Based Observer/Control	90	(11)
Velocity Observer Formulation	90	(2)
Controller Formulation	92	(2)
Composite Stability Result	94	(3)
Experimental Results	97	(4)
Linear Filter-Based Adaptive Control	101	(10)
Filter Formulation	101	(1)
Controller Formulation	102	(2)
Composite Stability Result	104	(4)
Experimental Results	108	(1)
Nonadaptive Extensions	108	(3)
Nonlinear Filter-Based Adaptive Control	111	(11)
Filter/Controller Formulation	113	(1)
Composite Stability Result	114	(2)
OFB Form of Filter/Controller	116	(2)
Simulation Results	118	(4)
Extensions	122	(1)
Notes	122	(7)
References	124	(5)
Strings and Cables	129	(34)
Introduction	129	(1)
Actuator-String System	130	(16)
System Model	130	(2)
Problem Statement	132	(1)
Model-Based Control Law	133	(4)
Adaptive Control Law	137	(2)
Extensions	139	(3)
Experimental Evaluation	142	(4)
Cable System	146	(12)
System Model	146	(3)
Problem Statement	149	(1)
Model-Based Control Law	149	(6)
Adaptive Control Law	155	(2)
Experimental Evaluation	157	(1)
Notes	158	(5)
References	159	(4)
Cantilevered Beams	163	(46)
Introduction	163	(1)
Euler-Bernoulli Beam	164	(21)
System Model	165	(1)
Problem Statement	166	(1)
Model-Based Control Law	166	(6)
Adaptive Control Law	172	(2)
Extensions	174	(3)
Experimental Evaluation	177	(8)
Timoshenko Beam	185	(19)
System Model	186	(1)
Problem Statement	187	(1)
Model-Based Control Law	187	(9)
Adaptive Control Law	196	(3)
Simulation Results	199	(5)
Notes	204	(5)
References	205	(4)
Boundary Control Applications	209	(64)
Introduction	209	(1)
Axially Moving String System	210	(17)
System Model	211	(3)
Problem Statement	214	(1)
Model-Based Control Law	214	(6)
Adaptive Control Law	220	(3)
Experimental Evaluation	223	(4)
Flexible Link Robot Arm	227	(22)
System Model	227	(3)
Problem Statement	230	(1)
Model-Based Control Law	230	(9)
Adaptive Control Law	239	(2)
Experimental Evaluation	241	(8)
Flexible Rotor System	249	(19)
System Model	249	(2)
Problem Statement	251	(1)
Model-Based Control Law	252	(7)
Adaptive Control Law	259	(2)
Experimental Evaluation	261	(7)
Notes	268	(5)
References	271	(2)
Appendices	273	(40)
A Mathematical Background	275	(8)
References	280	(3)
B Bounds for General Rigid Mechanical System	283	(2)
References	284	(1)
C Bounds for the Puma Robot	285	(4)
References	287	(2)
D Control Programs	289	(24)
D.1 DCAL Controller	290	(6)
D.2 Flexible Rotor	296	(17)
Index	313