An Approach to Parametric Nonlinear Least Square Optimization and . . .

This paper considers a parametric nonlinear least square (NLS) optimization problem. Unlike a classical NLS problem statement, we assume that a nonlinear optimized system depends on two arguments: an input vector and a parameter vector. The input vector can be modified to optimize the system, while the parameter vector changes from one optimization iteration to another and is not controlled. The optimization process goal is to find a dependence of the optimal input vector on the parameter vector, where the optimal input vector minimizes a quadratic performance index. The paper proposes an extension of the Levenberg--Marquardt algorithm for a numerical solution of the formulated problem. The proposed algorithm approximates the nonlinear system in a vicinity of the optimum by expanding it into a series of parameter vector functions, affine in the input vector. In particular, a radial basis function network expansion is considered. The convergence proof for the algorithm is presented. The proposed approach is applied to task-level learning control of a two-link flexible arm. Each evaluation of the system in the optimization process means completing a controlled motion of the arm. In the simulation example, the controlled motions take only about 1.5 periods of the lowest eigenfrequency oscillations. The algorithm controls this strongly nonlinear oscillatory system very efficiently. Without any prior knowledge of the system dynamics, it achieves a satisfactory control of arbitrary arm motions after only 500 learning (optimization) iterations

Nonlinear Input Shaping Control of . . .

This paper presents a design of a novel feedforward controller for a large-angle reorientation maneuver of a spacecraft with exible appendages, such as a telecommunication satellite. The controller combines collocated feedback and feedforward control. It uses an efficient and conceptually simple numerical method for the computation for an optimal feedforward input shape for a nonlinear flexible system. The method is based on a minimization of a single regularized performance index instead of solution of a terminal control problem. The paper describes a proposed exible spacecraft testbed developed at the Canadian Space Agency, and studies application of the designed control scheme to this testbed. The designed controller is shown to provide excellent performance in compensation of residual flexible vibrations for the nonlinear system in question

Nonparametric kernel smoothing and FIR filtering for model-free fault symptom generation

This paper describes some new theoretical and practical developments to a recently proposed approach to the generation of fault symptoms in nonlinear systems. The method is model-free, in the sense that no analytical model of the plant is needed. The kernel-smoother makes it possible to detect changes in the plant dynamics, possibly due to some malfunction. After recalling several basic definitions and results, a novel interpretation in the context of FIR filters is presented, and some practical implementation issues are addressed. Experimental results on the three-tank benchmark are finally reported, showing the effectiveness of the proposed methodology

High Precision Positioning of a Mechanism With Nonlinear Friction . . .

A new approach to very accurate positioning of mechanical devices with nonlinear (stick-slip) friction is presented in this paper. The proposed controller applies narrow torque pulses to move a mechanism to a desiredposition despite nonlinear friction. The pulse shapes generated by the controller are computed using a fuzzy logic approximation of the dependence between the desired displacement and the torque pulse shape. The closed-loop stability conditions for the proposed controller are derived taking into consideration a random variation of friction. A detailed experimental study of the system response to different torque pulse shapes and a detailed controller design are presented for a direct-drive mechanism. In the experiments it was demonstrated that the proposed controller achieves positioning accuracy which is within the limits of the position encoder resolution