一种基于LPV系统的$H_infty$切换控制器设计方法

针对线性参数变化(LPV)系统提出一种切换控制器参数化设计方法.基于Youla参数化思想,将控制器设计过程分解为两个步骤.首先,设计一个中心控制器保证闭环系统的全局$H_\infty$性能;其次,将参数变化区域划分为若干个子区域,在每个子区域中将中心控制器进行线性分式变换,得到切换控制器自由参数的状态空间实现,将切换控制器转换为自由参数之间的切换.基于所提出的切换LPV控制器线性分式变换实现方法,不仅可以保证在任意切换的情况下子系统各自局部的$H_\infty$性能,而且可以保证整个闭环系统满足某一整体的$H_\infty$性能,并通过仿真结果验证了所提出方法的有效性.     

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.

     

A novel design approach for switched LPV controllers

A novel design procedure for switched linear parameter-varying (LPV) controller is proposed. The new procedure, based on the Youla parameterisation ideas, decomposes the controller design into two steps. One focuses on ensuring global stability and the other on fulfilling the local performance specifications. This scheme allows the design of each local controller independently of each other, which may achieve higher performance without compromising the global stability and also simplifies the synthesis and the implementation of the local controllers. Any standard LPV synthesis procedure can be used to design these controllers. On the other hand, the stability during switching is ensured with convex constraints and no restrictions are imposed on the switching among controllers. The use of the proposed procedure is illustrated with an active magnetic bearing example.     

Gain-Scheduling of Minimax Optimal State-Feedback Controllers for Uncertain LPV Systems

A new robust control gain-scheduling scheme for uncertain linear parameter-varying (LPV) systems is proposed. The gain-scheduled controller consists of a set of minimax optimal robust controllers and incorporates a new interpolation rule to achieve continuity of the controller gain over a range of operating conditions. For every fixed system parameter, the proposed controller guarantees a certain bound on the worst-case performance of the corresponding uncertain closed loop system. Furthermore, a bound on the rate of parameter variations is obtained under which the closed loop LPV system is robustly stable     

Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.     

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.

     

Inverse system design for LPV systems using parameter-dependent Lyapunov functions

This paper addresses the design problem of gain-scheduled inverse systems (GSISs) for linear parameter-varying (LPV) systems, whose state-space matrices are represented as parametrically affine matrices, using parameter-dependent Lyapunov functions (PDLFs), and proposes a method for them via parametrically affine linear matrix inequalities (LMIs). Our method includes robust inverse system (RIS) design as a special case. For RIS design, our method theoretically encompasses the method using constant Lyapunov functions. A design example is included to illustrate our conclusions.     

A design of gain-scheduled control for a linear parameter varying system: an application to flight control

For multi-input–multi-output, multi-parameter, nonlinearly parameter-dependent linear parameter-varying systems, a gain-scheduled control design method using both minimum sensitivity eigenvalue assignment and quadratic stability check is proposed. The designed controller guarantees the stability of the closed-loop system and assigns the eigenvalues of the frozen parameter closed-loop LPV system in the prespecified disjointed regions. Fewer controllers than that of any other method are needed to cover the whole parameter space. The proposed design method is applied to the design of a flight vehicle's back-to-turn (BTT) controller and nonlinear six-degree-of-freedom (6-DOF) simulations are performed to show its usefulness as a gain-scheduled controller design method.     

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 Sequential Design Approach for Switching ℌ∞ LPV Control

This paper proposes a sequential design scheme for switching ℌ_∞ LPV (Linear Parameter-Varying) control, aiming to reduce the computational complexity of the associated optimization problem. Different from the traditional approach that simultaneously designs switching LPV controllers and solves a high-dimensional optimization problem, the proposed sequential design approach renders a bundle of low-dimensional optimization problems to be solved iteratively. Individual ℌ_∞ LPV controller for each subregion is synthesized by independent PLMIs (Parametric Linear Matrix Inequalities) to guarantee ℌ_∞ performance, and controller variables are interpolated on the overlapped subregions such that the ℌ_∞ performance is also guaranteed on the overlapped subregion. Numerical examples are used to demonstrate the effectiveness of this method to reduce the computational load in each design iteration and improved ℌ_∞ performance over the conventional simultaneous design method with well-tuned interpolation coefficient.

     

Smooth Switching Output Tracking Control for LPV Systems

This paper is concerned with the problem of smooth switching state feedback controller design for aircraft dynamic systems with multiple operating points. Based on the theory of robust control, a single state feedback controller which considers smooth switching is constructed. With the constant controller, the output response can be considerably improved in the switching process when the flight condition changes. An example for autopilot design of an F‐18 aircraft is given to illustrate the effectiveness of the proposed approach.     

Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

Stabilization for Switched LPV Systems with Markovian Jump Parameters and Its Application

This paper is concerned with the stabilization problem for a class of switched linear parameter‐varying (LPV) systems with Markovian jump parameters whose transition rate is completely unknown, or only its estimated value is known. Firstly, a new criterion for testing the stochastic stability of such systems is established. Then, using the multiple parameter‐dependent Lyapunov function method, we design a parameter‐dependent state‐feedback controller for individual switched LPV subsystem to guarantee stochastic stability of the closed‐loop switched LPV systems with Markovian jump parameters under uncertain transition rates. Finally, as an application of the proposed design method, the stabilization problem of a turbofan‐engine which cannot be handled by the existing methods is investigated.     

Disturbance Attenuation of LPV Systems with Bounded Inputs

A design technique is proposed for disturbance attenuation in linear parameter varying (LPV) systems with bounded inputs. The actuator constraints are handled via a typical LPV approach, in which the time varying parameter is related to the error between the command input and the actual input. Since these two signals are known in most applications, a standard LPV structure for the controller is possible. As a result, the design of controllers with bounded actuators is no more difficult – fundamentally – than the unconstrained control of the LPV system. For example, state feedback problem is convex and the output feedback problem is convex if all of the parameters are available on-line. Cases where the parameters are not available on-line (i.e., traditional robust problems), rate constraint or when the underlying Lyapunov matrix is itself parameter varying are also discussed.     

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.     

Gain-scheduled ℓ-optimal control for boiler-turbine dynamics with actuator saturation

This paper presents a gain-scheduled approach for boiler-turbine controller design. The objective of this controller design is to achieve tracking performance in the power output and drum pressure while regulating water level deviation. Also, the controller needs to take into account the magnitude and rate saturation constraints on actuators. The nonlinear boiler-turbine dynamics is brought into a linear parameter varying (LPV) form which is a parameter-dependent state-space realization. The LPV form of the boiler-turbine dynamics is characterized by nonlinear dependence on drum pressure, which is naturally the scheduling variable. The controller is designed by utilizing the set-valued method for l¹- optimization, which explicitly addresses state constraints and controller saturations in the design process. The overall gain-scheduled design is augmented by a reference governor to avoid performance degradation in the presence of large tracking commands.     

Robust multi-parametric model predictive control for LPV systems with application to anaesthesia

We present a multi-parametric model predictive controller (mpMPC) for discrete-time linear parameter-varying (LPV) systems based on the solution of the mpMPC problem for discrete-time linear time-invariant (LTI) systems. The control method yields a controller that adapts to parameter changes of the LPV system. This is accomplished by an add-on unit to the implementation of the mpMPC for LTI systems. No modification of the optimal mpMPC solution for LTI systems is needed. The mpMPC for LPV systems is entirely based on simple computational steps performed on-line. This control design method could improve the performance and robustness of a mpMPC for LPV systems with slowly varying parameters. We apply this method to process systems which suffer from slow variation of system parameters due, for example, to aging or degradation. As an illustrative example the reference tracking control problem of the hypnotic depth during intravenous anaesthesia is presented: the time varying system matrix mimics an external disturbance on the hypnotic depth. In this example the presented mpMPC for LPV systems shows a reduction of approximately 60% of the reference tracking error compared to the mpMPC for LTI systems.     

LPV系统加权函数法的鲁棒跟踪设计

线性时变系统的重要一类是处理对象中状态空间矩阵的时变物理参数,如何设计控制器使系统满足设计指标是控制中的关键问题。研究了基于加权函数法的线性变参数(LPV)系统设计方法与过程,并指出了参数不确定系统的信号跟踪、系统的稳定性和干扰抑制问题,这三者与控制性能指标设计问题之间是可以相互转化的。通过选择加权函数,转变为线性分式的控制问题求解,从而达到提高系统的鲁棒性能,降低保守性的目的。最后,通过实际的感应电机转子磁链跟踪系统,采用基于LPV鲁棒加权函数法设计其控制器,仿真实现了它对输入磁链参考信号的有效跟踪,且它能有效抑制外界干扰,从而验证了此方法设计的控制器的有效性。     

Robust Static Output Feedback H2/H∞ Control Synthesis with Pole Placement Constraints: An LMI Approach

This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H₂, and H_∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.