Nonlinear model predictive control for models in quasi‐linear parameter varying form

This article presents a nonlinear model predictive control (NMPC) approach based on quasi‐linear parameter varying (quasi‐LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi‐LPV representations of the system using velocity‐based linearization is presented in two examples.     

Performance‐oriented quasi‐LPV modeling of nonlinear systems

Polytopic quasi–linear parameter‐varying (quasi‐LPV) models of nonlinear processes allow the usage linear matrix inequalities (LMIs) to guarantee some performance goal on them (in most cases, locally, over a so‐called modeling region). In order to get a finite number of LMIs, nonlinearities are embedded on the convex hull of a finite set of linear models. However, for a given system, the quasi‐LPV representations are not unique, yielding different performance bounds depending on the model choice. To avoid such drawback, earlier literature on the topic used annihilator‐based approaches, which require gridding on the modeling region, and nonconvex BMI conditions for controller synthesis; optimal performance bounds are obtained, but with a huge computational burden. This paper proposes building a model by minimizing the projection of the nonlinearities onto directions, which are deleterious for performance. For a small modeling region, these directions are obtained from LMIs with the linearized model. Additionally, these directions will guide the selection of the polytopic embedding's vertices. The procedure allows gridding‐free LMI controller synthesis, as in standard LPV setups, with a very reduced performance loss with respect to the aforementioned BMI+gridding approaches, at a fraction of the computational cost.     

Prediction error method for identification of LPV models

This paper is concerned with identification of linear parameter varying (LPV) systems in an input-output setting with Box-Jenkins (BJ) model structure. Classical linear time invariant prediction error method (PEM) is extended to the LPV PEM. Under the new LPV framework, identification of two types of input-output LPV models is considered: one is based on parameter interpolation and the other is based on model interpolation. The effectiveness of the proposed solution is validated by comparison with other existing LPV identification approaches through simulation examples and demonstrated by experiment studies.     

线性参数变化系统建模与控制研究进展

在描述实际系统的非线性和时变特性方面,线性参数变化(Linear parameter varying,LPV)模型有着巨大的优越性,对于使用一些成熟的线性系统控制理论来解决非线性系统的控制问题,提供了良好的手段.文章对LPV系统的模型结构和建模方法,模型参数辨识方法,控制方法以及应用领域等方面的近几年的研究成果,做了比...     

Model and robust gain‐scheduled PID control of a bio‐inspired morphing UAV based on LPV method

In this paper, a linear parameter‐varying (LPV)‐based model and robust gain‐scheduled structural proportion integral and derivative (PID) control design solution are proposed and applied on a bio‐inspired morphing wing unmanned aerial vehicle (UAV) for the morphing process. In the LPV model method, the authors propose an improved modeling method for LPV systems. The method combines partial linearization and function substitution. Using the proposed method, we can choose the varying parameters simply, thus creating a model that is more flexible and applicable. Then, a robust gain‐scheduled structural PID control design method is given by introducing a structural matrix to design a structural PID controller, which is more consistent with the structure of the PID controller used in practice and has a simpler structure than representative ones in the existing literature. The simulation results show that the developed LPV morphing UAV model is able to catch the response of the original nonlinear model with a smaller error than the existing Jacobian linearization method and the designed controller can maintain stable flights in practice with satisfactory robustness and performance.     

机器人LFT变增益∞控制

针对平面两关节直接驱动机器人, 基于LMI技术提出一种设计能保证在整个运动范围内始终具有很好动态性能的LFT变增益H_∞ 控制器的新方法. 将机器人系统转化为以两关节夹角余弦值为变参数的LPV模型并表示为关于变参数的LFT结构, 利用变参数的测量值设计具有相同LFT结构的LPVH_∞ 控制器, 将此控制器的设计等价为以变参数为不确定项的LTI鲁棒控制器的设计并给出控制器可解的LMIs条件, 然后归纳出获得控制器的求解方法. 此控制器既克服了传统变增益控制器的缺陷,     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

Multiple Lyapunov Functions with Blending for Induced L2‐norm Control of Switched LPV Systems and its Application to an F‐16 Aircraft Model

This paper studies the induced L₂‐norm problem for switched linear parameter varying (LPV) systems using a blending method. For a switched LPV system where the parameters are grouped into slow‐varying and fast‐varying parameters, the blending method is used to construct blended Lyapunov functions based on the multiple Lyapunov functions conditions in terms of linear matrix inequalities (LMIs). The proposed method is applied to an F‐16 aircraft longitudinal model and the simulation results demonstrate the effectiveness of the approach.     

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.     

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.     

A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study

Model-based control strategies are widely used for optimal operation of chemical processes to respond to the increasing performance demands in the chemical industry. Yet, obtaining accurate models to describe the inherently nonlinear, time-varying dynamics of chemical processes remains a challenge in most model-based control applications. This paper reviews data-driven, Linear Parameter-Varying (LPV) modeling approaches for process systems by exploring and comparing various identification methods on a high-purity distillation column case study. Several LPV identification methods that utilize input–output and series expansion model structures are explored. Two LPV identification perspectives are adopted: (i) the local approach, which corresponds to the interpolation of Linear Time-Invariant (LTI) models identified at different steady-state operating points of the system and (ii) the global approach, where a parametrized LPV model structure is identified directly using a global data set with varying operating points. For the local approach, various model interpolation schemes are studied under an Output Error (OE) noise setting, whereas in the global case, a polynomial parametrization based OE prediction error minimization approach, an Orthonormal Basis Functions (OBFs) based model estimator and a Least-Square Support Vector Machine (LS-SVM) based non-parametric approach are investigated. Through extensive simulation studies, the aforementioned LPV identification approaches are analyzed in terms of the attainable model accuracy and local frequency response behavior of the obtained models. Recommendations are provided to achieve adequate choice between the methods for a particular process system at hand.     

