State and actuator fault estimation observer design integrated in a riderless bicycle stabilization system

This paper deals with an observer design for Linear Parameter Varying (LPV) systems with high-order time-varying parameter dependency. The proposed design, considered as the main contribution of this paper, corresponds to an observer for the estimation of the actuator fault and the system state, considering measurement noise at the system outputs. The observer gains are computed by considering the extension of linear systems theory to polynomial LPV systems, in such a way that the observer reaches the characteristics of LPV systems. As a result, the actuator fault estimation is ready to be used in a Fault Tolerant Control scheme, where the estimated state with reduced noise should be used to generate the control law. The effectiveness of the proposed methodology has been tested using a riderless bicycle model with dependency on the translational velocity v, where the control objective corresponds to the system stabilization towards the upright position despite the variation of v along the closed-loop system trajectories.     

速度测量不确定性影响下的无人车路径跟踪预瞄控制EI北大核心CSCD

预瞄距离是无人车路径跟踪预瞄控制系统设计中的一个关键参数,其选取往往依赖于车辆行驶速度.然而,车速的测量不可避免存在偏差,这必将影响系统的预瞄控制性能.本文针对这一问题,在充分考虑车速测量不确定性对预瞄距离选取影响的基础上,提出一种基于线性参数变化(LPV)系统的鲁棒H∞路径跟踪预瞄控制算法.首先,选取车速和预瞄距离为调度变量,将原系统转化为一种具有可变权重因子的LPV系统.然后,针对无人车系统状态的不完全可测性,设计一种基于观测器的鲁棒H∞控制器.最后,给出保证闭环系统鲁棒H∞性能的凸优化求解条件.仿真结果验证了本文提出控制算法的有效性.     

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

We address the design of dynamic parameter‐dependent controllers with antiwindup action to locally stabilize in the input‐to‐state sense a class of discrete‐time linear parameter‐varying (LPV) systems. Such a class consists of systems with delayed state, saturating actuators, and subject to energy bounded disturbances. Moreover, the interval time‐varying delay can have a limited variation rate between two consecutive instants allowing to achieve less conservative design conditions. Differently from other conditions in the literature, the proposed convex synthesis methods allow to design dynamic controllers of different orders. Additionally, the user can choose to feed back only the current output of the system or its delayed ones. Thanks to the embedded (parameter dependent) antiwindup action, it is possible, for instance, to enlarge the region of admissible initial conditions or the maximum admissible disturbance energy. To illustrate the efficiency of our approach, we present numerical examples to compare with other methods from the literature.     

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.     

高温气冷核反应堆变负荷过程的非线性模型预测控制

HTR-PM作为采用高温气冷堆以及“两堆带一机”特殊结构的新型核电站系统,其本身具有强耦合、非线性等复杂特性;HTR-PM自身的参数在运行过程中也会随负荷的变化而变化,动态特性发生很大的偏移.本文提出了一种适用于HTR-PM变负荷过程的非线性预测控制策略,基于操作轨迹LPV模型的辨识方法,克服了HTR-PM耦合、非线性及参数时变等问题.仿真结果表明,本文提出的方法能提高HTR-PM变负荷过程中的运行平稳性,各项控制指标均高于控制要求,明显优于线性模型预测控制方法.     

State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers

This paper proposes a linear parameter varying (LPV) interval observer for state estimation and unknown inputs decoupling in uncertain continuous-time LPV systems. Two different problems are considered and solved: (1) the evaluation of the set of admissible values for the state at each instant of time; and (2) the unknown input observation, i.e. the design of the observer in such a way that some information about the nature of the unknown inputs affecting the system can be obtained. In both cases, analysis and design conditions, which rely on solving linear matrix inequalities (LMIs), are provided. The effectiveness and appeal of the proposed method is demonstrated using an illustrative application to a two-joint planar robotic manipulator.     

Sensor fault diagnosis of singular delayed LPV systems with inexact parameters: an uncertain system approach

In this paper, sensor fault diagnosis of a singular delayed linear parameter varying (LPV) system is considered. In the considered system, the model matrices are dependent on some parameters which are real-time measurable. The case of inexact parameter measurements is considered which is close to real situations. Fault diagnosis in this system is achieved via fault estimation. For this purpose, an augmented system is created by including sensor faults as additional system states. Then, an unknown input observer (UIO) is designed which estimates both the system states and the faults in the presence of measurement noise, disturbances and uncertainty induced by inexact measured parameters. Error dynamics and the original system constitute an uncertain system due to inconsistencies between real and measured values of the parameters. Then, the robust estimation of the system states and the faults are achieved with H_∞ performance and formulated with a set of linear matrix inequalities (LMIs). The designed UIO is also applicable for fault diagnosis of singular delayed LPV systems with unmeasurable scheduling variables. The efficiency of the proposed approach is illustrated with an example.     

Switched state-feedback control for continuous time-varying polytopic systems

This article deals with switched state-feedback ?₂ control design of continuous time-varying polytopic systems. More specifically, the main goal is to determine, simultaneously, a set of state-feedback gains and a switching rule to orchestrate them, rendering the closed-loop system globally asymptotically stable for all time-varying uncertain parameter under consideration and assuring a guaranteed ?₂ cost. A contribution of the present switched control technique compared to the gain scheduling, widely used in the literature, is that the online measurement of the uncertain parameter is not required and no assumption on its time derivative is imposed. The conditions are based on modified Lyapunov–Metzler inequalities and can be solved by line search coupled with LMIs. An academic example illustrates the theoretical results and compares the present technique with other techniques from literature.     

Balanced truncation for temporal- and spatial-LPV interconnected systems based on the full block S-procedure

This paper presents a technique for model order reduction of exponentially stable temporal- and spatial-LPV (Linear Parameter Varying) interconnected systems represented in linear fractional transformation form, based on the application of full block S-procedure. The first stage of the proposed technique is to balance the system. The balancing transformation is applied to the nominal system; the reduced system is connected with the same scheduling block as the original system. The reduced models preserve exponential stability and the spatial structure of the system. The proposed approach simplifies the problem of model order reduction for LPV systems in the sense of avoiding gridding over the scheduling parameter range. The results are illustrated with the application to an experimentally identified spatially interconnected model of an actuated beam. In addition, extended reachability and observability matrices are presented.     

Stability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variations

The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature.