Uy-Loi Ly

Coprime factorization controller reduction with Bezout identity induced frequency weighting

Abstract This paper introduces a frequency-weighted controller reduction scheme which offers good closed-loop stability under use of the reduced order controller. By combining the use of a stable fractional representation of the controller with a frequency weighting in the reduction procedure derived by consideration of the closed-loop stability margin, we formulate a frequency-weighted controller reduction procedure with the weight simplified by the Bezout identity. Some examples are used to illustrate the reduction procedure.

Experimental evaluation of a hybrid position and force surface following algorithm for unknown surfaces

This paper experimentally implements a surface following algorithm for unknown surfaces under a hybrid position and force scheme. The mechanization uses a low friction roller at the end of a two-link manipulator so that primarily the normal force is measured. With the normal force information and joint angle information, the surface normal direction is calculated and a position reference is calculated along the surface tangent. Experimental evaluation shows the algorithm works for a line, a concave arc, and a convex arc. Also, when different force levels are commanded or different controllers are used, the algorithm still performs well. Thus, the algorithm allows a constant force to be applied while following a surface whose shape is not known a priori.

Exact computation of the infimum in H/sub infinity /-optimization via output feedback

The authors present a simple and noniterative procedure for the computation of the exact value of the infimum in the standard H/sub infinity /-optimal control with output feedback. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. The method is applicable to systems that satisfy the following conditions: (1) the transfer function from the control input to the controlled output is right-invertible and has no invariant zeros on the j omega axis, and (2) the transfer function from the disturbance to the measurement output is left-invertible and has no invariant zeros on the j omega axis. >

Robust Control Design using Nonlinear Constrained Optimization

This paper presents a systematic for designing robust low-order controllers using nonlinear constrained optimization, This method is applied to the control of a two mass-spring system representing a generic model of an uncertain dynamical system with non-colocated sensor and actuator. A step-by-step design procedure is presented resulting in a final design, a second-order compensator, that satisfy all the requirements stated in the benchmark design problem #1.

Sampled-data system with computation time delay - Optimal W-synthesis method

We treat the control problem for sampled-data systems that accounts for the time delay in the computation of the control action. The problem is formulated entirely in the w domain, and the optimum design is solved using an alternative method called optimal W-synthesis method. The method has been applied to the benchmark problem of a two-mass-spring system. Design results obtained indicate that the presence of computation time delay not only reduces the relative stability and robustness but also degrades the design performance. Loss in gain and phase margins is significant if the time delay is not accounted for in the control-law synthesis. Furthermore, control activity can be highly sensitive to the inherent time delay resulting in excessive change m the control action that may eventually lead to control saturation in a real system. It is found that, when the time delay is incorporated into the control-law synthesis, stability, robustness, and performance loss because of computation time delay can be reduced.

Closed-loop transfer recovery with observer-based controllers. I - Analysis

A detailed study is presented of three fundamental issues related to the problem of closed-loop transfer (CLT) recovery. The first issues concerns what can and cannot be achieved for a given system and for an arbitrary target CLT function (TCLTF). The second issue involves developing necessary and/or sufficient conditions for a TCLTF to be recoverable either exactly or approximately. The third issue involves the necessary and/or sufficient conditions on a given system such that it has at least one recoverable TCLTF. The results of the analysis identify some fundamental limitations of the given system as a consequence of its structural properties which enables designers to appreciate at the outset different design limitations incurred in the synthesis of output-feedback controllers. Then, the actual design of full-order or reduced-order observer-based controllers is addressed which will achieve as close as possibly the desired TCLTF. Three design methods are considered: (1) the ATEA method, (2) a method that minimizes the H2-norm of a recovery matrix, and (3) a method that minimizes the respective H(infinity) norm. The relative merits of the methods are discussed.

Experimental comparison of robust reduced-order hybrid position and force optimization techniques for a two-link flexible manipulator

This paper compares hybrid optimization schemes for designing robust reduced-order hybrid position and force controllers for a flexible two-link manipulator. As a baseline, these controllers are compared to full-order linear-quadratic-Gaussian (LQG) controllers. First, position and force controllers are designed separately and combined by the superposition method. Next, all the controllers are designed simultaneously using a direct optimization method. Experimental results show that the reduced-order controllers provide comparable performance to the full-order controllers. Also, results show that simultaneous optimization can provide better results than designing the force and position controllers separately.

Evaluation of reduced-order controllers on a two-link flexible manipulator

This paper examines the synthesis of various robust controllers for command tracking of trajectories that excite many of the arm dynamics. The model used for all the designs is a 20 degree of freedom lumped-spring-mass-damper model of 40th order which is reduced to 18th order by balanced truncation. First, a standard linear quadratic Gaussian (LQG) controller is designed and tested, and robustness at the control loop is recovered with a loop transfer recovery (LQG/LTR) controller design. Next, loop transfer recovery (LTR) based on the special coordinate basis analysis of the plant is covered. In order to make the LQG/LTR and LTR controllers more practical, controller reduction is applied using modal residualization and balanced truncation. Next, a 4th order SANDY direct optimization design is covered and experimentally evaluated. Finally, the performance of all the controllers is evaluated experimentally along a nominal trajectory. Results show that the lower order controllers can provide comparable performance to the full-order controllers.

Experimental evaluation of robust reduced-order hybrid position/force control on a two-link flexible manipulator

This paper compares the experimental evaluation of robust reduced-order hybrid position and force controllers to standard full-order and reduced-order linear-quadratic Gaussian (LQG) controllers. A robust reduced-order position controller and a reduced-order force controller are designed using the SANDY direct optimization program. Full-order LQG position and force controllers are designed and then reduced through balanced truncation. Experimental results show that the reduced-order controllers provide comparable performance to the full-order controllers. Thus, by use of direct-optimization, the benefits of smaller controllers (smaller memory requirements and faster sampling rates) can be achieved while accounting for varying plant conditions (robustness).

Simultaneous H 2 /H ∞ optimal control: the state feedback case

Abstract A simultaneous H 2 H ∞ control problem is considered. This problem seeks to minimize the H 2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H ∞ norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar ( Automatica, 27, 307–316, 1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H 2 H ∞ problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H 2 norm performance measure. This class of problems subsumes the class of regular problems.