Linear Parameter Varying Research Articles

Dynamic load change operation education in air separation processes using a multivariable and nonlinear model

An operator training system (OTS) for dynamic load change operation education in air separation processes is developed. A linear parameter varying (LPV) dynamic model based on an iterative optimization strategy is identified to represent the nonlinear characteristics of the air separation process. First, the local models at typical working points are identified. Second, the weighting functions between the local models are designed and estimated. Finally, an iterative optimization strategy optimizes the local models and weighting functions. The identified LPV model is used as the core training model of the OTS. Model validation with actual data shows that the identified OTS model has reasonable simulation accuracy. By designing a model predictive control (MPC) algorithm, a multidimensional skill evaluation algorithm based on MPC operation data is proposed. The developed OTS and skill evaluation algorithm are applied in a vocational skill competition. Results show that the operation skills of different operators can be reflected and distinguished.

Active fault tolerant control using zonotopic techniques for linear parameter varying systems: Application to wind turbine system

This paper deals with the design of an Active Fault Tolerant Control (AFTC) approach for polytopic uncertain Linear Parameter-Varying (LPV) systems subject to uncertainties and actuator faults. First, a fault estimation method is developed by integrating robust observer design with zonotopic techniques. The proposed observer is developed using L∞ norm to attenuate the effects of the uncertainties and to improve the accuracy of the estimation. Then, an AFTC strategy is used to compensate actuator fault effect and maintain system stability. Finally, the effectiveness of the proposed method is demonstrated by a case study on a 4.8MW wind turbine benchmark system.

Static output feedback [formula omitted]based integral sliding mode control law design for nuclear reactor power-level

This paper is concerned with the design of output feedback H∞ based integral sliding mode (ISM) control law. The control design strategy presented in this paper incorporates robust H∞ control design into sliding mode control (SMC). The design of the control law is achieved by first transforming the nonlinear model of the reactor into a linear parameter varying (LPV) model, from which a polytopic model is then derived. The control law is given into two parts, nominal and discontinuous control laws. The nominal control law is designed using H∞ control approach to achieve nominal system performance, while the discontinuous control law is designed by SMC to suppress the negative influence of uncertainties. The control law thus designed not only stabilizes the system but provides a robust performance to the system and efficiently follows the reference signal in the presence of both disturbances and uncertainties. Numerical simulations have been carried out. The designed control law was compared to PID-like, H∞ and SMC controllers in order to demonstrate its effectiveness and robustness.

Development of an autonomous fog computing platform using control-theoretic approach for robot-vision applications

This paper presents the dynamic modelling and linear matrix inequality (LMI) based controller design of a distributed fog computing framework for real-time robot vision applications. A mobile robot vision system acquires the images from an application environment such as a warehouse, where articles are stacked in numerous racks. We characterise the mobile robot vision data (MRVD) using frames per second (FPS) and the image resolution. From the MRVD, object detection is performed by an open-source deep learning (DL) platform for detecting and localising various objects. However, with higher FPS together with high-resolution images, the processing time by the DL algorithm increases significantly. This necessitates the deployment of a distributed computing platform with several computing nodes. In this work, we deploy a distributed fog computing environment (DFCE) for the real-time object detection in an application environment.The processing time required to handle the MRVD is called the service time. However, for efficient auto-scaling performance, the mathematical model of the DFCE, taking into consideration the characteristics of the MRVD is necessary. In this context, we envisage the application of control theory to build the dynamic model of the DFCE. A Linear Parameter Varying (LPV) model is proposed for the DFCE with the service time as the output, the number of fog nodes as the input, and the characteristics of MRVD as the time-varying parameters. At first, an LPV model for the DFCE is derived using system identification, and the model is validated using the real-time test data. The LPV model is converted to a Polytopic LPV (PLPV) model for LMI based controller design. Finally, we develop and validate a Linear Matrix Inequality (LMI) based LPV controller to meet the service time constraints for a given application environment.For localisation and trajectory tracking with obstacle avoidance in the application environment, the mobile robot implements an Extended Kalman Filter (EKF) based simultaneous localisation and mapping (SLAM) and a bug-based path planning algorithm respectively. Finally, we present, detailed controller validation results illustrating the mobile robot navigation together with the auto-scaling control for the fog computing platform to modulate the service time.

