scholarly journals Learning Input Shaping Technique for Non-LTI Systems

1998 ◽  
Vol 123 (2) ◽  
pp. 288-293 ◽  
Author(s):  
Juyi Park ◽  
Pyung-Hun Chang
Keyword(s):  
Natural Frequency ◽  
Closed Loop ◽  
Industrial Robot ◽  
Loop System ◽  
Input Shaping ◽  
Time Varying ◽  
Closed Loop System ◽  
Shaping Technique ◽  
Time Varying Systems

It is well known that conventional Input Shaping Technique (IST) is not very effective in suppressing residual vibrations for non-LTI systems, such as substantially nonlinear or time-varying systems. In an effort to increase the effectiveness such systems, this paper presents Learning Input Shaping Technique (LIST) which iteratively updates the parameters of IST from previous trials. Simulations are presented for four different cases: (1) when the natural frequency or damping of a system is not estimated well; (2) when a system has time varying vibration; (3) when a system has nonlinear flexibility; and (4) when a closed-loop system includes a saturation element in the loop. LIST is experimented on a six D.O.F industrial robot to evaluate its effectiveness. The results of the simulations and the experiment show that the residual vibrations become considerably smaller as iteration goes on, thereby demonstrating the effectiveness of LIST.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

Event-triggered Hꝏ control for NCS with time-delay and packet losses

2019 ◽  
Vol 37 (3) ◽  
pp. 918-934
Author(s):  
Jing Bai ◽  
Ying Wang ◽  
Li-Ying Zhao
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Packet Losses ◽  
Event Triggered

Abstract This paper is concerned with the discrete event-triggered dynamic output-feedback ${H}_{\infty }$ control problem for the uncertain networked control system, where the time-varying sampling, network-induced delay and packet losses are taken into account simultaneously. The random packet losses are described via the Bernoulli distribution. And then, the closed-loop system is modelled as an augmented time-delay system with interval time-varying delay. By using the Lyapunov stability theory and the augmented state space method, the sufficient conditions for the asymptotic stability of the closed-loop system are proposed in the form of linear matrix inequalities. At the same time, the design method of the ${H}_{\infty }$ controller is created. Finally, a numerical example is employed to illustrate the effectiveness of the proposed method.

scholarly journals Cooperative Attitude Control of Multiple Rigid Bodies with Multiple Time-Varying Delays and Dynamically Changing Topologies

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Ziyang Meng ◽  
Zheng You ◽  
Guanhua Li ◽  
Chunshi Fan
Keyword(s):  
Attitude Control ◽  
Closed Loop ◽  
Rigid Bodies ◽  
Loop System ◽  
Multiple Time ◽  
Time Varying ◽  
Communication Delays ◽  
Closed Loop System ◽  
Attitude Tracking ◽  
Uniformly Ultimate Boundedness

Cooperative attitude regulation and tracking problems are discussed in the presence of multiple time-varying communication delays and dynamically changing topologies. In the case of cooperative attitude regulation, we propose conditions to guarantee the stability of the closed-loop system when there exist multiple time-varying communication delays. In the case of cooperative attitude tracking, the result of uniformly ultimate boundedness of the closed-loop system is obtained when there exist both multiple time-varying communication delays and dynamically changing topologies. Simulation results are presented to validate the effectiveness of these conclusions.

Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

2011 ◽  
Vol 226 (2) ◽  
pp. 204-214 ◽  
Author(s):  
M M Arefi ◽  
M R Jahed-Motlagh
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Lyapunov Theory ◽  
Loop System ◽  
Time Varying ◽  
Closed Loop System ◽  
Mismatched Uncertainties ◽  
Non Linear ◽  
Non Linear Systems

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

scholarly journals Robust Optimal Attitude Controller for MIMO Uncertain Hexarotor MAVs: Disturbance Observer-Based

2016 ◽  
Vol 2016 ◽  
pp. 1-24 ◽  
Author(s):  
Nurul Dayana Salim ◽  
Dafizal Derawi ◽  
Hairi Zamzuri ◽  
Kenzo Nonami ◽  
Mohd Azizi Abdul Rahman
Keyword(s):  
Nonlinear Dynamics ◽  
Attitude Control ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Control Design ◽  
Loop System ◽  
Parametric Uncertainties ◽  
Time Varying ◽  
Closed Loop System ◽  
External Time

