Observer Based Adaptive Estimation/Cancellation of Unmatched Sinusoidal Disturbances in Known LTI Systems by State Derivative Measurement

2015 ◽  
Author(s):  
Halil Ibrahim Basturk
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Adaptive Estimation ◽  
Original System ◽  
Feedback System ◽  
Open Loop ◽  
The State ◽  
Adaptive Observer ◽  
Order System ◽  
Linear Time Invariant

In this paper, an adaptive observer and backstepping controller are designed to cancel and estimate sinusoidal disturbances forcing a linear time-invariant by using only the measurements of the state-derivatives. The parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters with the necessary filter designs enables to approach the problem as an adaptive control problem. An observer is designed for the unmeasured virtual input to apply a backstepping procedure which handles the unmatched disturbance and input condition. Firstly, it is shown that the disturbance and the unmeasured actuator state are observed perfectly in the open loop case. Secondly, the closed loop case is considered and it is proven that the equilibrium of the closed-loop adaptive system is stable and the state of the considered original system converge to zero as t → ∞ with perfect disturbance estimation. The effectiveness of the controller and the observers are illustrated with a simulation example of a third order system.

Adaptive Cancellation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Halil İ. Baştürk ◽  
Miroslav Krstic
Keyword(s):  
Linear Time ◽  
Feedback System ◽  
Adaptive Controller ◽  
Order System ◽  
Output Vector ◽  
Linear Time Invariant ◽  
Exponentially Stable ◽  
Adaptive Cancellation ◽  
Linear Time Invariant System ◽  
Time Invariant

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our design is based on three steps; (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector, (2) design of an adaptive disturbance observer and, (3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second-order system.

Adaptive Cancelation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

2011 ◽  
Author(s):  
Halil I˙. Bas¸tu¨rk ◽  
Miroslav Krstic
Keyword(s):  
Linear Time ◽  
Feedback System ◽  
Adaptive Controller ◽  
Order System ◽  
Output Vector ◽  
Linear Time Invariant ◽  
Exponentially Stable ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Linear And Nonlinear Systems

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our design is based on three steps; 1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector, 2) design of an adaptive disturbance observer and, 3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second order system.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

Adaptive Estimation Using Multiagent Network Identifiers With Undirected and Directed Graph Topologies

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Teymur Sadikhov ◽  
Michael A. Demetriou ◽  
Wassim M. Haddad ◽  
Tansel Yucelen
Keyword(s):  
Directed Graph ◽  
Adaptive Estimation ◽  
Parameter Estimate ◽  
The State ◽  
Adaptive Observer ◽  
Parameter Estimates ◽  
Communication Architecture ◽  
Adaptive Identifier ◽  
The Mean ◽  
Additive Term

In this paper, we present an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies. Specifically, the system state and plant parameters are identified online using N agents implementing adaptive observers with an interagent communication architecture. The adaptive observer architecture includes an additive term which involves a penalty on the mismatch between the state and parameter estimates. The proposed architecture is shown to guarantee state and parameter estimate consensus. Furthermore, the proposed adaptive identifier architecture provides a measure of agreement of the state and parameter estimates that is independent of the network topology and guarantees that the deviation from the mean estimate for both the state and parameter estimates converge to zero. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Complete moment convergence for the dependent linear processes with application to the state observers of linear-time-invariant systems

2020 ◽  
Vol 65 (4) ◽  
pp. 725-745
Author(s):  
Chao Lu ◽  
Chao Lu ◽  
Xuejun J Wang ◽  
Xuejun J Wang ◽  
Yi Wu ◽  
...  
Keyword(s):  
Linear Time ◽  
The State ◽  
Complete Moment Convergence ◽  
Linear Processes ◽  
Linear Time Invariant ◽  
Moment Convergence ◽  
State Observers ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Пусть $X_t=\sum_{j=-\infty}^{\infty}A_j\varepsilon_{t-j}$ - зависимый линейный процесс, где $\{\varepsilon_n, n\in \mathbf{Z}\}$ - последовательность $m$-обобщенных отрицательно зависимых ($m$-END) случайных величин с нулевым средним, которая стохастически доминируется случайной величиной $\varepsilon$, и пусть $\{A_n, n\in \mathbf{Z}\}$ - другая последовательность случайных величин с нулевым средним, обладающая свойством $m$-END. При подходящих условиях установлена полная моментная сходимость для зависимых линейных процессов. В частности, приведены достаточные условия полной моментной сходимости. В качестве приложения исследуется сходимость наблюдателей состояния для линейных стационарных систем.

scholarly journals Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 300
Author(s):  
Marcin Bąkała ◽  
Piotr Duch ◽  
J. A. Tenreiro Machado ◽  
Piotr Ostalczyk ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Linear Time ◽  
Classical Model ◽  
Linear Difference Equation ◽  
Discrete Models ◽  
Measured Velocity ◽  
Linear Time Invariant ◽  
Wheel Drive ◽  
Time Invariant

This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used as the reference. According to the sum of the squared error criterion (SSE), we compare a two-parameter integer order model with four-parameter non-commensurate and three-parameter commensurate FO descriptions. The computer simulation results are compared with the measured velocity of a real autonomous platform powered by a closed-loop electric individual-wheel drive.

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