Smooth switching LPV controller design for LPV systems

In this paper, a linear parameter-varying (LPV) control design method is evaluated experimentally on an active magnetic bearing (AMB) system. Linear matrix inequality (LMI) conditions for control design of affine parameter-dependent systems using parameter-dependent Lyapunov functions are proposed. A speed-dependent LPV model of the AMB system is derived. Speed-dependent model uncertainties are identified using artificial neural networks (ANNs), and a parameter-dependent uncertainty weighting function is approximated for LPV control synthesis. Experiments are conducted to verify the robustness of LPV controllers for a wide range of rotor speeds. This LPV control approach eliminates the need for gain-scheduling, and provides better performance and less conservativeness over a wide range of rotational speeds than controllers designed with constant uncertainty weighting functions.

In this paper, a linear parameter-varying (LPV) control design method is evaluated experimentally on an active magnetic bearing (AMB) system. LMI synthesis conditions for control design of affine parameter-dependent systems using parameter-dependent Lyapunov functions are proposed. A speed-dependent LPV model of the AMB system is derived. Speed-dependent model uncertainties are identified using artificial neural networks (ANNs), and a parameter-dependent uncertainty weighting function is approximated for LPV control synthesis. Experiments are conducted to verify the robustness of LPV controllers for a wide range of rotor speeds. This LPV control approach eliminates the need for gain-scheduling, and provides better performance and less conservativeness over a wide range of rotational speeds than controllers designed with constant uncertainty weighting functions.

It is challenging to design a controller for a wind turbine system because of its nonlinear time-varying dynamics. To solve this issue, linear parameter-varying (LPV) control theory has been applied in the recent ten years to deal with nonlinear and wind-speed-dependent dynamics. Before applying the LPV control method, it is required to transform the nonlinear model of the system to an LPV model. The main objectives of this research are to model a 5-MW Reference Wind Turbine for Offshore System as an LPV system, develop a nonlinear wind turbine simulator using MATLAB/Simulink to validate the LPV model, and conduct a preliminary study on LPV control design to test the simulator, which will be used in the future research for applying different LPV control techniques, such as switching LPV control, LPV antiwindup control, etc.

Smooth Switching of Multi-LPV Control Systems Based on Youla-Kucera Parameterization

Presents an alternative approach to solve robust performance problems for linear parameter-varying (LPV) control systems. In contrast to previous methods, which are focused on deterministic algorithms, this paper is based on a probabilistic setting. The proposed randomized algorithm provides a sequence of candidate solutions converging with probability one to a feasible solution in a finite number of steps. The main advantages of this method over the previous literature are as follows: (i) the randomized algorithm gives a direct method for general LPV plants with state-space matrices depending on scheduling parameters in a nonlinear manner, i.e. the probabilistic setting does not require any approximation, such as a linear fractional transformation (LFT), of the state space matrices or a gridding on the set of scheduling parameters; (ii) the proposed algorithm is sequential and, at each iteration, it does not require heavy computational effort, such as simultaneously solving a large number of linear matrix inequalities.

This paper proposes a linear parameter varying (LPV) control design for a Clipper Liberty C96 2.5 MW wind turbine to operate in all wind conditions. A standard approach is to use multiple single‐input, single‐output loops for control objectives at different wind speeds. This LPV controller instead takes these objectives into a uniformed multi‐input, multi‐output design framework. The key difference is that the LPV controller is specifically designed to smoothly transition from Region 2 to Region 3 operation. Reducing structural loads is another major concern in the design. Synthesis of the controller relies on a gridded‐based LPV model of the turbine, which is constructed by interpolation of linearized turbine models at different wind speeds. To overcome the conservativeness in the design, parameter varying rates will be considered based on turbulent wind conditions. The performance of the LPV controller is evaluated using a high fidelity FAST model provided by Clipper. The LPV controller is directly compared with the baseline controller currently operating on the turbine. Simulations and analysis show that the LPV controller meets all performance objectives and has better load reduction performance.

This paper investigates a potential advantage of utilizing blade pitch control over the conventional fixed blade pitch strategy in low wind speed for horizontal-axis offshore floating wind turbines mounted on a barge platform. To examine the advantage, simulation studies with a 5MW wind turbine model in the software FAST are conducted. The generated power and the platform pitch movement are compared among closed-loop systems with three feedback controllers, that is, a baseline controller with fixed blade pitch, a linear-parameter-varying (LPV) controller with fixed blade pitch, and an LPV controller with varying blade pitch. The LPV controllers are gain-scheduled in terms of wind speed. For the design of LPV controllers, an LPV model which represents a family of linearized models of the nonlinear model in FAST over the low wind speed range is employed, and a well-known LPV controller design technique is applied to the LPV model. Simulation results demonstrate that the utilization of blade pitch control can reduce the platform pitch oscillation by more than 5 percent compared to fixed blade pitch strategies, possibly by slight reduction in power capture. This suggests the usage of blade pitch control in low wind speed when the cost decrease due to the load reduction outweighs the cost increase caused by the loss of power generation.