This paper proposes a robust optimal attitude control design for multiple-input, multiple-output (MIMO) uncertain hexarotor micro aerial vehicles (MAVs) in the presence of parametric uncertainties, external time-varying disturbances, nonlinear dynamics, and coupling. The parametric uncertainties, external time-varying disturbances, nonlinear dynamics, and coupling are treated as the total disturbance in the proposed design. The proposed controller is achieved in two simple steps. First, an optimal linear-quadratic regulator (LQR) controller is designed to guarantee that the nominal closed-loop system is asymptotically stable without considering the total disturbance. After that, a disturbance observer is integrated into the closed-loop system to estimate the total disturbance acting on the system. The total disturbance is compensated by a compensation input based on the estimated total disturbance. Robust properties analysis is given to prove that the state is ultimately bounded in specified boundaries. Simulation results illustrate the robustness of the disturbance observer-based optimal attitude control design for hovering and aggressive flight missions in the presence of the total disturbance.

scholarly journals Disturbance Observer-Based Continuous Finite-Time Sliding Mode Control against Matched and Mismatched Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ngo Phong Nguyen ◽  
Hyondong Oh ◽  
Yoonsoo Kim ◽  
Jun Moon
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Time Varying ◽  
Time Stability ◽  
Closed Loop System ◽  
Finite Time Stability ◽  
Mismatched Disturbances

In this paper, we propose the disturbance observer-based continuous finite-time sliding mode controller (DOBCSMC) for input-affine nonlinear systems in which additive matched and mismatched disturbances exist. The objective is to show the robustness and disturbance attenuation performance of the closed-loop system with the proposed DOBCSMC subjected to general classes of matched and mismatched disturbances. The proposed DOBCSMC consists of three main features: (i) the nonlinear finite-time disturbance observer to obtain a fast and accurate estimation of matched and mismatched disturbances, (ii) the nonlinear sliding surface to ensure high precision in the steady-state phase of the controlled output, and (iii) the continuous supertwisting algorithm to guarantee finite-time convergence of the controlled output and reduce the chattering under the effect of matched and mismatched disturbances. It should be noted that the existing approaches cannot handle time-varying mismatched disturbances and/or cannot guarantee faster finite-time stability of the controlled output. We prove that the closed-loop system with the DOBCSMC guarantees both finite-time reachability to the sliding surface and finite-time stability of the controlled output to the origin. Various simulations are performed to demonstrate the effectiveness of the proposed DOBCSMC. In particular, the simulation results show that the DOBCSMC guarantees faster convergence of the closed-loop system to the origin, higher precision of the controlled output, and better robustness performance against various classes of (time-varying) matched and mismatched disturbances, compared with the existing approaches.

Vibration reduction in flexible systems using a time-varying impulse sequence

Robotica ◽  
1995 ◽  
Vol 13 (3) ◽  
pp. 305-313 ◽  
Author(s):  
Jung-Keun Cho ◽  
Youn-Sik Park
Keyword(s):  
Vibration Suppression ◽  
Linear Time ◽  
Robot Manipulator ◽  
Input Shaping ◽  
Time Varying ◽  
Vibrational Modes ◽  
Flexible Systems ◽  
Overhead Crane ◽  
Shaping Technique ◽  
Time Varying Systems

SummaryAn input shaping technique using a time-varying impulse sequence is presented to reduce the motion-induced vibration of flexible systems in a feedforward way.The decoupled modal responses for a general linear time-varying system are firstly approximated. Upon this approximation, the time-varying impulse sequences to suppress the vibrational modes are found. The reference inputs to the systems are shaped by convolving with the time-varying impulse sequence to suppress the multimode vibrations. This technique can be also applied to suppress the vibration of nonlinear time-varying systems.The performance of this method is demonstrated with two practical examples: a moving overhead crane and a two-link robot manipulator. Consequently, this study provides an input shaping technique applicable to the vibration suppression of broader classes of flexible systems.

scholarly journals Design of State-Feedback Controllers for Linear Parameter Varying Systems Subject to Time-Varying Input Saturation

2019 ◽  
Vol 9 (17) ◽  
pp. 3606
Author(s):  
Adrián Ruiz ◽  
Damiano Rotondo ◽  
Bernardo Morcego
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Loop System ◽  
Feasibility Problem ◽  
Time Varying ◽  
Linear Parameter ◽  
Closed Loop System ◽  
Linear Parameter Varying ◽  
Quadratic Lyapunov Functions ◽  
Parameter Varying

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.

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