scholarly journals Two-Valued Control for a Second-Order Plant with Additive External Disturbance

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Alejandro Rincon ◽  
Felipe Londoño ◽  
Fabiola Angulo
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Function Method ◽  
Controller Design ◽  
Tracking Error ◽  
Reference Signal ◽  
Second Order ◽  
State Feedback Control ◽  
Control Input ◽  
Residual Set

In this work a two-valued state feedback control for a plant of second order with known constant coefficients and an additive bounded disturbance is designed. In this controller the control signal can take only two possible values. The controller design is based on Lyapunov-like function method, achieving the convergence of the tracking error to a user-defined residual set. A boundedness condition for the user-defined reference signal is defined, which is necessary to allow out-put tracking. The developed scheme avoids large commutation rate of the control input. The controller design and stability analysis have important contributions with respect to closely related controllers based on the direct Lyapunov method, namely, (i) conditions to guarantee the expected convergence of the tracking error are established. These conditions are imposed on the reference signal and the extreme values of the control input. The stability analysis is developed by means of the Lyapunov-like function method and the Barbalat's Lemma and includes (ii) the bounded nature of the Lyapunov function, (iii) the monotonic convergence of the Lyapunov function to a residual set, and (iv) the asymptotic convergence of the tracking error to a residual set of user-defined size.

Synthesis, Stability Analysis, and Experimental Implementation of a Multirate Repetitive Learning Controller

2002 ◽  
Vol 124 (4) ◽  
pp. 668-674 ◽  
Author(s):  
Nader Sadegh ◽  
Ai-Ping Hu ◽  
Courtney James
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Tracking Error ◽  
Sampling Rate ◽  
Weighted Averaging ◽  
System Control ◽  
Control Input ◽  
Experimental Implementation ◽  
Repetitive Learning ◽  
Averaging Filter

This paper describes a multirate repetitive learning controller with an adjustable sampling rate that may be used as an “add-on” module to enhance the tracking performance of a feedback control system. The sampling rate of the multirate controller is slower than the remainder of the control system, and is selected by the user to achieve the required system performance based on a trade-off between the accuracy and the complexity of the controller. The multirate controller learns the system control input based on the tracking error down-sampled using a weighted averaging filter. The output of the multirate controller is up-sampled through an arbitrary hold mechanism determined by the user. This paper extends the existing stability results for single-rate repetitive learning controllers to the proposed multirate scheme. It provides an explicit procedure for its design and stability analysis. In addition, the proposed multirate repetitive learning controller is implemented on a mechanical system performing a non-colocated control task, where its effectiveness in reducing tracking errors while following periodic reference trajectories is shown experimentally.

Smooth second-order nonsingular terminal sliding mode control for reusable launch vehicles

2014 ◽  
Vol 7 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Shaobo Ni ◽  
Jiayuan Shan
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Tracking Error ◽  
Second Order ◽  
Convergence Time ◽  
Control Input ◽  
Terminal Sliding Mode ◽  
Content Type ◽  
Nonsingular Terminal Sliding Mode ◽  
Attitude Tracking

Purpose – The purpose of this paper is to present a sliding mode attitude controller for reusable launch vehicle (RLV) which is nonlinear, coupling, and includes uncertain parameters and external disturbances. Design/methodology/approach – A smooth second-order nonsingular terminal sliding mode (NTSM) controller is proposed for RLV in reentry phase. First, a NTSM manifold is proposed for finite-time convergence. Then a smooth second sliding mode controller is designed to establish the sliding mode. An observer is utilized to estimate the lumped disturbance and the estimation result is used for feedforward compensation in the controller. Findings – It is mathematically proved that the proposed sliding mode technique makes the attitude tracking errors converge to zero in finite time and the convergence time is estimated. Simulations are made for RLV through the assumption that aerodynamic parameters and atmospheric density are perturbed. Simulation results demonstrate that the proposed control strategy is effective, leading to promising performance and robustness. Originality/value – By the proposed controller, the second-order sliding mode is established. The attitude tracking error converges to zero in a finite time. Meanwhile, the chattering is alleviated and a smooth control input is obtained.

