Robust Linear Parameter-varying Control Research Articles

Robust linear parameter varying frequency control for islanded hybrid AC/DC microgrids

• The LPV representation of a nonlinear isolated hybrid microgrid model is investigated. • The intermittent nature of the wind speed, solar irradiation, and loads, and several parameter uncertainties are considered in the frequency control design procedure. • A dynamic robust LPV controller synthesis based on the three-step algorithm is proposed for the nonlinear model. • The proposed secondary frequency control approach suggests a practical dynamic output feedback controller with lower order than the IHMG model. • The algorithm superiority is verified in various disturbance-based and uncertain parameter-based scenarios. The applicability of a robust linear parameter varying (LPV) control for frequency fluctuation damping in an islanded hybrid microgrid (IHMG) system (DEG/WTG /PV/FC/ESSs) is investigated in this paper. Due to the erratic behavior of the majority of the renewable energy sources (RESs) and the varying time nature of loads, frequency deviation from the nominal value is inevitable, especially in the islanded mode. Load variation, solar irradiation, and wind power disturbance, as well as system parametric uncertainties, can significantly disturb the system frequency operation. In this paper, the wind speed and rotated speed of the nonlinear wind turbine are highlighted as scheduling parameters, and the nonlinearity of the wind turbine is hidden by the LPV approach. In the proposed method, a dynamic output feedback controller is obtained based on the power balance equation, by solving three LMIs to minimize the upper bound of the L 2 -Norm of the uncertain IHMG in an algorithmic approach. For better evaluation, the ultimate LPV control approach is compared with two other methods on the understudy IHMG model. The result represents a noticeable advantage of the proposed robust method compared to other methods in terms of frequency stability based on time-domain and norms characteristics in presence of the simultaneous disturbances and parametric uncertainties.

Parameter varying control of wind turbine smart rotor for structural load mitigation

This study investigates the Linear Parameter Varying (LPV) control of a Horizontal Axis Wind Turbine (HAWT) smart rotor in order to alleviate the structural loads. The smart rotor blades are equipped with actuators called Deformable Trailing Edge Flap (DTEF). These flaps benefit from a continuous airfoil deformation on the trailing edge in order to change the aerodynamic properties of blades. The objective of using a flap is to reduce the amplitude of load fluctuations in high wind speeds to decrease the fatigue loads on the wind turbine components and increase their working life. Here, the aerodynamic behavior of NACA 64-418 airfoil in the presence of DTEF deflection is studied numerically. The airfoil with 10% chord deformation is mounted on 5 MW NREL reference wind turbine blades in 67% to 95% of its length relative to the blade root. The nonlinear aeroelastic FAST code is used to determine the effects of DTEFs on structural load mitigation. Consequently, the modeling of nonlinear wind turbine system using LPV approach is discussed including the angle of DTEFs as a control input. A robust LPV controller has been designed using Linear Matrix Inequality (LMI) solution along the operating trajectory to guarantee the internal stability and H∞ robust performance of the closed-loop system in the presence of modeling uncertainties as well as wind turbulence. In sum, the idea of this study is the aerodynamic modeling of the wind turbine equipped with a smart rotor, designing an LPV controller and comparing the results with the conventional PI gain-scheduled controller. The principal objective is to reduce the amplitude of blade root flapwise bending moment oscillations about its mean values along the operating trajectory. As a summary of the results, a reduction in blade root flapwise bending moment fatigue load has been observed by 33% based on Damage Equivalent Load (DEL) calculation.

Robust LPV control synthesis for learning-aided driver assistance systems

This paper proposes a control design framework with guarantees for systems, which contains learning-based control elements. The framework is based on a supervisory control structure, which contains a supervisor, a robust Linear Parameter Varying (LPV) controller and the learning-based control elements. This paper presents the design of a lateral path following control for driver assistance systems, which is aided with a learning-based agent. In the paper the formulation of the supervisor, the design method of the robust LPV controller are provided, while the learning-based agent via an imitation learning process is considered to be given. The effectiveness of the method on driver-in-the-loop simulation scenario is demonstrated. It is shown that the proposed control system is able to provide guarantee on the limitation of the path following error, and to guarantee transition between the driver steering actuation and the automated control intervention.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Nested Robust Controller Design for Interconnected Linear Parameter Varying Aerial Vehicles

