LPV重复过程的H_∞滤波新方法

将时滞线性参数变化(LPV)思想应用于重复过程中,研究了其H∞滤波问题。基于参数依赖Lyapunov函数方法推出了该重复过程的稳定性和滤波器设计的充分条件。通过投影定理引入两个附加矩阵,解除了重复过程矩阵和依赖于参数的Lyapunov函数矩阵之间的耦合,使得到的条件便于求解。仿真实例证实了该设计方法的有效性。     

Detection filter design for LPV systems—a geometric approach

This paper investigates fault detection and isolation of linear parameter-varying (LPV) systems by using parameter-varying (C,A)-invariant subspace and parameter-varying unobservability subspaces. The so called “detection filter” approach, formulated as the fundamental problem of residual generation (FPRG) for linear time-invariant (LTI) systems, is extended for a class of LPV systems. The question of stability is addressed in the terms of Lyapunov quadratic stability by using linear matrix inequalities. The results are applied to the model of a generic small commercial aircraft.     

基于一类二阶线性变参系统特征结构配置的完全参数化方法

通过设计一个比例微分控制律u=K0(θ)q+K1(θ)q来对二阶线性变参系统q-A(θ)qC(θ)q=B(θ)u进行特征结构配置,其中状态空间矩阵[A(θ)B(θ)]取决于一系列在线可测的时变参数,同时为上述特征结构配置问题的解决提供了一种新的拥有最大设计自由度的参数化方法。该方法主要的计算量在于两组矩阵的初等变换,而且在选择一些合适的闭环特征值的前提下,实际计算仅涉及到一系列奇异值分解。同时,由于该方法直接应用原有二阶变参系统的系数矩阵A(θ)、B(θ)和C(θ),因此大多数的计算主要针对n维矩阵。最后针对航天器在轨加油姿态系统控制的仿真验证了该方法的有效性和实用性。     

Gain Scheduled Output Feedback Control Based on LTI Controller Interpolation that Preserves LPV H ∞ Performance

A new approach to the design of a gain scheduled output feedback controller based on linear time-invariant (LTI) controller interpolation that preserves H performance without a varying-parameter rate feedback is proposed. After the controller design is translated into parameterized linear matrix inequalities about parameter matrices based on a parameter-dependent Lyapunov function, the sufficient condition is given for the partition of the varying-parameter set based on the concept of H performance covering. The varying-parameter set is thus partitioned into sufficiently small subsets. After the constant matrices are found for each of the subsets, the required continuous parameter matrices are obtained by using interpolation. The proposed controller overcomes the drawback that the gain scheduled controller may not be found by using the existing gain scheduled linear parameter varying (LPV) controller synthesis. Moreover, the varying-parameter rate feedback is eliminated and the conservatism of the controller design is reduced by means of limiting the upper bound of the varying-parameter rate. Simulation and experiment results prove the effectiveness of the proposed controller.     

涡轮增压柴油机线性变参数模型

以平均值模型为基础,通过简化各子模型,得到包含4个变量的状态空间模型,并转化为线性变参数模型.4个状态变量分别是柴油机转速、扫气箱压力、排气管压力和压气机功率.以6S60MC型船用柴油机为例进行了仿真计算,并与平均值模型作了对比分析.结果表明,该模型相对简单而准确,可以直接用于基于模型的控制算法的设计分析.     

ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems

In this paper, the ??_∞ and l₂–l_∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ??_∞ and l₂–l_∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ??_∞ and l₂–l_∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust decentralized actuator fault detection and estimation for large-scale systems using a sliding mode observer

In this paper, robust decentralized actuator fault detection and estimation is considered for a class of non-linear large-scale systems. A sliding mode observer is proposed together with an appropriate coordinate transformation to find the sliding mode dynamics. Then, based on the features of the observer, a decentralized fault estimation strategy is proposed using an equivalent output error injection, and a decentralized reconstruction scheme follows by further exploiting the structure of the uncertainty which is allowed to have non-linear bounds. The estimation and reconstruction signals only depend on the available measured information and thus the proposed strategy can work on-line. The theoretical results which have been obtained are applied to an automated highway system. Simulation shows the feasibility and effectiveness of the proposed scheme.     

Gain-scheduled controller synthesis for a nonlinear PDE

Linear parameter-varying (LPV) modelling and control of a nonlinear partial differential equation (PDE) is considered in this article. The one-dimensional viscous Burgers' equation is discretised using a finite difference scheme; the boundary conditions are taken as control inputs and the velocities at two grid points are assumed to be measurable. A nonlinear high-order state space model is generated and proper orthogonal decomposition is used for model order reduction. After assessing the accuracy of the reduced model, a low-order functional observer is designed to estimate the reduced states which are linear combinations of the velocities at all grid points. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model. A polytopic LPV controller is synthesised based on a generalised plant containing the LPV model and the functional observer. More generally, the proposed method can be used to design an LPV controller for a quasi-LPV system with non-measurable scheduling parameters. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller compared with a linear quadratic Gaussian (LQG) controller based on a linearised model.     

Linear models‐based LPV modelling and control for wind turbines

The non‐linear behaviour of wind turbines demands control strategies that guarantee the robustness of the closed‐loop system. Linear parameter‐varying (LPV) controllers adapt their dynamics to the system operating points, and the robustness of the closed loop is guaranteed in the controller design process. An LPV collective pitch controller has been developed within this work to regulate the generator speed in the above rated power production control zone. The performance of this LPV controller has been compared with two baseline control strategies previously designed, on the basis of classical gain scheduling methods and linear time‐invariant robust H_∞ controllers. The synthesis of the LPV controller is based on the solution of a linear matrix inequalities system, proposed in a mixed‐sensitivity control scenario where not only weight functions are used but also an LPV model of the wind turbine is necessary. As a contribution, the LPV model used is derived from a family of linear models extracted from the linearization process of the wind turbine non‐linear model. The offshore wind turbine of 5 MW defined in the Upwind European project is the used reference non‐linear model, and it has been modelled using the GH Bladed 4.0 software package. The designed LPV controller has been validated in GH Bladed, and an exhaustive analysis has been carried out to calculate fatigue load reductions on wind turbine components, as well as to analyse the load mitigation in some extreme cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Model-based iterative learning control strategies for precise trajectory tracking in gasoline engines

In this paper trajectory tracking algorithms for gasoline engines are devised. Specifically, precise reference tracking in engine speed and air-to-fuel ratio is enabled while satisfying initial and final conditions on the center of combustion. Such a tracking of multiple reference trajectories requires a coordinated control action for the air path, the fuel path, and the ignition timing actuators. Combining a dedicated feedforward and feedback controller structure and multivariable model-based norm-optimal parallel iterative learning control strategies, feedforward control trajectories are generated that enable a precise tracking of desired reference trajectories. Experimental results focusing on the termination of the catalyst heating mode show the effectiveness of the proposed methodology, resulting in a control error reduction above 85%.