Discretization and event triggered digital output feedback control of LPV systems

This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.     

变体飞行器平滑切换LPV 鲁棒控制

针对一类变体飞行器控制问题, 提出一种平滑切换线性变参数(LPV) 鲁棒控制器设计方法. 建立变体飞行器切换LPV 模型, 设计平滑切换控制器, 其中偶数子系统控制器由相邻两个子系统控制器线性插值得到. 给出保证切换LPV 系统指数稳定且具有一定鲁棒性能的充分条件, 由于考虑了调参变量的渐变特性, 所得切换律没有平均驻留时间的限制. 仿真结果表明, 所提出方法使得飞行器系统既具有良好的稳定性和鲁棒性, 又能实现平滑切换.

     

LPV model development and control of a solution copolymerization reactor

In this paper, linear parameter-varying (LPV) control is considered for a solution copolymerization reactor, which takes into account the time-varying nature of the parameters of the process. The nonlinear model of the process is first converted to an exact LPV model representation in the state-space form that has a large number of scheduling variables and hence is not appropriate for control design purposes due to the complexity of the LPV control synthesis problem. To reduce such complexity, two approaches are proposed in this paper. First, an approximate LPV representation with only one scheduling variable is obtained by means of a parameter set mapping (PSM). The second approach is based on reformulating the nonlinear model so that it provides an LPV model with a fewer number of scheduling parameters but preserves the same input–output behavior. Moreover, in the implementation of the LPV controllers synthesized with the derived models, the unmeasurable scheduling variables are estimated by an extended Kalman filter. Simulation results using the nonlinear model of the copolymerization reactor are provided in order to illustrate the performance of the proposed controllers in reducing the convergence time and the control effort.     

基于多LPV 模型的调度离线鲁棒预测控制

针对一类具有大工作区域和快时变特性的约束非线性系统, 采用多个线性参数时变(LPV) 模型近似描述原非线性系统. 对于各LPV 模型, 设计基于参数独立Lyapunov 函数的局部离线预测控制器. 构造各局部控制器间的切换策略, 在保证切换稳定性的同时, 使相互重叠的稳定域覆盖期望的工作区域. 仿真结果表明, 相比于已有的调度预测控制方法, 所提出的方法不仅能够保证控制输入在给定的约束范围内, 而且在局部控制器切换次数少的情况下, 获得良好的控制性能.

     

LPV control for a wafer stage: beyond the theoretical solution

Although conventional PID-like SISO controllers are still most common in industry, there is a growing need for more advanced controller structures in order to comply with ever tighter performance requirements. In this paper we consider positioning devices in IC-manufacturing for which position-dependent plant dynamics are a performance limiting factor. We suggested to employ recently developed linear parameter varying (LPV) control techniques for designing position-dependent controllers that adapt themselves in order to achieve optimal closed-loop performance. Our main emphasis is on presenting a practical LPV design procedure which covers plant modeling, controller synthesis and actual implementation for an electromechanical positioning device, an advanced wafer-scanner. Our experimental results reveal that performance can be improved by LPV control if compared to a classical SISO design. We highlight a variety of troublesome aspects within the design cycle that lack a systematic theoretically founded solution and that limit the possible performance improvement achievable by LPV control.     

Gain-scheduling control of a floating offshore wind turbine above rated wind speed

This paper presents an application of gain-scheduling(GS) control techniques to a floating offshore wind turbine on a barge platform for above rated wind speed cases. Special emphasis is placed on the dynamics variation of the wind turbine system caused by plant nonlinearity with respect to wind speed. The turbine system with the dynamics variation is represented by a linear parameter-varying(LPV) model, which is derived by interpolating linearized models at various operating wind speeds. To achieve control objectives of regulating power capture and minimizing platform motions, both linear quadratic regulator(LQR) GS and LPV GS controller design techniques are explored. The designed controllers are evaluated in simulations with the NREL 5 MW wind turbine model, and compared with the baseline proportional-integral(PI) GS controller and non-GS controllers. The simulation results demonstrate the performance superiority of LQR GS and LPV GS controllers, as well as the performance trade-off between power regulation and platform movement reduction.     

移动机器人视觉伺服镇定quasi-min-max预测控制

针对受限移动机器人视觉伺服系统,提出一种移动机器人视觉伺服镇定准最小最大模型预测控制策略. 基于移动机器人视觉伺服镇定误差模型,建立移动机器人视觉伺服线性参数时变预测模型,进而引入准最小最大策略,设计移动机器人视觉伺服镇定模型预测控制器.与传统视觉伺服预测控制器相比,所提控制器只需求解线性矩阵不等式表示的凸优化问题,降低了视觉伺服预测控制器的计算耗时,同时保证了闭环视觉伺服系统的渐近稳定性.仿真结果验证了所提出策略的有效性和在计算效率上的优越性.     

