A QFT Framework for Antiwindup Control Systems Design

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
J. C. Moreno ◽  
A. Baños ◽  
M. Berenguel
Keyword(s):  
Control Systems ◽  
Robust Stability ◽  
Stability Problem ◽  
Degrees Of Freedom ◽  
Actuator Saturation ◽  
Linear Time ◽  
Design Method ◽  
Systems Design ◽  
Linear Matrix ◽  
Single Input Single Output

The paper is devoted to the robust stability problem of linear time invariant feedback control systems with actuator saturation, especially in those cases with potentially large parametric uncertainty. The main motivation of the work has been twofold: First, most of the existing robust antiwindup techniques use a conservative plant uncertainty description, and second, previous quantitative feedback theory (QFT) results for control systems with actuator saturation are not suitable to achieve robust stability specifications when the control system is saturated. Traditionally, in the literature, this type of problems has been solved in terms of linear matrix inequalities (LMIs), using less structured uncertainty descriptions as given by the QFT templates. The problem is formulated for single input single output systems in an input-output (I/O) stability sense, and is approached by using a generic three degrees of freedom control structure. In this work, a QFT-based design method is proposed in order to solve the robust stability problem of antiwindup design methods. The main limitation is that the plant has poles in the closed left half plane, and at most, has one integrator. The work investigates robust adaptations of the Zames–Falb stability multipliers result, and it may be generalized to any compensation scheme that admits a decomposition as a feedback interconnection of linear and nonlinear blocks (Lur’e type system), being antiwindup systems as a particular case. In addition, an example will be shown, making explicit the advantages of the proposed method in relation to previous approaches.

scholarly journals A New Anti-Windup Compensator Based on Quantitative Feedback Theory for an Uncertain Linear System with Input Saturation

2019 ◽  
Vol 9 (15) ◽  
pp. 2958 ◽  
Author(s):  
R. Jeyasenthil ◽  
Seung-Bok Choi
Keyword(s):  
Robust Stability ◽  
Actuator Saturation ◽  
Linear Time ◽  
Input Saturation ◽  
Design Procedure ◽  
Feedback System ◽  
Linear Matrix ◽  
Quantitative Feedback Theory ◽  
Uncertain Linear System ◽  
Effective Manner

This paper devotes to the robust stability problem for an uncertain linear time invariant (LTI) feedback system with actuator saturation nonlinearity. Based on a three degree of freedom (DOF) non-interfering control structure, the robust stability is enforced with the describing function (DF) approach for an uncertain LTI system to avoid the limit cycle. A new type of anti-windup (AW) compensator is designed using the quantitative feedback theory (QFT) graphical method, which results in a simple design procedure and low-order AW control system. One of the most significant benefits of the proposed method is free of the non-convexity (intractable) drawback of the linear matrix inequality (LMI)-based approach. The analysis conducted on the benchmark problem clearly reveals that the proposed QFT-based anti-windup design is able to handle both saturation and uncertainty in a very effective manner.

Parameter-Dependent Feedback Compensator Design for a Time-Fractional Reaction-Diffusion Equation

2021 ◽  
Author(s):  
Jun-Wei Wang ◽  
Hua-Cheng Zhou
Keyword(s):  
Linear Time ◽  
Design Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Linear Matrix ◽  
Parametric Form ◽  
Coupled Equations ◽  
Reaction Coefficient ◽  
Standard Linear ◽  
Parameter Dependent

Abstract This paper presents a parameter-dependent design of feedback compensator with space-varying gains for Mittag-Leffler stabilization of linear time fractional parabolic MIMO partial differential equations subject to space-varying diffusion and reaction coefficients. In the proposed design method, under a boundedness assumption, the reaction coefficient is written in a parametric form. By using the parametric form for the reaction coefficient and multiple non-collocated observation outputs, an observer-based state feedback compensator with space-varying gains is then constructed such that the resulting closed-loop coupled equations are Mittag-Leffler stable. By applying the Lyapunov technique with Caputo fractional derivative and variants of Poincaré–Wirtinger’s inequality, a sufficient condition for the existence of such feedback compensator is presented in terms of standard linear matrix inequalities. Finally, simulation results are presented to support the proposed design method.

scholarly journals Anti-Saturation Control of Uncertain Time-Delay Systems with Actuator Saturation Constraints

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 375
Author(s):  
Hejun Yao
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Saturation Control ◽  
Systems Model

The problem of anti-saturation control for a class of time-delay systems with actuator saturation is considered in this paper. By introducing appropriate variable substitution, a new delay time-delay systems model with actuator saturation systems is established. Based on the Lyapunov stability theory, the stability condition and the anti-saturation controller design method are obtained by using the linear matrix inequality approach. By introducing the matrix into the Lyapunov function, the proposed conditions are less conservative than the previous results. Finally, a simulation example shows the validity and rationality of the method.

