Stable Controller Interpolation and Controller Switching for LPV Systems

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Bryan P. Rasmussen ◽  
Young Joon Chang
Keyword(s):  
Closed Loop ◽  
A Priori ◽  
Gain Scheduling ◽  
Phase System ◽  
Closed Loop System ◽  
Linear Parameter Varying ◽  
Nonminimum Phase ◽  
Quadratic Stability ◽  
Critical Design ◽  
Guaranteed Stability

This paper examines the gain-scheduling problem with a particular focus on controller interpolation with guaranteed stability of the nonlinear closed-loop system. For linear parameter varying model representations, a method of interpolating between controllers utilizing the Youla parametrization is proposed. Quadratic stability despite fast scheduling is guaranteed by construction, while the characteristics of individual controllers designed a priori are recovered at critical design points. Methods for reducing the state dimension of the interpolated controller are also given. The capability of the proposed approach to guarantee stability despite arbitrarily fast transitions leads naturally to application to switched linear systems. The efficacy of the method is demonstrated in simulation using a multi-input, multi-output, nonminimum-phase system, while interpolating between two controllers of different sizes and structures.

Robust Gain-Scheduling Controller for Airbreathing Hypersonic Flight Vehicle

2014 ◽  
Vol 716-717 ◽  
pp. 1624-1630 ◽  
Author(s):  
Yuan Chuan Shen ◽  
Jian Qiao Yu ◽  
Guan Chen Luo ◽  
Rui Guang Yang
Keyword(s):  
Closed Loop ◽  
Dynamic Performance ◽  
Gain Scheduling ◽  
Flight Vehicle ◽  
Linear Parameter ◽  
Closed Loop System ◽  
Linear Parameter Varying ◽  
Technical Challenge ◽  
Hypersonic Flight Vehicle ◽  
Hypersonic Flight

This paper addresses issues related to robust control for an airbreathing hypersonic flight vehicle. Owing to aero-propulsion couplings caused by the unique structure shape, the model of the vehicle is greatly nonlinear and complex, which presents an enormous technical challenge for control. The nonlinear model is transformed into a linear fractional transformation (LFT) model, and a robust gain-scheduling controller based on linear parameter-varying control (LPV) with full block multipliers is obtained. Simulations illustrate great improvements of the dynamic performance in closed-loop system.

LPV Based Sliding Mode Control for Limit Protection of Aircraft Engines

2018 ◽  
Author(s):  
Shubo Yang ◽  
Xi Wang
Keyword(s):  
Closed Loop ◽  
Sliding Mode ◽  
Aircraft Engine ◽  
Gain Scheduling ◽  
Engine Control ◽  
Aircraft Engines ◽  
Sliding Surface ◽  
Closed Loop System ◽  
Limit Protection ◽  
The Stability

Limit protection, which frequently exists as an auxiliary part in control systems, is not the primary motive of control but is a necessary guarantee of safety. As in the case of aircraft engine control, the main objective is to provide the desired thrust based on the position of the throttle; nevertheless, limit protection is indispensable to keep the engine operating within limits. There are plenty of candidates that can be applied to design the regulators for limit protection. PID control with gain-scheduling technique has been used for decades in the aerospace industry. This classic approach suggests linearizing the original nonlinear model at different power-level points, developing PID controllers correspondingly, and then scheduling the linear time-invariant (LTI) controllers according to system states. Sliding mode control (SMC) is well-known with mature theories and numerous successful applications. With the one-sided convergence property, SMC is especially suitable for limit protection tasks. In the case of aircraft engine control, SMC regulators have been developed to supplant traditional linear regulators, where SMC can strictly keep relevant outputs within their limits and improve the control performance. In aircraft engine control field, we all know that the plant is a nonlinear system. However, the present design of the sliding controller is carried out with linear models, which severely restricts the valid scope of the controller. Even if the gain scheduling technique is adopted, the stability of the whole systems cannot be theoretically proved. Research of linear parameter varying (LPV) system throws light on a class of nonlinear control problems. In present works, we propose a controller design method based on the LPV model to solve the engines control problem and achieve considerable effectiveness. In this paper, we discuss the design of a sliding controller for limit protection task of aircraft engines, the plant of which is described as an LPV system instead of LTI models. We define the sliding surface as tracking errors and, with the aid of vertex property, present the stability analysis of the closed-loop system on the sliding surface. An SMC law is designed to guarantee that the closed-loop system is globally attracted to the sliding surface. Hot day (ISA+30° C) takeoff simulations based on a reliable turbofan model are presented, which test the proposed method for temperature protection and verify its stability and effectiveness.

Dynamic Analysis of Noncollocated Flexible Arms and Design of Torque Transmission Mechanisms

1994 ◽  
Vol 116 (2) ◽  
pp. 201-207 ◽  
Author(s):  
Jahng-Hyon Park ◽  
Haruhiko Asada
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Design Guidelines ◽  
Phase System ◽  
Nonminimum Phase ◽  
Transmission Mechanisms ◽  
Flexible Arm ◽  
Torque Transmission ◽  
Endpoint Control ◽  
Flexible Arms

A new actuation method for one-link flexible arms is presented. The endpoint control of a flexible arm has been known as a nonminimum phase system due to the noncollocated sensor and actuator. By relocating the actuator near the endpoint, the system can be modified to approximate a minimum phase system. In order to implement this, transmission mechanisms are developed which transform the actuator torque to a combination of force and torque and transmit them to an appropriate point on the arm link. Exact pole-zero configurations are analyzed with regard to the location of the actuation point and the type of actuator used. Guidelines for design of the transmission mechanisms and the actuation points are developed with respect to the operation bandwidth, stability and controllability. A prototype flexible arm is designed based on the design guidelines and open-loop and closed-loop tests are performed to verify the effectiveness.

