Linear Parameter-varying Form Research Articles

Linear parameter varying μ synthesis robust control of CDC semi‐active suspension system for nonlinearity and uncertainty

AbstractBecause the continuous damping control (CDC) semi‐active suspension system has complex nonlinear and uncertain characteristics that can significantly affect the performance of the system. And in the controller design process, achieving a balance of multiple performance objectives is often difficult. Therefore, this paper designs a linear parameter varying (LPV) μ synthesis robust controller for the vibration suppression and multi‐objective control of a 7‐degree‐of‐freedom (7‐DOF) vehicle suspension system equipped with CDC dampers. Firstly, the nonlinear force model of the solenoid valve CDC damper is developed based on the actual damping variation. Considering the nonlinear forces of the coil springs, the nonlinear model of the 7‐DOF suspension system is expressed as LPV form. Further, the linear fractional transformation (LFT) method is used to analyze and reconstruct the system model for multiple parameter uncertainties of the suspension. The actuator time delays are also simulated through a frequency domain transfer function, which is considered to be an unmodeled dynamic at the input of the system. Finally, an LPV‐μ synthesis robust controller based on nonlinearity and mixed uncertainty is designed to improve car ride comfort and achieve the best relationship between comfort and handling stability. Simulation and experimental results under random disturbance conditions show that the LPV‐μ synthesis controller has better anti‐jamming performance and controllability compared to the H∞ controller and μ synthesis controller.

Real-time adaptive model of mainstream parameters for aircraft engines based on OSELM-EKF

Gas path parameters play a crucial role in the health management of aeroengines, which are usually generated from the nonlinear component-level model. However, risks of stability and substantial time consumption confine online applications of conventional models. This paper proposes a mainstream parameter model that exclusively involves rotating components using fewer gas path parameters, including an adaptive strategy based on an online sequential extreme learning machine and an extended Kalman filter. The mainstream parameter model is designed in a linear parameter-varying form with a non-iterative smooth state-switching mechanism and enables real-time operation by simplifying the component complexity. Besides, some sensor measurements are employed to update rotor speeds, thus eliminating the need for derivative computations. Neural networks are introduced in compressor component calculations. Additionally, the extended Kalman filter is developed to estimate health parameters to tune the system equation residuals, and the learning machine is applied to compensate for rotating components’ pressure ratios under different degradation magnitudes. Finally, systematic tests are carried out to evaluate the computation accuracy and fast capabilities of the mainstream parameter adaptive model in various scenarios. Simulations demonstrate the proposed methodology's superiority over traditional adaptive correction schemes.

Direct data-driven LPV control of nonlinear systems: An experimental result

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points.

Ellipsoid-Based Interval Estimation for Lipschitz Nonlinear Systems

This article proposes an intervalestimation method for discrete-time Lipschitz nonlinear systems via observer design and ellipsoidal analysis. A robust observer with novel structure is presented, which provides more degrees of design freedom and can be applied to enhance the interval estimation performance. To handle the nonlinear term in Lipschitz systems, we use the reformulated Lipschitz property to transform the nonlinear error dynamics into a linear parameter-varying form. After the transformation, the robustness performance of the proposed observer is characterized with the aid of peak-to-peak index. Furthermore, the comprehensive interval estimation results are obtained by using the peak-to-peak performance and the ellipsoidal analysis. Numerical simulation results are conducted to demonstrate the viability and validity of the presented method.

A Linear Parameter Varying Strategy Based Integral Sliding Mode Control Protocol Development and Its Implementation on Ball and Beam Balancer

An Integral Sliding Mode (ISM) based robustified Linear Parameter Varying (LPV) control is presented for a laboratory scale ball on a beam balancer system. The inherent input channel nonlinearity and under-actuated coupled dynamics make it a challenging control problem. The ISM control, being famous for reaching phase elimination, operates under the action of a control input which is usually an algebraic sum of a continuous and a discontinuous component. In the design of continuous component, the LPV form is used to linearize the otherwise non linearizable input channel nonlinearity. Hence, an LPV control is designed to cope with the varying dynamics. On the other hand, the discontinuous component diminishes the effect of norm bounded matched disturbances. In addition, the discontinuous control component is made smooth (chattering free) in order to generate a continuous control signal. The stability of the proposed algorithm is presented rigorously in terms of a theorem and is validated experimentally.

