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.

Flight Control Law Design Using Dynamic Inversion for Linear Parameter Varying Systems

1998 ◽  
Vol 120 (2) ◽  
pp. 200-207 ◽  
Author(s):  
D. Malloy ◽  
B. C. Chang
Keyword(s):  
Flight Control ◽  
Closed Loop ◽  
Broad Class ◽  
Nonlinear Function ◽  
Loop System ◽  
Linear Parameter ◽  
Closed Loop System ◽  
Outer Loop ◽  
Linear Parameter Varying ◽  
Parameter Varying

A regulator design technique is presented for linear parameter varying (LPV) systems. This technique may be applied to many different types of systems, including nonlinear, due to the broad class of systems that may be represented by LPVs. The regulator, consisting of an inner loop and an outer loop, renders the closed-loop system’s steady-state input-output to be linear time invariant (LTI) and causes the output to track a commanded trajectory. With real-time, accurate parameter data, the inner loop effectively cancels the parameter dependent terms. The outer loop is designed using LTI H∞ synthesis to enable the closed loop system to meet stability and performance goals. Due to the inner loop controller and imperfect parameter cancellation, the complete closed-loop system is likely to be a nonlinear function of the parameters and their derivatives. To assess the stability using the quadratic Lyapunov test, we model the closed-loop system as a polytopic system. The key ideas are illustrated with a nonlinear aircraft flight control example.

Robust augmented lateral acceleration flight control design for a quasi-linear parameter-varying missile

2005 ◽  
Vol 219 (2) ◽  
pp. 171-181 ◽  
Author(s):  
L Bruyere ◽  
A Tsourdos ◽  
B A White
Keyword(s):  
Linear Model ◽  
Closed Loop ◽  
Loop System ◽  
Lateral Acceleration ◽  
Linear Parameter ◽  
Input Output ◽  
Closed Loop System ◽  
Linear Parameter Varying ◽  
Aerodynamic Derivatives ◽  
Operating Points

An augmented lateral acceleration autopilot is designed for a model of a tactical missile and robust stability of the closed-loop system investigated. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. This non-linear model is obtained from the Taylor linearized model of the horizontal motion by including explicit dependence of the aerodynamic derivatives on a state (side-slip velocity) and external parameters (longitudinal velocity and roll angle). The autopilot design is based on input-output pseudolinearization, which is a restriction of input-output feedback linearization to the set of equilibria of the non-linear model. The design makes Taylor linearization of the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one linear model will describe closed-loop dynamics, regardless of the rate of change in the operating points. Simulations for constant lateral acceleration demands show good tracking with fast response time. Robust autopilot design taking into account parametric stability margins for uncertainty aerodynamic derivatives is implemented using convex optimization and linear matrix inequalities.

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.

scholarly journals Average dwell time approach to H∞ filter for continuous-time switched linear parameter varying systems with time-varying delay

2018 ◽  
Vol 233 (1) ◽  
pp. 80-90
Author(s):  
Shenquan Wang ◽  
Wenchengyu Ji ◽  
Yulian Jiang ◽  
Keping Liu
Keyword(s):  
Dwell Time ◽  
Optimal Algorithm ◽  
Average Dwell Time ◽  
Time Varying ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Time Varying Delay ◽  
Parameter Varying ◽  
Varying Delay

Considering two types of delays including both time-varying delay and parameter varying delay in continuous switched linear parameter varying systems, the problem of [Formula: see text] filtering under average dwell time switching is illustrated. The [Formula: see text] filter depending on the linear time-varying parameter [Formula: see text] (mode-dependent parameterized filter) is designed at first. Then, based on multiple Lyapunov function and an improved reciprocally convex inequality, the corresponding existence sufficient conditions for the filter could ensure the obtained filter error system exponentially stable with a guaranteed [Formula: see text] performance in the form of linear matrix inequalities. In addition, the designed filter gains under allowed switching signals are computed via the proposed convex optimal algorithm. In the end, two numerical examples show the effectiveness of the results in this work.

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