Robust Global Identification of LPV Errors-in-Variables Systems With Incomplete Observations

This article develops a robust global strategy for identifying the linear parameter varying (LPV) errors-in-variables (EIVs) systems subjected to randomly missing observations and outliers. The parameter interpolated LPV autoregressive exogenous model with an uncertain/noisy input is investigated and a nonlinear state-space model is considered for the input generation model (IGM). The parameters estimation of the LPV EIV systems with nonideal observations is realized using the expectation-maximization algorithm which is particular effective for the incomplete data issue. To ensure the robustness in the identification, the Student's t-distribution which is characterized by its adjustable degree of freedom, is used to handle the measurement non-normality. Since the posterior distributions of the latent states in the IGM are also involved in the identification process and they are difficult to calculate directly, the particle filter is introduced to recursively approximate them instead. Finally, the verification examples are given to demonstrate the effectiveness of the developed strategy.

Aggressive Maneuver Oriented Robust Actuator Fault Estimation of a 3-DOF Helicopter Prototype Considering Measurement Noises

This article presents a robust actuator fault estimation strategy design for a three-degree of freedom (3-DOF) helicopter prototype which can be adapted to aggressive maneuvers. First, considering large pitch angle condition during flight, nonlinear coupling characteristic of the helicopter system is exploited. As the pitch angle can be measured in real time, a polytopic linear parameter varying (LPV) model is developed for the helicopter system. Furthermore, considering measurement noises in the actual helicopter system, the dynamical model of helicopter system is modified accordingly. Then, based on the modified polytopic LPV model, a robust unknown input observer is developed for the helicopter system to realize actuator fault estimation, in which both measurement noises and large pitch angle are considered. Robust performance of proposed fault estimation approach is guaranteed by using energy-to-energy strategy. And the observer gains are calculated by using linear matrix inequalities. Finally, based on a 3-DOF helicopter prototype, both simulations and experiments are conducted. The effects of measurement noises and large pitch angle on the fault estimation performance are sufficiently demonstrated. And effectiveness as well as advantages of the proposed observer is verified by using comparative analysis.

Cascaded Steering Control Paradigm for the Lateral Automation of Heavy Commercial Vehicles

The nonlinearity and complexity of the lateral dynamics of heavy commercial vehicles (HCVs) and their steering subsystems usually pose considerable challenges in realizing automatic lateral control for HCVs. In this article, a novel cascade control paradigm is presented for the automatic lateral guidance control of HCVs, which is equipped with an electrohydraulic coupling power steering (EHCPS) system. The objective is to propose a control framework for the satisfactory trajectory tracking performance of HCVs. This control framework consists of an outer vehicle chassis dynamics controller and an inner steering controller, which are implemented to mitigate the issues associated with the trajectory tracking process due to the intrinsic parameter-varying nonlinearity of the vehicle lateral dynamics model and the steering tracking process caused by the complex mapping relationship between the steering wheel angle input and front wheel angle output, respectively. Using the linear parameter-varying (LPV) technique as a general framework, an outer loop controller is designed to produce the desired front wheel angle, which features a gain scheduling mechanism to cope with the time-varying longitudinal velocity. Based on the analysis of the simplified physical model of the EHCPS system, a feedforward set-point scheduling inner loop controller with sliding-mode observer (SMO) is proposed to ensure good tracking performance of the front wheel angle for the steering subsystem. Through experimentation, conducted on the hardware-in-the-loop (HIL) test platform for HCV automatic lateral control, the feasibility and effectiveness of the proposed cascade steering control paradigm are demonstrated.

On interval observer design for active Fault Tolerant Control of Linear Parameter-Varying systems

This paper proposes an active Fault Tolerant Control (FTC) scheme for polytopic uncertain Linear Parameter-Varying (LPV) systems subject to uncertainties and actuator faults. First, a fault estimation interval observer is designed to estimate the system state and the actuator fault. A novel approach is developed using the L ∞ norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed observer. Then, based on the fault estimation information, the FTC strategy is designed using a linear state feedback control law and H ∞ technique to compensate actuator faults and maintain system performance and stability, even under faulty conditions. Finally, the effectiveness of the proposed method is demonstrated by its application to a vehicle lateral dynamic nonlinear model. • Fault Tolerant Control using interval state estimation and robust stabilization. • Set-membership framework for the design of Linear Parameter Varying systems. • Fault estimation observer design for descriptor system. • L ∞ norm-based design method to attenuate the effect of fault and uncertainties and to improve the estimation performance.

