Subspace identification of Bilinear and LPV systems for open- and closed-loop data

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence operating under open- and closed-loop conditions. A factorization is introduced which makes it possible to form a predictor that predicts the output, which is based on past inputs, outputs, and scheduling data. The predictor contains the LPV equivalent of the Markov parameters. Using this predictor, ideas from closed-loop LTI identification are developed to estimate the state sequence from which the LPV system matrices can be constructed. A numerically efficient implementation is presented using the kernel method. It turns out that if structure is present in the scheduling sequence the computational complexity reduces even more.     

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.     

Robust reliable tracking controller design against actuator faults for LPV systems

A robust reliable tracking controller design method is developed against actuator faults for linear parameter varying (LPV) systems under a passive control framework. This method is based on a newly proposed stability condition for LPV systems, which is a more general condition than the existing results. An important contribution of this method is that it could handle relatively wider range of actuator faults due to the extra freedom degree introduced by a new slack variable in the stability condition. Numerical example shows the effectiveness and superiority of our method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Integrated control design for driver assistance systems based on LPV methods

The paper proposes a control design method for a driver assistance system. In the operation of the system, a predefined trajectory required by the driver with a steering command is followed. During manoeuvres the control system generates differential brake moment and the auxiliary front-wheel steering angle and changes the camber angles of the wheels in order to improve the tracking of the road trajectory. The performance specifications are guaranteed by the local controllers, i.e. the brake, the steering, and the suspension systems, while the coordination of these components is provided by the supervisor. The advantage of this architecture is that local controllers are designed independently, which is ensured by the fact that the monitoring signals are taken into consideration in the formalisation of their performance specifications. The fault-tolerant control can be achieved by incorporating the detected fault signals in their performance specifications. The control system also uses a driver model, with which the reference signal can be generated. In the control design, the parameter-dependent linear parameter-varyingmethod, which meets the performance specifications, is used. The operation of the control system is illustrated through different normal and emergency vehicle manoeuvres with a high-accuracy simulation software.     

切换LPV系统的抗攻击无扰切换控制

本文针对遭受切换冲击和网络数据注入攻击影响的切换线性变参(LPV)系统,给出保护网络信息安全传输的抗攻击机制,提出一种无扰切换控制方法.首先,设计一种新颖的基于编码/解码器的抗攻击机制,可抵御恶意注入攻击信号对系统反馈通信的干扰.基于此,建立切换LPV系统的抗攻击动态输出反馈闭环控制模型.考虑到模式之间的无扰过渡问题,给出与动态输出反馈控制设计互为补充的,满足无扰切换设计需求和H∞性能指标的控制增益可行条件.在本文提出的控制律下,进一步获取了能保证切换LPV系统指数稳定性的充分条件.最后,通过数值仿真验证所提出抗攻击无扰切换控制方法的有效性.     

LPV controller design for the nonlinear RTAC system

This paper proposes three kinds of state‐feedback controllers for the nonlinear rotational and translational actuator (RTAC) benchmark problem. Interpolating a nonlinear system into an LPV system associated with time‐varying and state‐dependent weighting functions allows one to apply various linear system theories and techniques for analysing and synthesizing nonlinear systems, and thus to generate LMI criteria to supply various stabilizers and guaranteed cost controllers. This approach is more flexible for this benchmark problem than existing approaches in the literature because the other controllers excessively depend on the structure of the nonlinear system. Simulation results show the performance of the resulting controllers. Copyright © 2001 John Wiley & Sons, Ltd.     

具有时变时延的网络化LPV系统的容错控制

针对一类具有时变时延以及Lipschitz非线性项的网络化线性参数变化系统,研究了系统中存在外部扰动、执行器和传感器同时发生随机故障时的容错控制问题。用Bernoulli分布序列描述执行器和传感器发生的随机故障,利用自由权矩阵方法处理时变时延。根据Lyapunov-Krasovskii稳定性定理和线性矩阵不等式（LMI）方法求出◢H◣▼∞▽容错控制器存在的充分条件,然后通过利用近似基函数和网格化技术将无限维的LMI求解问题转换为有限维的LMI问题,得到了相应的容错控制器增益。最后,通过数值仿真验证了所设计方法的有效性。     

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.     

Stability analysis and control of a class of LPV systems with piecewise constant parameters

Stability criteria characterizing the asymptotic stability of a class of LPV systems with piecewise constant parameters under constant and minimum dwell-time are derived. It is shown that, for such systems, the conditions for the stability under minimum dwell-time can be seen as a unifying stability concept lying in between quadratic and robust stability, thereby including them as extremal cases. The results are then extended to address the stabilization problem using a particular class of time-dependent gain-scheduled state-feedback controllers. Several examples are given for illustration.     

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 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.     

