Lyapunov-Based Control of Mechanical Systems

The design of nonlinear controllers for mechanical systems has been an ex tremely active area of research in the last two decades. From a theoretical point of view, this attention can be attributed to their interesting dynamic behavior, which makes them suitable benchmarks for nonlinear control the oreticians. On the other hand, recent technological advances have produced many real-world engineering applications that require the automatic con trol of mechanical systems. the mechanism for de Often, Lyapunov-based techniques are utilized as veloping different nonlinear control structures for mechanical systems. The allure of the Lyapunov-based framework for mechanical system control de sign can most likely be assigned to the fact that Lyapunov function candi dates can often be crafted from physical insight into the mechanics of the system. That is, despite the nonlinearities, couplings, and/or the flexible effects associated with the system, Lyapunov-based techniques can often be used to analyze the stability of the closed-loop system by using an energy like function as the Lyapunov function candidate. In practice, the design procedure often tends to be an iterative process that results in the death of many trees. That is, the controller and energy-like function are often constructed in concert to foster an advantageous stability property and/or robustness property. Fortunately, over the last 15 years, many system the ory and control researchers have labored in this area to produce various design tools that can be applied in a variety of situations.

Texte du rabat

The design of nonlinear controllers for mechanical systems has been an ex­ tremely active area of research in the last two decades. From a theoretical point of view, this attention can be attributed to their interesting dynamic behavior, which makes them suitable benchmarks for nonlinear control the­ oreticians. On the other hand, recent technological advances have produced many real-world engineering applications that require the automatic con­ trol of mechanical systems. the mechanism for de­ Often, Lyapunov-based techniques are utilized as veloping different nonlinear control structures for mechanical systems. The allure of the Lyapunov-based framework for mechanical system control de­ sign can most likely be assigned to the fact that Lyapunov function candi­ dates can often be crafted from physical insight into the mechanics of the system. That is, despite the nonlinearities, couplings, and/or the flexible effects associated with the system, Lyapunov-based techniques can often be used to analyze the stability of the closed-loop system by using an energy­ like function as the Lyapunov function candidate. In practice, the design procedure often tends to be an iterative process that results in the death of many trees. That is, the controller and energy-like function are often constructed in concert to foster an advantageous stability property and/or robustness property. Fortunately, over the last 15 years, many system the­ ory and control researchers have labored in this area to produce various design tools that can be applied in a variety of situations.

Résumé

"This book describes how Lyapunov-based techniques can be used to design nonlinear controllers for mechanical systems.... The text is well written, easy to read, and many examples clarify the theoretical discussions. The book can be useful both to newcomers in the field and to graduate students and researchers in the area of control applications."

-Zentralblatt Math

"This book deals with Lyapunov-based control techniques. It gives a rather complete and at the same time technically accurate overview of the modern state of the art in control methods using Lyapunov functions.... The reviewed material is intended for an audience of researchers and graduate students in the area of control applications."

-Mathematical Reviews

Contenu
1 Introduction.- 1.1 Lyapunov-Based Control.- 1.2 Rigid Mechanical Systems.- 1.3 Flexible Mechanical Systems.- 1.4 Real-Time Control Implementation.- 2 Control Techniques for Friction Compensation.- 2.1 Introduction.- 2.2 Reduced-Order Friction Model.- 2.3 Control Designs for Reduced-Order Model.- 2.4 Full-Order Friction Model.- 2.5 Control Designs for Full-Order Model.- 2.6 Notes.- 3 Full-State Feedback Tracking Controllers.- 3.1 Introduction.- 3.2 System Model.- 3.3 Problem Statement.- 3.4 Standard Adaptive Control.- 3.5 Desired Trajectory-Based Adaptive Control.- 3.6 Control/Adaptation Law Modularity.- 3.7 Notes.- 4 Output Feedback Tracking Controllers.- 4.1 Introduction.- 4.2 Problem Statement.- 4.3 Model-Based Observer/Control.- 4.4 Linear Filter-Based Adaptive Control.- 4.5 Nonlinear Filter-Based Adaptive Control.- 4.6 Notes.- 5 Strings and Cables.- 5.1 Introduction.- 5.2 Actuator-String System.- 5.3 Cable System.- 5.4 Notes.- 6 Cantilevered Beams.- 6.1 Introduction.- 6.2 Euler-Bernoulli Beam.- 6.3 Timoshenko Beam.- 6.4 Notes.- 7 Boundary Control Applications.- 7.1 Introduction.- 7.2 Axially Moving String System.- 7.3 Flexible Link Robot Arm.- 7.4 Flexible Rotor System.- 7.5 Notes.- Appendices.- A Mathematical Background.- References.- B Bounds for General Rigid Mechanical System.- References.- C Bounds for the Puma Robot.- References.- D Control Programs.- D.1 DCAL Controller.- D.2 Flexible Rotor.