Nonlinear H∞-Output Regulation of a Nonminimum Phase Servomechanism With Backlash

2006 ◽  
Vol 129 (4) ◽  
pp. 544-549 ◽  
Author(s):  
L. T. Aguilar ◽  
Y. Orlov ◽  
J. C. Cadiou ◽  
R. Merzouki
Keyword(s):  
Experimental Study ◽  
System Performance ◽  
Closed Loop ◽  
Output Regulation ◽  
Feedback Controller ◽  
Control Synthesis ◽  
Closed Loop System ◽  
External Disturbances ◽  
Nonminimum Phase ◽  
Output Regulation Problem

Nonlinear H∞ control synthesis is extended to an output regulation problem for a servomechanism with backlash. The problem in question is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. Provided the servomotor position is the only measurement available for feedback, the proposed extension is far from trivial because of nonminimum phase properties of the system. Performance issues of the nonlinear H∞-output regulator constructed are illustrated in an experimental study.

End Point Control of Nonlinear Flexible Manipulators With Control Constraint Using SDRE Method

2002 ◽  
Author(s):  
Woosoon Yim ◽  
Sahjendra N. Singh
Keyword(s):  
Nonlinear Systems ◽  
Closed Loop ◽  
Loop System ◽  
Suboptimal Control ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Elastic Mode ◽  
Nonminimum Phase ◽  
End Point ◽  
Elastic Modes

The paper treats the question of end point regulation of multi-link light-weight manipulators using the state dependent Riccati equation (SDRE) method. It is assumed that each link is flexible and deforms when maneuvered. It is well known that end point trajectory control using widely used feedback linearization technique is not possible since the system is nonminimum phase. Furthermore, control saturation is a major problem in controlling nonlinear systems. In this paper, an optimal control problem is formulated for the derivation of control law with and without control constraints on the joint torques and suboptimal control laws are designed using the SDRE method. This design approach is applicable to minimum and as well as nonminimum phase nonlinear systems. For the purpose of control, psuedo joint angles and elastic modes of each link are regulated to their equilibrium values which correspond to the target end point under gravity. Weighting matrices in the quadratic performance index provide flexibility in shaping the psuedo angle and elastic mode trajectories. In the closed-loop system, the equilibrium state is asymptotically stable, and vibration is uppressed. Simulation results are presented for a single link flexible manipulator which shows that in the closed-loop system, end point regulation is accomplished even with hard bounds on the control torque, and that the transient characteristics of the psuedo angles and elastic modes are easily shaped by the choice of the the performance criterion.

The Study on Blade Pitch Control of Wind Power with Gain Scheduling

2012 ◽  
Vol 522 ◽  
pp. 364-368
Author(s):  
Ji Zhe Hai ◽  
Wen Lei Sun ◽  
Guo Yu Hu ◽  
An Wu
Keyword(s):  
Wind Speed ◽  
Closed Loop ◽  
Simulation Analysis ◽  
Gain Scheduling ◽  
Closed Loop System ◽  
Control Effect ◽  
Pitch Control ◽  
Simulink Model ◽  
Power Regulation ◽  
The Moment

In this paper, we demonstrate the design and simulation of a baseline PID rotor collective pitch controller with a gain scheduling for WindPACT) operation. We use a FAST-Simulink model of the closed-loop system to describe simulating this controller.Through the simulation analysis and comparing the result, control effect with the control strategy of gain scheduling results in better power regulation. At the moment of wind speed make more close to the rated wind speed, the changes of pitch angle is more sensitive, and the output power is larger and more smoothly.

scholarly journals Robust Sliding Control of SEIR Epidemic Models

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Asier Ibeas ◽  
Manuel de la Sen ◽  
Santiago Alonso-Quesada
Keyword(s):  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
A Priori ◽  
Vaccination Strategy ◽  
Loop System ◽  
Theoretic Approach ◽  
Closed Loop System ◽  
Sliding Control ◽  
Mode Control

This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack ofa prioriknowledge on the system.

Gain Scheduling Control of Gas Turbine Engines: Stability by Computing a Single Quadratic Lyapunov Function

2013 ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Lyapunov Function ◽  
Gas Turbine ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Gain Scheduling ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Closed Loop System ◽  
Quadratic Lyapunov Function ◽  
Turbine Engine

We develop and describe a stable gain scheduling controller for a gas turbine engine that drives a variable pitch propeller. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. Simulation results show the developed gain scheduling controller is capable of regulating a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

Analytical Statistical Study of Linear Parallel Feedforward Compensators for Nonminimum-Phase Systems

2019 ◽  
Author(s):  
Keyvan Noury ◽  
Bingen Yang
Keyword(s):  
Feedback Loop ◽  
Closed Loop ◽  
Controller Design ◽  
Phase System ◽  
Main Concern ◽  
Nonminimum Phase ◽  
Loop Design ◽  
Nonminimum Phase Systems ◽  
Phase Systems ◽  
Feedforward Compensators

Abstract In this work, a new parallel feedforward compensator for the feedback loop of a linear nonminimum-phase system is introduced. Then, analytical statistical arguments between the existing developed methods and the innovated method are brought. The compelling arguments suggest the parallel feedforward compensation with derivative (PFCD) method is a strong method even though at its first survey it seems to be optimistic and not pragmatic. While most of the existing methods offer an optimal integral of squared errors (ISE) for the closed-loop response of the nominal plant, the PFCD offers a finite ISE; in reality, typically, the nominal plant is not of main concern in the controller design and the performance in the presence of mismatch model, noise, and disturbance has priority. In this work, there are several arguments brought to bold the importance of the innovated PFCD design. Also, there is a closed-loop design example to show the PFCD effectiveness in action.

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.

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