Parameterized Regulator Design Method for Switched Linear Systems

2006 ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Design Method ◽  
Loop System ◽  
Closed Loop System ◽  
Switched Linear System ◽  
Switched Linear Systems ◽  
Central Controller ◽  
Synthesis Approach ◽  
System Switching

In this paper, a parameterized regulator design method based on bilinear matrix inequalities (BMIs) is presented for switched linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. Switching among plant models as well among disturbance and reference signals is defined according to a switching surface. The regulator design approach consists of three steps. The first step consists of constructing a switched observer-based state-feedback central controller for the switched linear system. Switching in the controller is performed according to the same switching rule as in the plant. The second step involves augmenting the switched central-controller to construct a parameterized set of switched controllers. Conditions for internal stability of the resulting switched closed loop system are presented. In the third step, regulation conditions are derived for the switched closed loop system. Based on the regulation conditions, a regulator synthesis approach is proposed based on solving properly formulated BMIs. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.

scholarly journals Parameterized Regulator Synthesis for Bimodal Linear Systems Based on Bilinear Matrix Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Linear Systems ◽  
Design Method ◽  
Second Step ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Switched Linear System ◽  
Central Controller ◽  
Bilinear Matrix Inequalities ◽  
Synthesis Approach ◽  
Selection Of

A regulator design method is presented for switched bimodal linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. The switching in the bimodal system is defined by a switching surface. The regulator design approach consists of three steps. The first step is based on constructing a switched observer-based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics to construct a parameterized set of switched controllers. In the third step, two sufficient regulation conditions are derived for the resulting switched closed loop system. The regulation conditions present guidelines for the selection of the additional dynamics used to parameterize the switched controllers to yield the desired regulator. A regulator synthesis approach is proposed based on solving properly formulated bilinear matrix inequalities. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.

Application of Approximate I/O Linearization to Aircraft Flight Control

1994 ◽  
Vol 116 (3) ◽  
pp. 429-436 ◽  
Author(s):  
A. W. Lee ◽  
J. K. Hedrick
Keyword(s):  
Control Problem ◽  
Flight Control ◽  
Closed Loop ◽  
Performance Enhancement ◽  
Design Method ◽  
Loop System ◽  
Closed Loop System ◽  
Aircraft Flight Control ◽  
Original Plant ◽  
Control Saturation

This paper examines the performance enhancement of a statically unstable aircraft subject to the input and state constraints. Under control saturation, i/o linearizability is destroyed and the state trajectories may not be attracted to the sliding surface. If the reference signals are sufficiently large and the zero-dynamics is lightly damped, the i/o linearizing control may become unreasonably large in magnitude, making the closed-loop system susceptible to the damaging effects of control saturation. In addition to performance degradations such as increased tracking errors, control saturation can drive the closed-loop system to instability. In this paper, a new design method called approximate i/o linearization is presented to enhance the performance of the SISO longitudinal flight control problem under saturation. The new approximate i/o linearization law is obtained by solving a pointwise minimization problem. The function to be minimized consists of a surface whose relative degree is one, its derivative, and weighted square of the input u. The advantages of the approximate i/o linearization is that the adverse effects of control saturation can be minimized by properly selecting the weight on the usage of the control. The only requirement for the new technique is that the original plant be locally i/o linearizable. Thus approximate i/o linearization does not impose additional strict requirements on the plant. In the remaining sections of the paper, stability and bounded tracking properties of the approximate i/o linearization are proven. Finally, a longitudinal flight control problem is used to demonstrate the application of approximate i/o linearization.

The Application of Fractional Order Calculus in Closed-Loop System Control

2012 ◽  
Vol 442 ◽  
pp. 315-320
Author(s):  
Yun Fang Feng
Keyword(s):  
Closed Loop ◽  
Design Method ◽  
Open Loop ◽  
Loop System ◽  
System Control ◽  
Closed Loop System ◽  
Open Loop System ◽  
System Robustness ◽  
Fractional Controller ◽  
Frequency Phase

A design method of fractional controller has been developed to meet the five different specifications, including for the closed-loop system robustness. The specifications of cross frequency, phase to get financing ϕ meters and robustness and complete performance curve based on level off the stage of open loop system, ensure damping is worse reaction time of model uncertainty gain change.

Passivity-Based Stabilization of Underactuated Mechanical Systems

2013 ◽  
Vol 421 ◽  
pp. 16-22
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Closed Loop ◽  
Control Method ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Stabilization Control

A new stabilization control method for underactuated linear mechanical systems is presented in this paper. By proper setting the desired closed-loop system, the matching condition for controller design is reduced to one equation and an adjustable parameter (damping coefficient) is introduced to the controller. Stability of the closed-loop system is proved based on passivity. As an application example, stabilization control of 2-DOF Pendubot is studied. The system is linearized at its equilibrium point and the proposed controller design method is applied to the linearized system. The procedure of solving matching condition and design controller for the Pendubot is provided. The simulation results verify feasibility of the proposed method.

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.

Reliable Η∞ Control for Discrete-Time Switched Linear Systems with Intermittent Measurements

2011 ◽  
Vol 181-182 ◽  
pp. 145-150
Author(s):  
Dong Sheng Du
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Stochastic Variable ◽  
Switched Linear Systems ◽  
Stochastically Stable ◽  
Intermittent Measurements

In this paper, a scheme of reliable control for switched linear systems with intermittent measurements is developed. The stochastic variable is assumed to be a Bernoulli distributed white sequence appearing in measured output. Sufficient conditions for the existence of the switched observer and the switched controller are derived in terms of linear matrix inequalities (LMIs), which can maintain the closed-loop system is stochastically stable with a prescribed performance level.

Stochastic disturbance observer-based adaptive anti-disturbance control for non-linear systems with stochastic non-harmonic multiple disturbances

2017 ◽  
Vol 40 (10) ◽  
pp. 3222-3231 ◽  
Author(s):  
Yanpeng Pan
Keyword(s):  
Linear Systems ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Loop System ◽  
State Feedback Control ◽  
Closed Loop System ◽  
Stochastic Disturbance ◽  
Multiple Disturbances ◽  
Non Linear ◽  
Non Linear Systems

In this paper, the problem of anti-disturbance control is studied for non-linear systems with stochastic multiple disturbances. The multiple disturbances include two types: one is the stochastic harmonic disturbance and the other non-harmonic noise generated by a linear stochastic exogenous system. An adaptive stochastic disturbance observer (ASDO) is constructed to estimate both the two aforementioned disturbances. Combining the disturbance estimation with a conventional state feedback control law, a composite anti-disturbance control scheme is constructed such that the closed-loop system is stochastically stable, and different types of disturbances may be attenuated and rejected. By using the Lyapunov function method and linear matrix inequalities technique, sufficient conditions for the stochastic stability of the closed-loop system are established. Moreover, an adaptive stochastic extended state observer (ASESO) is proposed for the output feedback case. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.

scholarly journals Anti-windup design with guaranteed regions of stability for discrete-time linear systems with saturating controls

2004 ◽  
Vol 15 (1) ◽  
pp. 3-9 ◽  
Author(s):  
João Manoel Gomes da Silva Jr. ◽  
Romeu Reginatto ◽  
Sophie Tarbouriech
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Basin Of Attraction ◽  
Loop System ◽  
Discrete Time System ◽  
Closed Loop System ◽  
Model Stability ◽  
Quadratic Lyapunov Functions ◽  
Time Linear

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be modeled by a linear system connected to a deadzone nonlinearity. From this model, stability conditions based on quadratic Lyapunov functions are stated. Algorithms based on LMI schemes are proposed for computing both the anti-windup gain and an associated stability region.

Sampled-data mixed H∞ and passive control for attitude stabilization and vibration suppression of flexible spacecrafts with input delay

2018 ◽  
Vol 24 (22) ◽  
pp. 5401-5417 ◽  
Author(s):  
Baolong Zhu ◽  
Zhiping Zhang ◽  
Mingliang Suo ◽  
Ying Chen ◽  
Shunli Li
Keyword(s):  
Closed Loop ◽  
Passive Control ◽  
Vibration Suppression ◽  
Design Method ◽  
Performance Criterion ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Sampled Data ◽  
Closed Loop System

This paper deals with the problem of mixed [Formula: see text] and passive control for flexible spacecrafts subject to nonuniform sampling and time-varying delay in the input channel. An impulsive observer-based controller is introduced and the resulting closed-loop system is a hybrid system consisting of a continuous time-delay subsystem and an impulsive differential subsystem. As a first result, we derive a generalized bounded real lemma (GBRL), that is, a generalized [Formula: see text] performance criterion, for the impulsive differential subsystem by constructing a time-varying Lyapunov functional. Then, on the basis of this GBRL and utilizing the Lyapunov–Krasovskii approach, a sufficient condition is derived to asymptotically stabilize the closed-loop system and simultaneously guarantee a prescribed mixed [Formula: see text] and passivity performance index. A design method is proposed for the desired controller, which can be readily constructed by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, numerical experiments are provided to support the theoretical results, and comparisons with former approaches are also discussed.

Passivity-Based Tracking Control Design for Underactuated Mechanical Systems

2012 ◽  
Vol 591-593 ◽  
pp. 1225-1230 ◽  
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Design Procedures

Passivity-based tracking control of the underactuated linear mechanical systems is investigated in this paper. As our main contribution, the matching condition is decreased into two equations and an adjustable gain (damping gain) is introduced into the controller by setting the desired closed-loop system properly. Stability of the closed-loop system is proved based on passivity of the system. Furthermore, as examples, tracking control of 2-DOF Acrobot and 2-DOF Pendubot are studied. The systems are linearized at their equilibriums and the passivity-based controller design method is applied to the linearized systems. Matching conditions are solved and the design procedures of associate controllers for the two robots are provided. The simulation results show that the designed controllers can realize asymptotical tracking for the given desired trajectories.

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