The purpose of this study is to introduce a novel ”completed” LPV controller and observer design approach for control of particular class of nonlinear systems. The developed tools allow to use classical linear controller design theorems via LPV framework without the advanced Linear Matrix Inequality (LMI) theorems. The developed method combines the classical state feedback theorems and a supplementary controller and observer structure which basis is the special properties of the parameter space of the linear parameter varying (LPV) system. The main benefit of the proposed method is that the controller design does not require highly advanced mathematical tools and high computational capacity. We have proven the usability of the method in case of a highly nonlinear compartmental model. The results have shown that the completed LPV controller is able to handle the system with good performance.

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This paper investigates the design of a robust linear parameter-varying (LPV) controller for speed regulation of surface permanent magnet synchronous motors (SPMSMs). Motor dynamics is defined in the α–β stationary frame and a parameter-varying model formulation is provided to describe its nonlinear dynamics. A robust gain-scheduled LPV dynamic output-feedback controller is designed to guarantee the asymptotic stability and performance requirements, as well as, guarantee robustness against parameter perturbations and torque load disturbances. As a novel aspect in the SPMSM control, the real-time impact of temperature variation on the winding resistance and magnet flux during motor operation is explicitly considered in the LPV modeling as a scheduling parameter and the subsequent LPV control design compensating for demagnetization effects in the motor response. The controller synthesis conditions guaranteeing stability and robust performance to norm-bounded uncertainty in the system matrices are formulated in a convex linear matrix inequality (LMI) optimization framework. Finally, the validity of the proposed method is assessed in simulation studies. The closed-loop simulation studies demonstrate that the proposed LPV controller provides improved transient response with respect to settling time, overshoot, and disturbance rejection in tracking the velocity profile under the influence of parameter perturbation, temperature variations, and load disturbances.

This paper describes a Linear Parameter Varying (LPV) controller design for a quadrotor vehicle. The controller synthesis requires the LPV plant model which is obtained by linearisation of the modelling equations, to be in an affine form. However, the LPV representation of the quadrotor dynamic is not affine; hence it has been transformed into to a convex polytopic form using Tensor Product (TP) transformation. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> self gain scheduling control method has been applied to obtain a LPV controller which is tested on a simplified nonlinear model of the quadrotor. The LPV controller performance was compared with a separate H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller. The LPV controller exhibited significant close tracking capabilities with respect to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller.

Recent results in multivariable robust control synthesis for linear parameter-varying (LPV) systems are applied to the control of a turbofan engine over its entire range of operation. Ten linear, timeinvariant (LTI) models are used in the control design. An LPV model of the turbofan engine is constructed and used to design an LPV controller. An Hoo model matching approach is employed such that the resulting closed loop resembles a decoupled set of second-order systems with specified rise time and overshoot. The performance of linear, Tioo point designs are compared with the LPV controller under both constant and parametervarying conditions. The LPV controller achieves excellent tracking of the desired values across large variations in power code.

This paper examines the stabilization and deflection control of an electrostatic microelectromechanical-system (MEMS) actuator using linear parameter-varying (LPV) control methodology. As a case study, a 1-DOF model of an electrostatic MEMS actuator is considered, and its static and dynamic characteristics are discussed. The presented model captures the significant characteristics of the actuator such as the pull-in effect and bifurcation instability. Designed and compared in this paper are control strategies for set-point tracking of the MEMS device deflection, namely: 1) an LPV output-feedback <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex></formula> controller; 2) an LPV state-feedback <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex></formula> controller integrated with an observer; and 3) a time-invariant <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex></formula> controller. To design the LPV controllers, the system dynamics is first reformulated in a quasi-LPV form, considering the actuation charge as the scheduling parameter. We subsequently provide a reduced-order parameter-dependent proportional–integral (PI) controller from the full-order LPV controller for ease of practical implementation. The time-invariant <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex></formula> controller is provided for comparison purposes. The design of the dynamic output-feedback controllers uses a mixed-sensitivity loop shaping, where the weighting selection is discussed. Step reference tracking results are presented and compared for the three control-design approaches. The simulation results illustrate the following: 1) the asymptotic stability and desired performance satisfaction for the controllers against the pull-in effect and random vibration disturbances and 2) the improved performance achieved using the output-feedback LPV controller in terms of the transient tracking response, tracking bandwidth, and control effort over the full range of the device operation. <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hfill$</tex></formula> [2010-0129]

This paper deals with robust control of linear parameter varying (LPV) system (synchronous motor) by a LPV controller. State space equations of asynchronous motor in d-q rotating frame are nonlinear with respect to rotor speed. Nonlinear equations are rewritten to parameter form describing dependency on rotor speed which is assumed to be known by measurement or by estimation. LPV controller is designed using H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> theory to govern stator currents of synchronous motor. Simulation results presented in this paper show that current controller provides good current tracking over whole range of rotor speeds.

This paper presents a controller design method for dealing with the induced ℒ 2 -norm problem for switched linear parameter-varying (LPV) systems. Considering the arbitrary switchings caused by the parameters varying, a common parameter-dependent Lyapunov function is employed to derive sufficient linear matrix inequality (LMI) conditions for the switched LPV systems. A family of LPV controllers are designed according to the LMI conditions, and each of them is suitable for the corresponding parameter region. The proposed switching LPV control method is applied to an F-16 aircraft longitudinal model and simulation results demonstrate the effectiveness of the approach.