Input Shaping Design for Multi-Input Flexible Systems

Abstract

This paper investigates a new design technique of input shaping filters for multi-input flexible systems using convex optimization synthesis techniques for finite impulse response filters (FIR filters). The objective of the input shaping filter design is to find the minimum length and the minimum number of nonzero impulses of the FIR filter that forces the system to track the reference command without any residual vibration, while satisfying additional performance and control constraints. This multi-objective optimization is solved using a two-step algorithm that sequentially solves two quasi-convex optimization problems. Compared with previously published nonlinear optimization approaches, this new approach does not require a priori knowledge of the forms of input shaping filters and enables much greater flexibility for including additional performance and robustness objectives. Furthermore, this convex-based approach can be applied to multi-input systems. The multiple input shaping filter has been experimentally verified on the Stanford University Two-Link Flexible Manipulator.

A New Command Shaper Design for Residual Vibration Reduction in Flexible Systems Using Artificial Mode Constraints

“…The command shaper for two-mode systems that has three impulses can be written in the Laplace domain as [6]. 3 Here, we will introduce a command shaper that can manipulate the input command, thereby lowering excitation. The principle can be explained by pole-zero cancellation [4]- [7].…”

Disturbance Filtering and Identification on the Naval Postgraduate School 3-Axis Spacecraft Simulator

“…Ref. [5][6][7][8][9]. In addition, its effectiveness has been experimentally validated on several systems including coordinate measuring machines, long reach manipulators, and cranes (e.g.…”

Command modification using input shaping for automated highway systems with heavy trucks

“…In addition, expansion to multi-input, multi-output (MIMO) systems is quite easy. A few of the objectives, relevant to automated highways, are listed below [32]. In the following, 's are design variables that allow tight/loose control, depending on acceptable compromise between performance and cost.…”

“…The input shaper design is then a special case of FIR filter design problem. In this framework, a filter with the minimum length and minimum number of non-zero impulses is designed to shape reference commands so that a system tracks the shaped reference command with little residual while satisfying performance constraints such as bounded control effort [32].…”

“…A more sophisticated method using convex optimization has been developed to extend input shaping techniques for multi-input systems and additional constraints such as slew rate and transient response [32]. It has been shown that objectives associated with input shaper design can be approximately reformulated as quasi-convex optimization problems in the discrete domain [59].…”