Shaped Time-Optimal Feedback Controllers for Flexible Structures

2004 ◽  
Vol 126 (1) ◽  
pp. 173-186 ◽  
Author(s):  
Lucy Y. Pao ◽  
Chanat La-orpacharapan
Keyword(s):  
Phase Plane ◽  
Closed Loop ◽  
Flexible Structures ◽  
Input Shaping ◽  
Feedback Controllers ◽  
Control Laws ◽  
Loop Control ◽  
Flexible Mode ◽  
Time Optimal ◽  
Acceleration And Deceleration

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.

Closed-Loop Input Shaping for Flexible Structures Using Time-Delay Control1

1999 ◽  
Vol 122 (3) ◽  
pp. 454-460 ◽  
Author(s):  
Vikram Kapila ◽  
Anthony Tzes ◽  
Qiguo Yan
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Flexible Structures ◽  
System Stability ◽  
Structural Vibration ◽  
Delay Systems ◽  
Linear Matrix ◽  
Input Shaping ◽  
Closed Loop Control ◽  
Loop Control

Input shaping techniques reduce the residual vibration in flexible structures by convolving the command input with a sequence of impulses. The exact cancellation of the residual structural vibration via input shaping is dependent on the amplitudes and instances of impulse application. A majority of the current input shaping schemes are inherently open-loop where impulse application at inaccurate instances can lead to system performance degradation. In this paper, we develop a closed-loop control design framework for input shaped systems. This framework is based on the realization that the dynamics of input shaped systems give rise to time delays in the input. Thus, we exploit the feedback control theory of time delay systems for the closed-loop control of input shaped flexible structures. A Riccati equation-based and a linear matrix inequality-based frameworks are developed for the stabilization of systems with uncertain, multiple input delays. Next, the aforementioned framework is applied to two input shaped flexible structure systems. This framework guarantees closed-loop system stability and performance when the impulse train is applied at inaccurate instances. Two illustrative numerical examples demonstrate the efficacy of the proposed closed-loop input shaping controller. [S0022-0434(00)00103-9]

Oscillations-Induced Transitions and Their Application in Control of Dynamical Systems

1990 ◽  
Vol 112 (3) ◽  
pp. 313-319 ◽  
Author(s):  
J. Bentsman
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Closed Loop ◽  
Distributed Parameter ◽  
Control Laws ◽  
Loop Control ◽  
Finite Dimensional ◽  
Analytical Tools ◽  
Semilinear Parabolic ◽  
Qualitative Changes

Studies of the use of oscillations for control purposes continue to reveal new practically important properties unique to the oscillatory open and closed loop control laws. The goal of this paper is to enlarge the available set of analytical tools for such studies by introducing a method of analysis of the qualitative changes in the behavior of dynamical systems caused by the zero mean parametric excitations. After summarizing and slightly refining a technique developed previously for the finite dimensional nonlinear systems, we consider an extension of this technique to a class of distributed parameter systems (DPS) governed by semilinear parabolic equations. The technique presented is illustrated by several examples.

scholarly journals Accurate Motion Control of a Pneumatic Linear Peristaltic Actuator

Actuators ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 63 ◽  
Author(s):  
João Falcão Carneiro ◽  
João Bravo Pinto ◽  
Fernando Gomes de Almeida
Keyword(s):  
Closed Loop ◽  
Low Cost ◽  
Dynamic Performance ◽  
Control Law ◽  
Control Loop ◽  
Control Laws ◽  
Loop Control ◽  
Error Band ◽  
Short Service Life ◽  
High Mechanical Stress

Pneumatic linear peristaltic actuators can offer some potential advantages when compared with conventional ones. The low cost, virtually unlimited stroke and easy implementation of curved motion profiles are among those benefits. On the downside, these actuators suffer high mechanical stress that can lead to short service life and increased leakage among chambers during the actuator lifetime. One way to cope with this problem is to impose the force—instead of the displacement—between rollers, as this has been shown to improve the endurance of the hose while reducing leakage during the actuator lifetime. This paper presents closed control loop results using such a setup. Previous studies with linear peristaltic actuators have revealed that, although it is possible to reach zero steady state error to constant references with closed loop control, the dynamic response obtained is very slow. This paper is mainly focused on this topic, namely on the development of several control laws to improve the dynamic performance of the system while avoiding limit cycles. The new developed control law leads to an average time of 1.67 s to reach a 0.1 mm error band in an experiment consisting of a series of 16 steps ranging from 0.02 to 0.32 m in amplitude.

scholarly journals Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yong-Ren Pu ◽  
Thomas A. Posbergh
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Numerical Algorithms ◽  
Open Loop ◽  
Rigid Bodies ◽  
Feedback Stabilization ◽  
Conserved Quantities ◽  
Control Laws ◽  
Loop Control ◽  
Closed Loop Systems

The problem of stabilization of rigid bodies has received a great deal of attention for many years. People have developed a variety of feedback control laws to meet their design requirements and have formulated various but mostly open loop numerical algorithms for the dynamics of the corresponding closed loop systems. Since the conserved quantities such as energy, momentum, and symmetry play an important role in the dynamics, we investigate the conserved quantities for the closed loop control systems which formally or asymptotically stabilize rigid body rotation and modify the open loop numerical algorithms so that they preserve these important properties. Using several examples, the authors first use the open loop algorithm to simulate the tumbling rigid body actions and then use the resulting closed loop one to stabilize them.

