A performance-oriented multi-loop control of systems with constraints and uncertainties

Lu Lu, Purdue University

Abstract

In many control applications, the controllers need to be designed such that multiple performance requirements, such as good steady-state tracking accuracy and fast transient response speed, should be achieved simultaneously. However, real systems are often subject to various types of disturbances, uncertainties and physical constraints that make the satisfaction of the multiple performance requirements extremely difficult. In this thesis, a performance-oriented multi-loop control theory is developed to solve the problem. In Chapter 1, the difficulties of designing a control law to meet multiple performance requirements under varieties of system constraints and uncertainties are analyzed, and varieties of traditional control strategies are briefly reviewed with their merits and limitations clearly pointed out. In Chapter 2, a simple system described by a chain of integrators with input saturation and disturbance is used as an introductory example to demonstrate the proposed multi-loop control design and its superiority over previous algorithms. The proposed controller consists of two loops. In the inner loop, a nonlinear control law is designed in continuous-time domain to have an arbitrarily good disturbance rejection performance at the steady-state while keeping the tracking errors with respect to on-line replanned trajectory within certain positive invariant set. In the outer loop, a trajectory replanning unit implemented in discrete-time domain is constructed to generate a replanned trajectory that minimizes the converging time of the replanned trajectory to the desired target. It is theoretically shown that the resulting closed-loop system is globally stable and can track any feasible desired trajectory with a guaranteed steady-state tracking accuracy. Comparative simulation results have been obtained for a third-order integrator to verify the superior performance of the proposed controller over existing major methods in terms of the disturbance rejection capability and the overall respond speed of the resulting closed-loop system. In Chapter 3, the proposed approach is extended to a class of general MIMO nonlinear systems with matched uncertainties and constraints. The uncertainties include both unknown parameters and uncertain disturbances. For the constraints, both input saturation and state constraints are considered. The overall control structure still has two loops as in Chapter 2. However, the design of the inner-loop control law combines the Lyapunov design method with adaptive robust control method to deal with more general MIMO coupling dynamics, parametric uncertainties, lumped disturbances and modeling errors simultaneously. In the outer loop, numerical algorithms are proposed to solve the general constrained time-optimal trajectory planning problem online. The proposed algorithm is successfully simulated on a planar two-axis robotic manipulator system. For many physical systems, the uncertainties show up in the dynamic equations that do not directly contain the control input. These uncertainties are often referred to as "unmatched uncertainties". When the system has both unmatched uncertainties and input saturation, the control law design becomes extremely difficult. In Chapter 4, the challenges of controlling such type of systems are discussed first. It is shown that when both control input saturation and unmatched uncertainties are present, arbitrarily good tracking accuracy at steady state becomes unattainable. Then, a two-loop tracking control strategy for a chain of integrator with unmatched disturbances and input saturation is proposed. In particular, how to select the controller gains such that the proposed control theory is valid is discussed in detail. Finally, the above two-loop control strategy and the gain selection procedure are extended to deal with systems with unmatched parametric uncertainties, disturbances, input saturation and state constraints. In chapter 5, the proposed multi-loop control theory is applied to different industrial systems to show its effectiveness in solving real control problems. Four different physical systems are studied. They include 1-DOF linear motor driven stage, 2-DOF linear motor driven gantry, linear motor driven flexible beam and hydraulic manipulator. For each of the four physical systems, the dynamics and the control objectives are different from others. The uniqueness of the control of these systems is fully discussed. Then, different versions of multi-loop control algorithms are proposed to solve the problems. Experimental results are also presented to verify the effectiveness of the proposed algorithms and their superiorities over some of the traditional control strategies.

Degree

Ph.D.

Advisors

Yao, Purdue University.

Subject Area

Engineering|Mechanical engineering

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