Data-Driven Predictive Control for Linear Parameter-Varying Systems

Based on the extension of the behavioral theory and the Fundamental Lemma for Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven Predictive Control (DPC) scheme capable to ensure reference tracking and satisfaction of Input-Output (IO) constraints for an unknown system under the conditions that (i) the system can be represented in an LPV form and (ii) an informative data-set containing measured IO and scheduling trajectories of the system is available. It is shown that if the data set satisfies a persistence of excitation condition, then a data-driven LPV predictor of future trajectories of the system can be constructed from the IO data set and online measured data. The approach represents the first step towards a DPC solution for nonlinear and time-varying systems due to the potential of the LPV framework to represent them. Two illustrative examples, including reference tracking control of a nonlinear system, are provided to demonstrate that the data-based LPV-DPC scheme, achieves similar performance as LPV model-based predictive control.

A Control-Oriented Linear Parameter-Varying Model of a Commercial Vehicle Air Brake System

This paper presents a control-oriented LPV (Linear Parameter-Varying) model for commercial vehicle air brake systems, where a pneumatic valve actuator is used to control the brake chamber pressure. To improve the brake system response time and reduce the vehicle stopping distance, the traditional treadle valves used in the air brake system are replaced by electro-pneumatic valves. Also, to develop the model-based brake control strategy, a nonlinear mathematical model is developed based on Newton’s second law, fluid dynamics of the orifice, force balance of spool, and solenoid dynamic characteristics. The brake chamber dynamics is also considered during the charging and discharging processes. The developed nonlinear model is calibrated based on both valve actuator geometry and test bench experimental results. It is proposed to model the nonlinear system in the LPV form so that gain-scheduling controllers can be developed. To obtain the LPV model, system identification is conducted using the calibrated nonlinear model to obtain a set of linearized models under different brake chamber pressure levels, and the resulting identified linear models are assembled to form the LPV model with brake chamber pressure as the varying parameters. A linear infinite-horizon continuous-time LQR (Linear Quadratic Regulator) controller was designed for the braking system based on the developed LPV model with the fixed parameter to demonstrate the effectiveness of the developed LPV model.

Recurrent Neural Network Based Robust Actuator and Sensor Fault Estimation for Satellite Attitude Control System

For the satellite attitude control system with actuator and sensor fault, the paper proposes a neural network based robust state and fault estimation method. Compared with the traditional model-based approach that relies on the accurate model of the system, we train the recurrent neural network with the inputs and outputs of the current attitude control system to achieve the purpose of modeling and improving the accuracy of the model. Then, through the expansion of the system state vectors, the neural state space model is transformed into a generalized nonlinear system without sensor fault terms. Furthermore, a combination of the generalized unknown input observer scheme with the robust ${H}\infty $ linear parameter-varying (LPV) approach is developed to estimate the system state and actuator faults simultaneously. According to Lyapunov theory, the stability analysis of observer is considered by transforming the dynamic error into the discrete time polytopic LPV form. Finally, some tests are performed on the satellite attitude control system to validate the effectiveness of the proposed method.

Linear Parameter Varying Representation of a class of MIMO Nonlinear Systems

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying an LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, especially if a first principles based understanding of the system is unavailable. Converting a nonlinear model to an LPV form is also non-trivial and requires systematic methods to automate the process. Inspired by these challenges, a systematic LPV embedding approach starting from multiple-input multiple-output (MIMO) linear fractional representations with a nonlinear feedback block (NLFR) is proposed. This NLFR model class is embedded into the LPV model class by an automated factorization of the (possibly MIMO) static nonlinear block present in the model. As a result of the factorization, an LPV-LFR or an LPV state-space model with affine dependency on the scheduling is obtained. This approach facilitates the selection of the scheduling variable and the connected mapping of system variables. Such a conversion method enables to use nonlinear identification tools to estimate LPV models. The potential of the proposed approach is illustrated on a 2-DOF nonlinear mass-spring-damper example.

Gain-scheduled H∞ admissibilisation of LPV discrete-time systems with LPV singular descriptor

ABSTRACTThis paper deals with the admissibilisation with guaranteed H∞ performance of linear parameter-varying (LPV) discrete-time singular systems under gain-scheduled (GS) state-feedback control. In particular, we focus on systems with descriptor matrix of LPV form and unknown/unmeasurable disturbance input. To our best knowledge and despite its practical interest, this problem has not been fully investigated and still poses relevant issues, which motivates our study. By means of a proposed descriptor redundancy approach, in combination with the bounded real lemma and Finsler's Lemma, a method based on linear matrix inequalities is proposed to design a GS state-feedback control with maximum H∞ performance. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

Identification and Multivariable Gain-Scheduling Control for Cloud Computing Systems