Discrete Time-Coupled State-Dependent Riccati Equation Control of Nonlinear Mechatronic Systems

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Xin Wang
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Disturbance Attenuation ◽  
Infinite Time ◽  
Mechatronic Systems ◽  
Feedback Controllers ◽  
Control Laws ◽  
State Dependent ◽  
Time Optimal ◽  
Nonlinear Plant

Abstract A discrete-time-coupled state-dependent Riccati equation (CSDRE) control strategy is structured in this paper for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator (NLQR) and H∞ robust control performance objectives. Under smoothness assumptions, the nonlinear plant dynamics can be formulated into state-dependent coefficient form through direct parameterization. By solving a pair of coupled state-dependent Riccati equations, the optimal stabilizing solutions can achieve inherent stability, nonlinear quadratic optimality, and H∞ disturbance attenuation performance. The established two-player Nash's game theory is utilized for developing both of the finite and infinite time optimal control laws. Furuta swing-up pendulum, a representative nonholonomic underactuated nonlinear system, is stabilized in real-time for validating the robustness and potential of proposed approach in mechatronics applications.

Projected Phase-Plane Switching Curves for Vibration Reduction Filters With Negative Amplitudes

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Abhishek Dhanda
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Phase Plane ◽  
Closed Loop ◽  
Vibration Reduction ◽  
Shaping Filter ◽  
Negative Impulse ◽  
Acceleration And Deceleration ◽  
Analytical Expressions ◽  
Loop Scheme

In this paper, we extend the phase-plane based closed-loop scheme of implementing commands shaped with vibration-reduction filters. A generalized shaping filter is considered in this work which can have negative impulse intensities and different acceleration and deceleration limits. Switching conditions are derived in terms of the filter parameters for both convolution-based and closed-form based shaping techniques. Analytical expressions are provided for the switching curves and various schemes are discussed for selecting appropriate phase-planes and implementing shaped-commands on real-time servomechanisms.

CLOSED-LOOP CONTROL OF THE THALAMOCORTICAL RELAY NEURON'S PARKINSONIAN STATE BASED ON SLOW VARIABLE

2013 ◽  
Vol 23 (04) ◽  
pp. 1350017 ◽  
Author(s):  
CHEN LIU ◽  
JIANG WANG ◽  
YING-YUAN CHEN ◽  
BIN DENG ◽  
XI-LE WEI ◽  
...  
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Closed Loop ◽  
Slow Variable ◽  
Closed Loop Control ◽  
Fast Variable ◽  
Qualitative And Quantitative Analysis ◽  
Feedback Controllers ◽  
Loop Control ◽  
Qualitative And Quantitative

A novel closed-loop control strategy is proposed to control Parkinsonian state based on a computational model. By modeling thalamocortical relay neurons under external electric field, a slow variable feedback control is applied to restore its relay functionality. Qualitative and quantitative analysis demonstrates the performance of feedback controller based on slow variable is more efficient compared with traditional feedback control based on fast variable. These findings point to the potential value of model-based design of feedback controllers for Parkinson's disease.

Specification Guided Automated Synthesis of Feedback Controllers

2021 ◽  
Vol 20 (5s) ◽  
pp. 1-26
Author(s):  
Nikhil Kumar Singh ◽  
Indranil Saha
Keyword(s):  
Closed Loop ◽  
Matrix Decomposition ◽  
Parameter Tuning ◽  
Controller Synthesis ◽  
Formal Specifications ◽  
System Matrix ◽  
Feedback Controllers ◽  
Loop Control ◽  
Automated Technique ◽  
High Level

The growing use of complex Cyber-Physical Systems (CPSs) in safety-critical applications has led to the demand for the automatic synthesis of robust feedback controllers that satisfy a given set of formal specifications. Controller synthesis from the high-level specification is an NP-Hard problem. We propose a heuristic-based automated technique that synthesizes feedback controllers guided by Signal Temporal Logic (STL) specifications. Our technique involves rigorous analysis of the traces generated by the closed-loop system, matrix decomposition, and an incremental multi-parameter tuning procedure. In case a controller cannot be found to satisfy all the specifications, we propose a technique for modifying the unsatisfiable specifications so that the controller synthesized for the satisfiable subset of specifications now also satisfies the modified specifications. We demonstrate our technique on eleven controllers used as standard closed-loop control system benchmarks, including complex controllers having multiple independent or nested control loops. Our experimental results establish that the proposed algorithm can automatically solve complex feedback controller synthesis problems within a few minutes.

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