Linear parameter varying switching attitude control for a near space hypersonic vehicle with parametric uncertainties

This paper deals with the problem of linear parameter varying (LPV) switching attitude control for a near space hypersonic vehicle (NSHV) with parametric uncertainties. First, due to the enormous complexity of the NSHV nonlinear attitude dynamics, a slow–fast loop polytopic LPV attitude model is developed by using Jacobian linearisation and the tensor product model transformation approach. Second, for the purpose of less conservative attitude controller design, the flight envelope is divided into four subregions. For each parameter subregion, slow-loop and fast-loop LPV controllers are designed. By the defined switching character function, these slow–fast loop LPV controllers are then switched in order to guarantee the closed-loop NSHV system to be asymptotically stable and satisfy a specified tracking performance criterion. The condition of LPV switching attitude controller synthesis is given in terms of linear matrix inequalities, which can be readily solved via standard numerical software, and the robust stability analysis of the closed-loop NSHV system is verified based on multiple Lypapunov functions. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.     

Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings

A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of linear parameter varying (LPV) models. The embedding LPV models can yield much better approximation of the nonlinear system dynamics than a single LTV model. For each LPV model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the original nonlinear system. This approach can greatly reduce computational burden in traditional nonlinear predictive control strategy. Finally a simulation example illustrating the strategy is presented. Supported by the National Natural Science Foundation of China (Grant Nos. 60774015, 60825302, 60674018), the National High-Tech Research & Development Program of China (Grant No. 2007AA041403), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060248001), and partly by Shanghai Natural Science Foundation (Grant No. 07JC14016)     

LPV decoupling for control of multivariable systems

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.     

Linear,parameter-varying control of a supercavitating vehicle

A systematic approach to parameter-dependent control synthesis of a high-speed supercavitation vehicle (HSSV) is presented. The aim of the control design is to provide robust reference tracking across a large flight envelope, while directly accounting for the interaction of liquid and gas phases with the vehicle. A nonlinear dynamic HSSV model is presented and discussed relative to the actual vehicle. A linear, parameter-varying (LPV) controller is synthesized for angle rate tracking in the presence of model uncertainty. The control design takes advantage of coupling in the governing equations to achieve improved performance. Multiple LPV controllers synthesized for smaller overlapping regions of the parameter space are blended together, providing a single controller for the full flight envelope. Time-domain simulations implemented on high-fidelity simulations, provide insight into the performance and robustness of the proposed scheme.     

喷水推进式水面机器人H∞鲁棒航向跟踪控制

针对水面机器人(unmanned surface vehicle, USV)航向跟踪容易受到风、浪与水流干扰影响的问题,提出了一种基于线性变参(linear parameter varying, LPV)模型的H_∞鲁棒航向跟踪控制器.首先从水动力学机理出发,提出了基于速度变参的LPV模型.然后基于提出的速度变参LPV模型,利用线性矩阵不等式设计了USV的H_∞鲁棒航向控制器,用以抵抗风、浪与水流对机器人的影响.最后,在自主研发的3自由度欠驱动喷水推进式USV平台上进行了实验.实验结果表明,控制器可以实现鲁棒的航向跟踪控制.     

Multiple fuzzy model-based temperature predictive control for HVAC systems

In this paper, a multiple model predictive control (MMPC) strategy based on Takagi–Sugeno (T–S) fuzzy models for temperature control of air-handling unit (AHU) in heating, ventilating, and air-conditioning (HVAC) systems is presented. The overall control system is constructed by a hierarchical two-level structure. The higher level is a fuzzy partition based on AHU operating range to schedule the fuzzy weights of local models in lower level, while the lower level is composed of a set of T–S models based on the relation of manipulated inputs and system outputs correspond to the higher level. Following this divide-and-conquer strategy, the complex nonlinear AHU system is divided into a set of T–S models through a fuzzy satisfactory clustering (FSC) methodology and the global system is a fuzzy integrated linear varying parameter (LPV) model. A hierarchical MMPC strategy is developed using parallel distribution compensation (PDC) method, in which different predictive controllers are designed for different T–S fuzzy rules and the global controller output is integrated by the local controller outputs through their fuzzy weights. Simulation and real process testing results show that the proposed MMPC approach is effective in HVAC system control applications.     

