Design and stability analysis of a switching contact task controller for hydraulic actuators

Electrohydraulic servo actuators are used extensively in industry due to their high payload capability, high durability, rapid response, and high power-to-weight ratio. In this thesis, a switching contact task control scheme is designed for hydraulic actuators. The control scheme essentially consists of three distinct control laws for asymptotic position regulation in free space motion, impact suppression during transition from free to constrained motion, and asymptotic force regulation in the sustained-contact period of motion, all in the presence of actuator's dry friction as well as viscous friction and Stribeck effect.; At the control design stage, the extension of Lyapunov stability theory to nonsmooth systems based on Filippov's solution theory is employed to derive the control laws for various modes of operation of a hydraulic actuator interacting with a non-moving environment. None of the controllers require exact knowledge of the actuator friction, servovalve dynamics, environment stiffness, or hydraulic parameters for the control action as in most practical cases such knowledge is not available. For an actuator with initially centered piston that travels within the mid-point vicinity of the cylinder, the theoretical Lyapunov stability of each phase of motion is studied considering nonlinear hydraulic functions, servovalve dynamics, complete discontinuous model of actuator friction, and realistic impact/contact dynamics (if present) modeled by Hertz contact theory. The performance of each individual controller is then tested through experiments on a fully instrumented hydraulic test rig and their practicality and effectiveness in real operations is verified.; Combination of the three control schemes yields a so-called "switching contact task control scheme". The most important but difficult part of analyzing such a nonsmooth system is the stability analysis. Although Lyapunov stability theory is the basis in deriving the individual control laws at the design stage, switchings between control laws during the complete contact task necessitates an overall stability analysis for the complete task. Removing the dynamic modeling assumptions of the design stage and generalizing the system dynamics by allowing the full stroke piston travel comes with the price of adding extreme difficulty in deriving the Lyapunov functions for the overall non-smooth system. Therefore, in this thesis, a systematic approach is developed for stability analysis of the overall contact task using the concept of Lyapunov exponents. Since Lyapunov exponents have been initially introduced to analyze smooth dynamical systems, their application to nonsmooth systems involves a number of issues that need special consideration. Solution analysis, linearization at the instants of discontinuity, existence of Lyapunov exponents, and stability of numerical computations are among such important issues that did not exist in the conventional applications of Lyapunov exponents on smooth dynamic systems. These issues are thoroughly addressed using a combination of various existing theorems and algorithms and the resulting methodology has laid a solid framework for stability analysis of switching systems with capability of being extended to other nonsmooth engineering problems.