This paper presents the dynamic modeling and performance control of a Web server hosted on a private cloud. The cloud hosting Web server is a variable capacity system with two control inputs: 1) the number of virtual machines (VMs), which is indicative of the capacity of the cloud, and 2) the admission control used for regulating workload. As the workload and the hosting conditions change frequently, the linear parameter-varying (LPV) framework is well suited to derive the model. For the hosted Web server, we obtain an multiple input multiple output (MIMO) LPV model with performance metrics such as the response time and the throughput, which is then converted to polytopic LPV form using tensor product transformation. Finally, we design a gain scheduled linear quadratic regulator controller for performance guarantees with optimal cost of VMs. The identification, validation, and control experiments are demonstrated on the open source Eucalyptus cloud platform. The HTTP requests are generated using customized synthetic workload generator tool.

Sideslip Angle Estimation of an Electric Ground Vehicle via Finite-Frequency $\mathcal {H}_{\infty}$ Approach

The lateral stability is critically important especially when the vehicle is steered at a high longitudinal speed. Loss of lateral stability would lead to severe accidents. Therefore, the study of lateral stability has been a hot topic for decades. In order to monitor the lateral stability or improve the stability by using the feedback control, the sideslip angle is an important index. However, the sideslip angle is not measurable by using an affordable physical sensor. An alternative approach is to estimate the sideslip angle with the measurements of relatively cheap sensors. In this paper, we investigate the problem of sideslip angle observer design for an electric ground vehicle (EGV). The EGV is equipped with an advanced navigation system. The lateral velocity, the longitudinal velocity, and the yaw rate are available. Thus, the sideslip angle which is defined as the ratio of lateral velocity and longitudinal velocity is also available. Meanwhile, the hand-wheel steering angle is also measurable in this application. The main work is to estimate the sideslip angle with the measurements of yaw rate based on the vehicle lateral dynamics. The dynamic model is first established and the parameters are identified with experimental data. Since the dynamic model is nonlinear, in order to facilitate the system analysis and observer design, the nonlinear model is transformed to a linear-parameter-varying (LPV) system. An observer is proposed based on the LPV form. By defining the estimation error, a compact system which contains the estimation error and the original dynamics is obtained. Considering the frequency of the front-wheel steering angle, the finite-frequency $\mathcal {H}_{\infty}$ performance of the compact system is exploited. An optimal observer design method is then developed. For the EGV, the observer is designed according to the developed method. The performance of the designed observer is illustrated with experimental test data.

Embedding of Nonlinear Systems in a Linear Parameter-Varying Representation

This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are originally defined by control affine state-space representations. The conversion approach results in LPV state-space representations in the observable canonical form. Based on the relative degree concept of NL systems, the states of a given NL representation are transformed to new coordinates that provide its normal form. In the SISO case, all nonlinearities of the original system are embedded in one NL function which is factorized to construct the LPV form. An algorithms is proposed for this purpose. The resulting transformation yields an LPV model where the scheduling parameter depends on the derivatives of the inputs and outputs of the system. In addition, if the states of the NL model can be measured or estimated, then the procedure can be modified to provide LPV models scheduled by these states. Examples are included for illustration.

Control of variable‐speed wind turbines by LPV gain scheduling

AbstractThis article considers gain‐scheduling control of variable‐speed wind energy conversion systems (WECS) in the context of linear parameter‐varying (LPV) systems. The typical problems of the classic gain‐scheduling techniques, such as stability guarantees, undesirable transient responses in the controller commutations and arduous design procedures, can be avoided with this new formulation. A model of a variable‐speed WECS expressed in LPV form and an optimal LPV gain‐scheduling control strategy are presented. Copyright © 2004 John Wiley & Sons, Ltd.

Gain-scheduled ℓ1-optimal control for boiler-turbine dynamics with actuator saturation

Abstract This paper presents a gain-scheduled approach for boiler-turbine controller design. The objective of this controller design is to achieve tracking performance in the power output and drum pressure while regulating water level deviation. Also, the controller needs to take into account the magnitude and rate saturation constraints on actuators. The nonlinear boiler-turbine dynamics is brought into a linear parameter varying (LPV) form which is a parameter-dependent state-space realization. The LPV form of the boiler-turbine dynamics is characterized by nonlinear dependence on drum pressure, which is naturally the scheduling variable. The controller is designed by utilizing the set-valued method for l1- optimization, which explicitly addresses state constraints and controller saturations in the design process. The overall gain-scheduled design is augmented by a reference governor to avoid performance degradation in the presence of large tracking commands.