Identification of multi-model LPV models with two scheduling variables

In order to model complex industrial processes, this work studies the identification of linear parameter varying (LPV) models with two scheduling variables. The LPV model is parameterized as blended linear models, which is also called multi-model structure. Several weighting functions, linear, polynomial and Gaussian functions, are used and compared. The usefulness of the method is tested using a high purity distillation column model in a case study. The case study shows that a good fit of identification data is not enough to verify model quality and can even be misleading in nonlinear process identification; other measures related to process knowledge should be used in model validation. The case study also shows that commonly used LPV model based on parameter interpolation can fail for the high purity distillation column. Finally, several pitfalls in nonlinear process identification are pointed out.     

Fault estimation for aero‐engine LPV systems based on LFT

In this paper, a fault estimator with linear fractional transformation (LFT) parameter dependency is designed for the linear parameter‐varying (LPV) system of the aero‐engine with both sensor and actuator faults under disturbances. After an aero‐engine affine parameter‐dependent LPV model is derived by the linear fitting method and matrix pseudo‐inverse method, the LPV model with disturbances and fault signals is transformed into a LFT structure. Based on the full block S‐procedure, the sufficient condition for the existence of the fault estimator is proposed, which can lead to less conservative results. Then the fault estimator design algorithm which can adjust to the current system dynamic adaptively is presented. Finally, a fault estimator is designed for a turbofan aero‐engine under multiple types of faults and disturbances to demonstrate the effectiveness of the proposed method.     

Model predictive control for LPV models with maximal stabilizable model range

This paper characterizes model predictive control (MPC) for linear parameter varying (LPV) models subject to state and input constraints, which is based on the homogeneous polynomially parameterized (HPP) Lyapunov function and HPP control law with tunable complexity degrees. The controller guarantees the closed‐loop asymptotic stability and finds the control move through the convex optimization. While it is known that this technique can improve the control performance and reduce conservatism, we suggest that it also enlarges, and maximizes with the sufficiently large complexity degrees, the stabilizable LPV model range. The computational burden becomes heavier when the complexity degrees increase. However, the main contributions of this paper are more on theory than on practice. It explores to what extent robust MPC can be applied for stabilization of LPV models. Numerical examples are provided to illustrate the effectiveness of the proposed technique.     

MPTL板翅式换热器性能的数值分析

研究机械泵驱动的两相冷却回路(MPTL)换热器传热效能优化问题,由于换热器的应用环境极为复杂,目前的实验数据极度匮乏,而且结构特殊,现有的标准叉流板式换热器的设计方法并不适用。为了提出可行的设计优化方法,针对某典型MPTL板翅式换热器,建立一种简化的三维物理数学模型,采用有限体积法及流固耦合方法深入研究该换热器在典型结构及设计工况下的流场特性,随后研究其在不同翅高及进口雷诺数时的换热性能变化规律。数值仿真结果表明,换热器换热效率较高,压力损失较小,且随着翅高的降低、进口雷诺数的增加,换热性能逐渐提高。结果证明,可为换热器的进一步设计与优化提供有益的参考。     

Quasi-LPV modeling,identification and control of a twin rotor MIMO system

This paper describes the quasi-linear parameter varying (quasi-LPV) modeling, identification and control of a Twin Rotor MIMO System (TRMS). The non-linear model of the TRMS is transformed into a quasi-LPV system and approximated in a polytopic way. The unknown model parameters have been calibrated by means of the non-linear least squares identification approach and validated against real data. Finally, an LPV state observer and state-feedback controller have been designed using an LPV pole placement method based on LMI regions. The effectiveness and performance of the proposed control approach have been proved both in simulation and on the real set-up.     

Design and fabrication of a cross flow micro heat exchanger

A cross flow micro heat exchanger was designed to maximize heat transfer from a liquid (water-glycol) to a gas (air) for a given frontal area while holding pressure drop across the heat exchanger of each fluid to values characteristic of conventional scale heat exchangers. The predicted performance for these plastic, ceramic, and aluminum micro heat exchangers are compared with each other and to current innovative car radiators. The cross flow micro heat exchanger can transfer more heat/volume or mass than existing heat exchangers within the context of the design constraints specified. This can be important in a wide range of applications (automotive, home heating, and aerospace). The heat exchanger was fabricated by aligning and then bonding together two identical plastic parts that had been molded using the LIGA process. After the heat exchanger was assembled, liquid was pumped through the heat exchanger, and minimal leakage was observed     

常减压蒸馏过程换热网络的粒子群优化设计方法

提出了1种换热网络的粒子群优化设计方法,提高大规模无分流换热网络的设计速度和效果。采用超结构建立换热网络模型,以各个换热器和换热量为演化个体,以投资和运行费用最小化为优化目标,发挥粒子群的群智特点寻优计算。避免传统设计的计算复杂、不能同时优化投资和运行费用等问题,解决了换热器的换热量受换热条件约束、相互制约而影响设计的难题,保证演化过程中解的可行性,实现设计过程的智能化。以某炼油厂的常减压蒸馏过程的换热网络为实验对象,仿真研究,证明了算法有效和优越。     

Fouling detection in a heat exchanger: A polynomial fuzzy observer approach

The paper presents new results on state estimation of nonlinear systems based on a fuzzy polynomial Takagi–Sugeno representation. Using sum of squares tools and some matrix properties, conditions to compute the gains of the observers can be obtained easily. Then, the results are applied on the detection of the fouling occurring in a counter flow heat exchanger, which involves many polynomial terms. Simulations and a comparison with previous approaches show the interest of the approach.