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

2004 ◽  
Vol 10 (1) ◽  
pp. 55-84
Author(s):  
Raffi Derkhorenian ◽  
Nader Jalili ◽  
D M Dawson
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Linear Time ◽  
Vibration Absorber ◽  
Primary System ◽  
Control Input ◽  
Adaptation Algorithm ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output

In this paper we describe the design and implementation of a nonlinear adaptive disturbance rejection approach for single-input-single-output linear-time-invariant uncertain systems subject to sinusoidal disturbances with unknown amplitude and frequency. This is an extension of our earlier study to a more complicated plant, a two-degrees-of-freedom (2DOF) system representing a vibration absorber setting. The controller design is based on a single Lyapunov function incorporating both the error states and the update laws and, hence, global stability and improved transient performance are readily achieved. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through real-time simulations, both for regulation and tracking, on a 2DOF system representing an active vibration absorber setup. It is shown that when the primary system is subjected to an unknown sinusoidal disturbance, the proposed controller in the absorber subsection completely suppresses the primary system vibration in the presence of unknown disturbance.

scholarly journals H∞Guaranteed Cost Control for Networked Control Systems under Scheduling Policy Based on Predicted Error

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Qixin Zhu ◽  
Kaihong Lu ◽  
Yonghong Zhu
Keyword(s):  
Control Systems ◽  
Prediction Error ◽  
Networked Control Systems ◽  
Design Method ◽  
Networked Control ◽  
Collision Probability ◽  
Linear Matrix ◽  
Scheduling Policy ◽  
Network Bandwidth ◽  
Guaranteed Cost

Scheduling policy based on model prediction error is presented to reduce energy consumption and network conflicts at the actuator node, where the characters of networked control systems are considered, such as limited network bandwidth, limited node energy, and high collision probability. The object model is introduced to predict the state of system at the sensor node. And scheduling threshold is set at the controller node. Control signal is transmitted only if the absolute value of prediction error is larger than the threshold value. Furthermore, the model of networked control systems under scheduling policy based on predicted error is established by taking uncertain parameters and long time delay into consideration. The design method ofH∞guaranteed cost controller is presented by using the theory of Lyapunov and linear matrix inequality (LMI). Finally, simulations are included to demonstrate the theoretical results.

Semi-Active Vibration Isolation Control for Multi-Degree-of-Freedom Structures

2002 ◽  
Author(s):  
Hidekazu Nishimura ◽  
Yasuhiko Okumura ◽  
Seiji Shimodaira
Keyword(s):  
Vibration Isolation ◽  
Linear Time ◽  
Design Method ◽  
Linear Matrix ◽  
Orifice Area ◽  
Convex Interpolation ◽  
Active Vibration ◽  
Active Damper ◽  
Gain Scheduled ◽  
Active Vibration Isolation

In this paper, we propose a design method of a controller for semi-active vibration isolation. We introduce a mechanism of a semi-active damper, which can change the damping in the ratio of the orifice area, in order to obtain the parameter-varying system model. Consideration of the semi-active damper mechanism is appropriate for the design of the gain-scheduled (GS) controller based on linear matrix inequalities (LMIs). The GS controller consists of four-vertex linear time-invaxiant controllers are obtained by the convex interpolation of these controllers. The designed controller switches at zero velocity of the damper and varies according to both the orifice area and the relative velocity of the isolation layer. By carrying out simulations, it is shown that our proposed method is effective for the suppression of seismic response.

Full Flight Envelope Transient Main Control Loop Design Based on LMI Optimization

2020 ◽  
Author(s):  
Keqiang Miao ◽  
Xi Wang ◽  
Meiyin Zhu
Keyword(s):  
Robust Stability ◽  
Design Method ◽  
Settling Time ◽  
Pole Placement ◽  
Linear Matrix ◽  
Control Loop ◽  
Turbofan Engine ◽  
Loop Design ◽  
Gain Schedule ◽  
Flight Envelope

Abstract To solve the problem of full flight envelope transient main control loop design of turbofan engine, a design method based on linear matrix inequality (LMI) is proposed. Robust stability of the closed-loop turbofan engine system in all conditions is proved by using Lyapunov inequalities. The robust performance is ensured by gain-schedule and pole-placement. Reduced order multivariable gain-schedule and minimum trace optimization algorithm are presented to guarantee the feasibility of the design method. Full flight envelope simulations based on a nonlinear turbofan engine model were done. The results show that the maximum settling time of N1cor is 4.3s and the maximum overshoot is 1.7%. The maximum settling time of N2cor is 4.5s and the maximum overshoot is 0.1%. The robust stability and consistent performance in full flight envelope are also shown in the results.

scholarly journals Fault Detection of Networked Control Systems Based on Sliding Mode Observer

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jie Zhang ◽  
Ming Lyu ◽  
Hamid Reza Karimi ◽  
Yuming Bo
Keyword(s):  
Fault Detection ◽  
Control Systems ◽  
Discrete Time ◽  
Networked Control Systems ◽  
Sliding Mode ◽  
Design Method ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Linear Matrix ◽  
Bounded Disturbances

This paper is concerned with the network-based fault detection problem for a class of nonlinear discrete-time networked control systems with multiple communication delays and bounded disturbances. First, a sliding mode based nonlinear discrete observer is proposed. Then the sufficient conditions of sliding motion asymptotical stability are derived by means of the linear matrix inequality (LMI) approach on a designed surface. Then a discrete-time sliding-mode fault observer is designed that is capable of guaranteeing the discrete-time sliding-mode reaching condition of the specified sliding surface. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

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