Fault-Tolerant Control of Switched LPV Systems: A Bumpless Transfer Approach

For switched linear parameter-varying (LPV) systems with possible actuator failures, the parameter-dependent multiple piecewise Lyapunov function is constructed to handle the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> bumpless transfer fault-tolerant control problem. First, a generalized bumpless transfer concept is presented for switched LPV systems to describe the transient performance, for which only the local bumpless transfer condition is required. Second, an event-triggered switching law, depending on the system states, external parameters, and dwell time, is designed to ensure a time span among adjacent switchings. Third, a solvability condition of the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> bumpless transfer fault-tolerant control problem is developed. A family of time-driven switching controllers with bumpless transfer constraint and fault-tolerant requirement are also designed. Finally, an application example of an aero-engine is given to verify the effectiveness of the developed methods.

Imbalance compensation of active magnetic bearing systems using model predictive control based on linear parameter-varying models

Active magnetic bearing (AMB) is a suspension system to levitate a rotating shaft freely without any physical contact which allows extremely fast rotation speeds. One big control challenge of the AMB systems, which appears during high rotation speeds, is the non-uniform distribution of the rotor weight about its rotating axis. This is usually referred to as the rotor imbalance problem which produces sinusoidal disturbance forces. These disturbances lead to undesirable vibrations and large deviations of the rotor shaft from its desired trajectories. We adopt in this work model predictive control (MPC) to reduce the effect of these sinusoidal disturbances and to achieve a stable levitation of the rotor shaft while tracking a reference trajectory. Owing to the MPC capability of handling constraints in an optimal manner, physical input constraints can be committed. Moreover, state constraints can be imposed to ensure safety of operation. For tractable implementation, we embed the nonlinear dynamics of the system in a linear parameter-varying (LPV) representation. To guarantee stability of the closed-loop system, a terminal cost and a terminal constraint set are included in the MPC optimization problem. For tractable computations of these terminal ingredients, a reduced LPV model is considered. The performance of the proposed LPV-MPC scheme is validated via simulation on the nonlinear model of an experimental setup of an AMB system and it is compared with two other classical controllers commonly used for these AMB systems in practice.

Direct identification of continuous-time LPV state-space models via an integral architecture

In this paper, we present a block-structured architecture for direct identification of continuous-time Linear Parameter-Varying (LPV) state-space models. The proposed architecture consists of an LPV model followed by an integral block. This structure is used to approximate the continuous-time LPV system dynamics. The unknown LPV model matrices are estimated along with the state sequence by minimizing a properly constructed dual-objective criterion. A coordinate-descent algorithm is employed to optimize the desired objective, which alternates between computing the unknown LPV matrices and estimating the state sequence. Thanks to the linear parametric structure induced by the LPV model, the optimization variables within each coordinate-descent step can be updated analytically via ordinary least squares. Furthermore, in order to handle large-size datasets, we discuss how to perform optimization based on short-size subsequences. The effectiveness of the proposed methodology is demonstrated via an academic example and two case studies. The first case study consists of identifying an LPV model describing the behaviour of an electronic bandpass filter from benchmark experimental data. The second case study involves identification of the plasma safety factor from a tokamak plasma simulator.