Switching LPV control designs using multiple parameter-dependent Lyapunov functions

In this paper we study the switching control of linear parameter-varying (LPV) systems using multiple parameter-dependent Lyapunov functions to improve performance and enhance control design flexibility. A family of LPV controllers is designed, each suitable for a specific parameter subregion. They are switched so that the closed-loop system remains stable and its performance is optimized. Two switching logics, hysteresis switching and switching with average dwell time, are examined. The control synthesis conditions for both switching logics are formulated as matrix optimization problems, which are generally non-convex but can be convexified under some simplifying assumptions. The hysteresis switching LPV control scheme is then applied to an active magnetic bearing problem.     

A virtual actuator and sensor approach for fault tolerant control of LPV systems

In this paper, a fault tolerant control (FTC) strategy using virtual actuators and sensors for linear parameter varying (LPV) systems is proposed. The main idea of this FTC method, initially developed for LTI systems, is to reconfigure the control loop such that the nominal controller could still be used without need of retuning it. The plant with the faulty actuator/sensor is modified adding the virtual actuator/sensor block that masks the actuator/sensor fault. The suggested technique is an active FTC strategy that reconfigures the virtual actuator/sensor on-line taking into account faults and operating point changes. The stability of the reconfigured control loop is guaranteed if the faulty plant is stabilizable/detectable. The LPV virtual actuator/sensor is designed using polytopic LPV techniques and linear matrix inequalities (LMIs). A two-tank system simulator is used to assess the performance of the proposed method. In particular, it is shown that the application of the proposed technique results in an improvement, in terms of performance, with respect to the LTI counterpart.     

Mixed H2/H∞ multi-channel linear parameter-varying control in discrete time

This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H₂/H_∞ specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem.     

H∞ output tracking control for a class of switched LPV systems and its application to an aero‐engine model

This paper aims to investigate the problem of H_∞ output tracking control for a class of switched linear parameter‐varying (LPV) systems. A sufficient condition ensuring the H_∞ output tracking performance for a switched LPV system is firstly presented in the format of linear matrix inequalities. Then, a set of parameter and mode‐dependent switching signals are designed, and a family of switched LPV controllers are developed via multiple parameter‐dependent Lyapunov functions to enhance control design flexibility. Even though the H_∞ output tracking control problem for each subsystem might be unsolvable, the problem for switched LPV systems is still solved by the designed controllers and the designed switching law. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an H_∞ speed adjustment problem of an aero‐engine. Copyright © 2016 John Wiley & Sons, Ltd.     

Predictive LPV control of a liquid–gas separation process

The problem of controlling a liquid–gas separation process is approached by using LPV control techniques. An LPV model is derived from a nonlinear model of the process using differential inclusion techniques. Once an LPV model is available, an LPV controller can be synthesized. The authors present a predictive LPV controller based on the GPC controller [Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part I. Automatica 1987;23(2):137–48; Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part II. Extensions and interpretations. Automatica 1987;23(2):149–60]. The resulting controller is denoted as GPC–LPV. This one shows the same structure as a general LPV controller [El Gahoui L, Scorletti G. Control of rational systems using linear-fractional representations and linear matrix inequalities. Automatica 1996;32(9):1273–84; Scorletti G, El Ghaoui L. Improved LMI conditions for gain scheduling and related control problems. International Journal of Robust Nonlinear Control 1998;8:845–77; Apkarian P, Tuan HD. Parametrized LMIs in control theory. In: Proceedings of the 37th IEEE conference on decision and control; 1998. p. 152–7; Scherer CW. LPV control and full block multipliers. Automatica 2001;37:361–75], which presents a linear fractional dependence on the process signal measurements. Therefore, this controller has the ability of modifying its dynamics depending on measurements leading to a possibly nonlinear controller. That controller is designed in two steps. First, for a given steady state point is obtained a linear GPC using a linear local model of the nonlinear system around that operating point. And second, using bilinear and linear matrix inequalities (BMIs/LMIs) the remaining matrices of GPC–LPV are selected in order to achieve some closed loop properties: stability in some operation zone, norm bounding of some input/output channels, maximum settling time, maximum overshoot, etc., given some LPV model for the nonlinear system. As an application, a GPC–LPV is designed for the derived LPV model of the liquid–gas separation process. This methodology can be applied to any nonlinear system which can be embedded in an LPV system using differential inclusion techniques.