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

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 LPV controller design for LPV systems

One of the performance-limiting factors in the design of robust controllers for active magnetic bearing systems is the fact that the controller needs to be robust to the gyroscopic effects, that is rotational speed-dependent dynamics of the system. Studies in the literature show that better performance and stability can be achieved when gyroscopic effects are explicitly handled by a cross-feedback control for rigid rotor-active magnetic bearing systems. For flexible rotor-active magnetic bearing systems, gyroscopic effects are mainly dealt by defining the rotational speed as an uncertain parameter of the model or with linear parameter-varying controllers. This study explores the novel idea of compensating gyroscopic effects of a flexible rotor-active magnetic bearing system with an add-on controller and investigates its effects on the achieved performance of μ-controllers. The study is carried out on an experimental active magnetic bearing test rig with relatively high gyroscopic effects. An add-on controller is designed to compensate the gyroscopic effects of the first and second flexible modes of the rotor. Two μ-controllers are designed for the system: (1) benchmark controller that is designed using a standard control approach for active magnetic bearing systems and (2) controller designed with a modified model of the system in which the gyroscopic effects for the first and second flexible modes are reduced because of the presence of the add-on controller. Both controllers are implemented, and their performances are compared for initial levitation, run-up test from 0 to 10,000 r/min, orbit sizes at various speeds, and the computational cost of implementing each controller. The results suggest that better performance is potentially possible at the cost of significant increase in the computational complexity of the controller.

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 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.

In the paper the nonlinear control strategy based on feedback linearization for nonlinear active magnetic bearing (AMB) system is discussed. In this context, self-sensing AMB dynamics, in affine-form is investigated. The extended relative degree of AMB dynamics model is considered. Since AMB system is strongly nonlinear a modification of the classical geometric control linearization is used. Numerical simulations are carried out to verify the theoretical approach.

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 presents a robust nonlinear control law that combines a parametric uncertainty of the single one-degree-of-freedom active magnetic bearing (AMB) system with disturbance. The robust nonlinear feedback tool such as control Lyapunov function (CLF) and robust stability techniques are developed. The control objective is to globally stabilise the mass position of an AMB with flux feedback. The flux-based control model for an AMB system is derived due to voltage switching strategy with voltage saturation. This strategy enables the flux control under a zero-bias or low-bias flux operation. In the zero-bias control, only one electromagnet in each axis of the AMB is active at any given time, depending on the rotor displacement. The proposed robust nonlinear CLF with a zero-bias for an uncertain AMB system can achieve a dynamic performance superior to that of a linear controller with the zero-bias or with the classical bias operations.

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.

Integrated design of radial active magnetic bearing systems using genetic algorithms

In this paper, the application of particle swarm optimization (PSO) algorithm based fuzzy PID control for the stable control of an active magnetic bearing (AMB) system is studied. Active magnetic bearings are known to be highly nonlinear multivariable systems. An AMB system is used in motors, turbines and various other machineries in different industries to provide an active suspension to the rotor shafts. The heuristic PSO algorithm is applied to optimize the parameters of the PID controller offline. The fuzzy PID controller based on PSO algorithm is designed to adjust the control parameters of AMB system online. The comparison of controlled responses of closed-loop systems resulting from the use of conventional PID, Incomplete differential PID and particle swarm optimization-based fuzzy logic PID control strategies is discussed. The proposed controller performance is superior as compared to PID and incomplete differential PID controllers in improving the system response of an AMB under normal conditions as well as under external 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.

Linear parameter-varying (LPV) modelling and control of a nonlinear partial differential equation (PDE) is considered in this article. The one-dimensional viscous Burgers' equation is discretised using a finite difference scheme; the boundary conditions are taken as control inputs and the velocities at two grid points are assumed to be measurable. A nonlinear high-order state space model is generated and proper orthogonal decomposition is used for model order reduction. After assessing the accuracy of the reduced model, a low-order functional observer is designed to estimate the reduced states which are linear combinations of the velocities at all grid points. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model. A polytopic LPV controller is synthesised based on a generalised plant containing the LPV model and the functional observer. More generally, the proposed method can be used to design an LPV controller for a quasi-LPV system with non-measurable scheduling parameters. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller compared with a linear quadratic Gaussian (LQG) controller based on a linearised model.