Simultaneous state and unknown input set‐valued observers for quadratically constrained nonlinear dynamical systems

AbstractIn this article, we propose fixed‐order set‐valued (in the form of ‐norm hyperballs) observers for several classes of quadratically constrained nonlinear dynamical systems with unknown input signals that simultaneously/jointly find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of linear matrix inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for ()‐quadratically constrained (()‐QC) systems, which includes several classes of nonlinear systems: (I) Lipschitz continuous, (II) ()‐QC* and (III) linear parameter‐varying (LPV) systems. This new quadratic constraint property is at least as general as the incremental quadratic constraint property for nonlinear systems and is proven in the paper to embody a broad range of nonlinearities. In addition, we design the optimal observer among those that satisfy the quadratic stability conditions and show that the design results in uniformly bounded‐input bounded‐state (UBIBS) estimate radii/error dynamics and uniformly bounded sequences of the estimate radii. Furthermore, we provide closed‐form upper bound sequences for the estimate radii and sufficient conditions for their convergence to steady state. Finally, the effectiveness of the proposed set‐valued observers is demonstrated through illustrative examples, where we compare the performance of our observers with some existing observers.

Gain-scheduling LPV synthesis H∞ robust lateral motion control for path following of autonomous vehicle via coordination of steering and braking

This paper proposes a robust gain-scheduling lateral motion control strategy via coordination of the active front-wheel steering (AFS) and direct yaw moment control (DYC) for path following of autonomous vehicle. Distinguishing from other relevant researches, a seamless application of the DYC is designed to reduce the influence of braking for the vehicle longitudinal dynamics. In order to achieve this objective, the weighting function with a self-scheduling parameter is designed. Based on the above, a novel LPV (Linear Parameter Varying) synthesis H∞ performances lateral motion controller is designed considering the vehicle longitudinal velocity as a time-varying parameter. The path following is realised through achieving a desired yaw rate, which is generated based on the path-following dynamics. The feedback gains can be derived by solving the LMI (Linear Matrix Inequalities). Furthermore, the physical limitations of the actuators (steer-by wire and brake-by-wire) are considered by weighting functions. Finally, experiments in the HIL system are carried out to verify the effectiveness and real-time performance of the proposed control strategy, and the results show that the proposed controller has good tracking capability under different manoeuvres and can reduce the possibility of actuator saturation and the influence of braking for the vehicle longitudinal dynamics.

Gain-scheduled output-feedback control of uncertain input-delay LPV systems with saturation via polytopic differential inclusion

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints. A linear differential inclusion approach is implemented to formulate the saturation nonlinearity. Subsequently, a gain-scheduled dynamic output-feedback controller is structured to conform to the saturation representation. By means of a Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived for the analysis and feedback control synthesis of the closed-loop system in the presence of uncertainties and exogenous disturbances. Disturbance rejection objectives following an induced -norm and an norm formulation are examined. Estimation of the domain of attraction with the parametrisation of the admissible LPV controllers is presented. Three different optimisation objectives with respect to disturbance rejection, disturbance tolerance, and domain of attraction expansion are formulated. The proposed design methodology is examined in the context of the air-fuel ratio (AFR) regulation in a spark ignition (SI) engine with a speed-dependent delay and model parameters in the presence of canister purge disturbances and AFR dynamics uncertainty. The injector is restricted in the amount of fuel it can deliver to the cylinder. The three-way catalytic converter's performance in terms of oxygen storage and emission reduction is taken into consideration. Closed-loop simulation results are provided to validate the methodology.

An LPV-Based Online Reconfigurable Adaptive Semi-Active Suspension Control with MR Damper

This study introduces an online reconfigurable road-adaptive semi-active suspension controller that reaches the performance objectives with satisfying the dissipativity constraint. The concept of the model is based on a nonlinear static model of the semi-active Magnetorheological (MR) damper with considering the bi-viscous and hysteretic behaviors of the damper. The input saturation problem has been solved by using the proposed method in the literature that allows the integration of the saturation actuator in the initial system to create a Linear Parameter Varying (LPV) system. The control input meets the saturation constraint; therewith, the dissipativity constraint is fulfilled. The online reconfiguration and adaptivity problem is solved by using an external scheduling variable that allows the trade-off between driving comfort and road holding/stability. The control design is based on the LPV framework. The proposed adaptive semi-active suspension controller is compared to passive suspension and Bingham model with Simulink simulation, and then the adaptivity of the controller is validated with the TruckSim environment. The results show that the proposed LPV controller has better performance results than the controlled Bingham and passive semi-active suspension model.