Relaxed observer-based controller design method of discrete-time multiplicative noised LPV systems via an extended projective lemma

ABSTRACT

The aim of this paper is to discuss a relaxed observer-based control problem of multiplicative noised Linear Parameter Varying (LPV) systems with unmeasurable states. For discussing the problem, positive definite matrices without neglecting any element are employed to construct a novel parameter-dependent Lyapunov function. Based on the Lyapunov function, some relaxed sufficient conditions are derived to hold the freedom in searching feasible solutions. Furthermore, an extended projective lemma is developed to convert those conditions into Linear Matrix Inequality (LMI) form. Solving these LMI conditions, controller gain and observer gain can be simultaneously obtained in one-step procedure via using convex optimization algorithm. Therefore, an observer-based controller can be established to guarantee the asymptotical stability of the multiplicative noised LPV systems in the sense of mean square. At last, two numerical examples are used to show effectiveness and applicability of the proposed design method.     

For model-based control design, closed-loop identification gives better performance

We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. Our measure of controller performance (which is used as our design criterion for identification) is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model). Under those conditions, we show that, when the controller is a smooth function of the input-output dynamics and the disturbance spectrum, the best controller performance is achieved by performing the identification in closed loop with an operating controller that we characterize. For minimum variance and model reference control design criteria, we show that this ‘optimal operating controller for identification’ is the ideal controller. This then leads to a suboptimal but feasible iterative scheme.     

An optimal approach to output‐feedback robust model predictive control of LPV systems with disturbances

An observer‐based output feedback predictive control approach is proposed for linear parameter varying systems with norm‐bounded external disturbances. Sufficient and necessary robust positively invariant set conditions of the state estimation error are developed to determine the minimal ellipsoidal robust positively invariant set and observer gain through offline computation. The quadratic upper bound of state estimation error is updated and included in an ‐type cost function of predictive control to optimize transient output feedback control performance. Recursive feasibility of the dynamic convex optimization problem is guaranteed in the proposed predictive control strategy. With the input‐to‐state stable observer, the closed‐loop control system states are steered into a bounded set. Simulation results are given to demonstrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

风力发电系统的Hamilton建模及其无速度传感器控制

本文研究了基于端口受控Hamilton(port-controlled Hamiltonian, PCH)模型的永磁同步风力发电系统的无速度传感器控制问题. 首先根据风力发电系统本身的物理结构特性, 建立其端口受控Hamilton结构模型, 然后基于此模型设计了系统的全维状态观测器, 得到系统的速度估计, 从而实现了系统无速度传感器控制. 在控制器设计中还考虑了系统存在参数不确定情况下的自适应控制问题, 以及在控制器设计中用状态量的估值直接替代不可测状态量时存在的误差问题. 最后仿真实验证明了控制器的有效性.     

On linear‐parameter‐varying (LPV) slip‐controller design for two‐wheeled vehicles

This paper describes the application of linear‐parameter‐varying (LPV) control design techniques to the problem of slip control for two‐wheeled vehicles. A nonlinear multi‐body motorcycle simulator is employed to derive a control‐oriented dynamic model. It is shown that, in order to devise a robust controller with good performance, it is necessary to take into account the dependence of the model on the velocity and on the wheel slip. This dependence is modeled via an LPV system constructed from Jacobian linearizations at different velocities and slip values. The control problem is formulated as a model‐matching control problem within the LPV framework; a specific modification of the LPV control synthesis algorithm is proposed to alleviate controller interpolation problems. Linear and nonlinear simulations indicate that the synthesized controller achieves the required robustness and performance. Copyright © 2008 John Wiley & Sons, Ltd.     

大型风力发电机变桨控制系统设计

变桨距风力发电机已成为风力发电机组的主要研究和发展方向,文章以大型风力发电机组的变桨距系统为研究对象,通过对硬件系统的功能描述,设计了变桨系统的总硬件电路和伺服电路。在此基础上,为实现硬件电路的良好调节作用,对风机启动后变桨程序和调功程序的软件流程图作了详细设计。经过以上的软硬件设计,满足了大型风力发电机组变桨的控制要求。在实际应用中,获得了良好控制效果。     

Simultaneous fault detection and control for switched LPV systems with inexact parameters and its application

This paper investigates the simultaneous fault detection and control problem for a switched linear parameter-varying (LPV) system. The inexact scheduling parameter-dependent fault detection filters and controllers are designed based on the output framework. To realise the detection and control goals, the inexact scheduling parameter-dependent sufficient LMI conditions are obtained by using multiple Lyapunov functions technique. A mode-dependent average dwell-time switching method is used, which is less strict than the general average dwell-time switching method. Simulation results on an aero-engine model show the feasibility and validity of the designed scheme.     

An improved approach to robust stability analysis and controller synthesis for LPV systems

This paper revisits the problem of robust stability analysis and synthesis for linear parameter varying (LPV) systems. By introducing two new slack variables, new conditions for the polyquadratic stability and for the affine quadratic stability of LPV systems are presented in terms of linear matrix inequalities. These results are then applied for robust controller synthesis. Owing to the extra freedom degree introduced by the real slack variable, this proposed approach could lead to less conservative results than that of from the literature, especially for robust controller synthesis. The effectiveness and superiority are demonstrated by the comparison between this proposed approach and the existing results on a well‐known numerical example. Copyright © 2010 John Wiley & Sons, Ltd.