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.

Contenu

1 Introduction.- 1.1 Lyapunov-Based Control.- 1.2 Rigid Mechanical Systems.- 1.3 Flexible Mechanical Systems.- 1.4 Real-Time Control Implementation.- References.- 2 Control Techniques for Friction Compensation.- 2.1 Introduction.- 2.2 Reduced-Order Friction Model.- 2.3 Control Designs for Reduced-Order Model.- 2.3.1 Standard Adaptive Control.- 2.3.2 Modular Adaptive Control.- 2.3.3 Adaptive Setpoint Control.- 2.3.4 Experimental Evaluation.- 2.4 Full-Order Friction Model.- 2.5 Control Designs for Full-Order Model.- 2.5.1 Model-Based Control: Asymptotic Tracking.- 2.5.2 Model-Based Control: Exponential Tracking.- 2.5.3 Adaptive Control: Case.- 2.5.4 Adaptive Control: Case.- 2.5.5 Experimental Evaluation.- 2.6 Notes.- References.- 3 Full-State Feedback Tracking Controllers.- 3.1 Introduction.- 3.2 System Model.- 3.3 Problem Statement.- 3.4 Standard Adaptive Control.- 3.4.1 Controller Formulation.- 3.4.2 Stability Result.- 3.5 Desired Trajectory-Based Adaptive Control.- 3.5.1 Controller Formulation.- 3.5.2 Stability Results.- 3.5.3 Experimental Results.- 3.5.4 Nonadaptive Extensions.- 3.6 Control/Adaptation Law Modularity.- 3.6.1 Input-to-State Stability Result.- 3.6.2 Position Tracking Result.- 3.6.3 Experimental Results.- 3.6.4 Discussion of Results.- 3.7 Notes.- References.- 4 Output Feedback Tracking Controllers.- 4.1 Introduction.- 4.2 Problem Statement.- 4.3 Model-Based Observer/Control.- 4.3.1 Velocity Observer Formulation.- 4.3.2 Controller Formulation.- 4.3.3 Composite Stability Result.- 4.3.4 Experimental Results.- 4.4 Linear Filter-Based Adaptive Control.- 4.4.1 Filter Formulation.- 4.4.2 Controller Formulation.- 4.4.3 Composite Stability Result.- 4.4.4 Experimental Results.- 4.4.5 Nonadaptive Extensions.- 4.5 Nonlinear Filter-Based Adaptive Control.- 4.5.1 Filter/Controller Formulation.- 4.5.2 Composite Stability Result.- 4.5.3 OFB Form of Filter/Controller.- 4.5.4 Simulation Results.- 4.5.5 Extensions.- 4.6 Notes.- References.- 5 Strings and Cables.- 5.1 Introduction.- 5.2 Actuator-String System.- 5.2.1 System Model.- 5.2.2 Problem Statement.- 5.2.3 Model-Based Control Law.- 5.2.4 Adaptive Control Law.- 5.2.5 Extensions.- 5.2.6 Experimental Evaluation.- 5.3 Cable System.- 5.3.1 System Model.- 5.3.2 Problem Statement.- 5.3.3 Model-Based Control Law.- 5.3.4 Adaptive Control Law.- 5.3.5 Experimental Evaluation.- 5.4 Notes.- References.- 6 Cantilevered Beams.- 6.1 Introduction.- 6.2 Euler-Bernoulli Beam.- 6.2.1 System Model.- 6.2.2 Problem Statement.- 6.2.3 Model-Based Control Law.- 6.2.4 Adaptive Control Law.- 6.2.5 Extensions.- 6.2.6 Experimental Evaluation.- 6.3 Timoshenko Beam.- 6.3.1 System Model.- 6.3.2 Problem Statement.- 6.3.3 Model-Based Control Law.- 6.3.4 Adaptive Control Law.- 6.3.5 Simulation Results.- 6.4 Notes.- References.- 7 Boundary Control Applications.- 7.1 Introduction.- 7.2 Axially Moving String System.- 7.2.1 System Model.- 7.2.2 Problem Statement.- 7.2.3 Model-Based Control Law ..- 7.2.4 Adaptive Control Law.- 7.2.5 Experimental Evaluation.- 7.3 Flexible Link Robot Arm.- 7.3.1 System Model.- 7.3.2 Problem Statement.- 7.3.3 Model-Based Control Law.- 7.3.4 Adaptive Control Law.- 7.3.5 Experimental Evaluation.- 7.4 Flexible Rotor System.- 7.4.1 System Model.- 7.4.2 Problem Statement.- 7.4.3 Model-Based Control Law.- 7.4.4 Adaptive Control Law.- 7.4.5 Experimental Evaluation.- 7.5 Notes.- References.- 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.