Shaped Time-Optimal Feedback Controllers for Flexible Structures

Abstract

This paper describes the design of closed-loop control laws for servomechanisms with one dominant flexible mode. An input shaping technique is employed to alter the rigid body phase-plane trajectory that is used in time-optimal servomechanisms. The resulting controllers lead to near time-optimal performance without unwanted residual vibrations. After the basic technique is outlined for a system with one undamped flexible mode, extensions are given considering different acceleration and deceleration capabilities, damping, and slew rate limits.

Wave-based control of non-linear flexible mechanical systems

“…Previous approaches [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] have included various classical and state feedback control techniques (often using simplified dynamic models); modal control (often considering a rigid-body, or zero frequency mode separately from vibration modes); sliding mode control; input command shaping [6][7][8]; time-delay filters; optimal control leading to bang-bang control; systems designed to have more easily controllable dynamics [11]; wave-based control [15,16]; and control based on real-virtual system models [17,18]. Each method has special characteristics and drawbacks, discussed in the literature.…”

Command shaping for flexible systems: A review of the first 50 years

“…157 Implementation on these types of industrial machines may require the input-shaping algorithm to deal with friction, 116,158,159 saturation, 75,160 or rate limiting. 81,[161][162][163][164][165] Command shaping has also proven beneficial for spacecraft. 67,[69][70][71][73][74][75]95,97,99,100,106,109,115,[166][167][168][169][170] Input shapers were tested in space using the Middeck Active Control Experiment (MACE).…”

Proximal time-optimal control of flexible systems made robust though feedback

“…If the system parameters are known the time optimal switching times can be found using equations (1) and (2). The required actuator trajectory profile (blue line in Figure 1), denoted Q(s), is given by ( ) …”

“…When the actuator constraint is specified as a maximum acceleration / deceleration, the minimum time for rest-to-rest manoeuvres implies bang-bang control [1][2][3][4][5][6]. That is, the actuator acceleration is always at a limiting value, maximum positive or maximum negative.…”