scholarly journals Complex Scaling Approach for Stability Analysis and Stabilization of Multiple Time-Delayed Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jun Zhou ◽  
Ketian Gao ◽  
Xinbiao Lu
Keyword(s):  
Stability Analysis ◽  
Linear Time ◽  
Open Loop ◽  
State Feedback Control ◽  
Multiple Time ◽  
Control Input ◽  
Complex Scaling ◽  
Delayed Systems ◽  
Static State ◽  
Linear Time Invariant

Based on complex scaling, the paper copes with stability analysis and stabilization of linear time-invariant continuous-time systems with multiple time delays in state, control input, and measured output, under state and/or output feedback. More specifically, the paper establishes stability criteria for exponential/asymptotical stability with Hurwitz complex scaling being applied to the related characteristic polynomials. The stability conditions are necessary and sufficient, delay-dependent, and independent of feedback structures and open-loop poles distribution. The criteria can be implemented graphically with locus plotting or numerically without it; moreover, no prior frequency sweeping is involved, and the contour and locus encirclement orientations can be self-defined. Exploiting the complex scaling approach and embracing its technical merits, it is considered to design static state feedback control for robustly stabilizing time-delayed systems. A small-gain interpretation for the suggested stabilization is also elaborated. Examples are included to illustrate the main results.

scholarly journals Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiao Yu
Keyword(s):  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
State Feedback Control ◽  
Control Action ◽  
Linear Matrix ◽  
Reference Trajectory ◽  
Integral Control ◽  
Control Approach ◽  
Output Tracking Control

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

scholarly journals A New Robust Controller with Applications to Bioreactors

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Alejandro Rincón ◽  
Christian Camilo Erazo Ordoñez ◽  
Felipe Londoño ◽  
Gerard Olivar Tost ◽  
Fabiola Angulo
Keyword(s):  
Tracking Error ◽  
Input Saturation ◽  
Function Technique ◽  
Model Parameters ◽  
Control Input ◽  
Input Output ◽  
Parameter Uncertainties ◽  
Observer Error ◽  
Residual Set ◽  
Input Output Linearization

In this work an anaerobic digester is controlled using input-output linearization and Lyapunov-like function methods. It is assumed that model parameters are unknown, time-varying, and bounded, and upper or lower bounds are also unknown. To tackle the effect of input saturation, a state observer is designed. The tracking and observer errors are defined in terms of the noisy measured output instead of ideal output, given by the mathematical model. The design of the observer mechanism and the update laws is based on the Lyapunov-like function technique, whereas the design of the control law is based on the input-output linearization method. In this paper two important properties of the controlled system are proven. First, the observer error converges asymptotically to a residual set whose size is user-defined, and such convergence is not disrupted, neither by the input saturation nor by the parameter uncertainties. Second, when the control input is nonsaturated the tracking error converges to a residual set whose size is user-defined. The model parameter uncertainties are included to prove the convergence of errors. Finally, a numerical example to validate the developed control is presented.

scholarly journals Tracking Control Strategy Using Filter-Based Approximation for the Unknown Control Direction Problem of Uncertain Pure-Feedback Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1341
Author(s):  
Yun Ho Choi ◽  
Sung Jin Yoo
Keyword(s):  
Controller Design ◽  
Tracking Error ◽  
Design Procedure ◽  
Control Input ◽  
State Variables ◽  
Feedback Systems ◽  
Unknown Control Directions ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction

A filter-based recursive tracker design approach is presented for the problem of unknown control directions of pure-feedback systems with completely unknown non-affine nonlinearities. In the controller design procedure, the first-order filters for error surfaces, a control input, and state variables are employed to design nonadaptive virtual and actual control laws independent of adaptive function approximators. In addition, for the unknown control direction problem, the filtering signals are incorporated with Nussbaum functions. Different from existing adaptive approximation-based control schemes in the presence of unknown control directions, the proposed approach does not require any adaptive technique regardless of completely unknown nonlinear functions. Therefore, a simplified tracking structure can be constructed. Using the Lyapunov stability analysis, it is shown that the tracking error is reduced within an adjustable neighborhood of the origin while ensuring all the closed-loop signals are bounded.

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