Electrolyte flow rate control for vanadium redox flow batteries using the linear parameter varying framework

In this article, an electrolyte flow rate control approach is developed for an all-vanadium redox flow battery (VRB) system based on the linear parameter varying (LPV) framework. The electrolyte flow rate is regulated to provide a trade-off between stack voltage efficiency and pumping energy losses, so as to achieve an energy efficient battery operation. The nonlinear process model is embedded in a linear parameter varying state–space description and a set of state feedback controllers are designed to handle fluctuations in current during both charging and discharging. Simulation studies have been conducted under different operating conditions to demonstrate the performance of the proposed approach. This control approach was further implemented on a laboratory scale VRB system.

Zonotopic Linear Parameter Varying SLAM Applied to Autonomous Vehicles.

This article presents an approach to address the problem of localisation within the autonomous driving framework. In particular, this work takes advantage of the properties of polytopic Linear Parameter Varying (LPV) systems and set-based methodologies applied to Kalman filters to precisely locate both a set of landmarks and the vehicle itself. Using these techniques, we present an alternative approach to localisation algorithms that relies on the use of zonotopes to provide a guaranteed estimation of the states of the vehicle and its surroundings, which does not depend on any assumption of the noise nature other than its limits. LPV theory is used to model the dynamics of the vehicle and implement both an LPV-model predictive controller and a Zonotopic Kalman filter that allow localisation and navigation of the robot. The control and estimation scheme is validated in simulation using the Robotic Operating System (ROS) framework, where its effectiveness is demonstrated.

Distributed control for complex missions: Quasi‐linear parameter varying approach

AbstractA distributed flocking control scheme is presented for a swarm of non‐holonomic vehicles modeled as linear parameter varying (LPV) systems. The vehicles are assumed to perform tasks that arise when exploring scalar fields on , which may represent, for example, concentration levels of a toxic substance in air or water. Here we consider in particular level surface tracking and level surface monitoring missions. It is assumed that agents can sense gradient and Hessian information of the scalar field at their current position. The control architecture of each vehicle is structured into two modules: a flocking filter which represents a virtual layer of the network, and local tracking controllers for vehicles on the physical layer. The flocking filter receives data from neighboring vehicles and generates a reference signal. An LPV tracking controller for the vehicles, and a network flocking filter that stabilizes the whole network, are designed separately. Simulated mission scenarios with swarm of autonomous underwater vehicles demonstrate the practicality of the proposed approach.

Tensor product model HOSVD based polytopic LPV controller for suspension anti-vibration system

This paper presents a polytopic linear parameter varying (LPV) controller design methodology for nonlinear anti-vibration suspension based on stochastic road identification. As the main nonlinear component in semi-active suspension, the continuous damping control (CDC) damper value is mapped by damping velocity and control current through a bench experiment. linear parameter varying gain-scheduled method is applied for dealing with the nonlinear deterministic model. As the uncertainties caused by road stochastic excitation to suspension cannot be ignored, it is essential to identify the excitation signal as a measurable variable parameter. Empirical-mode-decomposition (EMD) and support vector machine (SVM) are utilized to identify and classify the road stochastic signal input into standard level, so polytopic LPV controller can be designed with CDC damper velocity, control current, and road level as variable parameters. Meanwhile the exponential increase of high-order plant elements in multi-parameter LPV model makes it too complicated for real-time computing. Hence the tensor product model transformation is utilized to identify the orthogonal basis of system plant so that low-rank approximation of it can be implemented by truncated high-order singular value decomposition (T−HOSVD) method. Real-time simulation shows the performance and feasibility of controller, which can efficaciously identify the road stochastic excitation as measurable variable parameters for nonlinear suspension polytopic LPV control.

Improved ℋ2 and ℒ2 control designs for discrete-time LPV/LFR systems

This paper addresses novel and norm-based controller designs for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). Despite the importance of LPV/LFR systems to the control literature, there is a lack of works on this topic. The distinctive formulation of the proposed controller designs is given by using parameter-dependent Lyapunov functions in combination with slack variables and general full-block multipliers. Such proposed formulation leads to less conservative synthesis conditions characterised in terms of a finite number of linear matrix inequalities for both state-feedback and static output-feedback controllers subject to and performances for discrete-time LPV/LFR systems. Improvements obtained by the proposed controller design conditions over existing methods in the area are assessed by numerical examples.