A framework for a systematic design of robust controllers to guarantee desired output performance for an interconnected group of multi-input–multi-output dynamic systems is presented. The framework enables design of a robust linear parameter varying (LPV) controller for all individual vehicles as well as the interconnected group to account for uncertainties associated with the individual vehicles as well as the interconnections. In this paper, the robust controller design methodology for the individual systems and the cooperative system is implemented in a nested manner to enhance the performance. The application of the nested robust controller is distributed wherein well-known robust performance analysis is adopted and modified, and the controller synthesis methodology is developed on top of the same performance condition. Nested robust LPV controllers are synthesized for the short-period dynamics of F-16 VISTA over a flight envelope defined by Mach number and altitude of the aircraft. Then a group of homogeneous F-16 VISTA with individually designed LPV controllers is interconnected using a connection topology that suffers time delays, and a cooperative controller is designed using two methods described in this work. Numerical simulation results presented in the paper show that the group performance is enhanced with the robust LPV controller design methodology.

Disturbance Observer Enhanced Neural Network LPV Control for a Blended-Wing-Body Large Aircraft

The problem of trajectory tracking control for a blended-wing-body (BWB) large aircraft with model parameter uncertainties and unknown disturbances is considered. A linear parameter-varying (LPV) model is derived from the nonlinear dynamics of the BWB aircraft from which a robust linear parameter-varying controller is designed to track a desired trajectory. Using a single quadratic Lyapunov function (SQLF) and an infinite number of linear matrix inequalities to be evaluated at all vertices, a pair of positive definite symmetric matrix solutions are determined via Lyapunov stability theory and linear matrix inequality technique. Furthermore, a disturbance-observer is designed to process the unknown disturbances. Considering the plant exists some model errors except for disturbances, a radial basis function neural network approximation is embedded into the SQLF LPV controller to improve tracking performances, and a composite disturbance-observer based neural network single quadratic Lyapunov function (NNSQLF) controller can realize desired trajectory tracking of the linear parameter-varying system through regulating performance weighting functions. The closed-loop system of trajectory tracking control is proved to be asymptotically stable by using Lyapunov theory. Simulation results of forward flight speed and altitude tracking control of the BWB aircraft show that the proposed disturbance-observer based NNSQLF control can robustly stabilize the LPV system and precisely track the desired trajectory by comparing with conventional SQLF control and parameter-dependent Lyapunov function control, even in unknown exterior disturbances and model uncertainties.

Design of LPV control for autonomous vehicles using the contributions of big data analysis

The paper deals with a robust autonomous path-following functionality, in which the safe velocity and the motion profile of the vehicle with varying tyre-road contact must be guaranteed. The integration of Linear Parameter-Varying (LPV) control and the results of the machine learning-based analysis on the big data of autonomous vehicles is proposed. The integration is achieved in two steps. First, an estimation method on the adhesion coefficient through decision trees is presented. The result of the estimation is incorporated in the robust LPV control through a scheduling variable. During the control design, the error of the machine-learning algorithm is incorporated. Second, an optimisation method of the longitudinal velocity on a predicted horizon is proposed, which is aided with the machine learning-based reachability set approximation of the steering intervention. The effectiveness of the control strategy is illustrated through CarSim simulations.

Robust Linear Parameter Varying Scalar Control Applied in High Performance Induction Motor Drives

This article presents a robust stabilizer designed to damp low-frequency electromechanical oscillations which occurs in induction machines controlled by scalar control when operating at low speed and light load. The robust stabilizer design is based on the linear parameter varying (LPV) approach. A discrete LPV model is identified to allow the design of the robust LPV controller. Experimental tests are performed on a 7.5-kW induction motor dynamometer using an industrial inverter driver. The results show satisfactory improvement of the motor performance with the damping controller activated.

DO-LPV-based robust 3D path following control of underactuated autonomous underwater vehicle with multiple uncertainties

This study investigates a path following problem of underactuated autonomous underwater vehicle under multiple uncertainties in three-dimensional space. The uncertainties are partly induced by hydrodynamic coefficient uncertainty, ocean currents and unmodeled hydrodynamics, namely dynamic uncertainties. In addition, velocities are assumed to be measured with bounded noise, which is called velocity measurement uncertainties. To address this issue, a compound robust path following control strategy is developed. At the kinematic level, an improved kinematic controller is developed by utilizing disturbance observer to recover the unknown time-varying attack and side-slip angular velocity. At the dynamic level, a novel dynamic tracking model is firstly established via linear parameter varying (LPV) technique, by which multiple uncertainties are expressed in a comprehensive way. Subsequently, a robust LPV controller is employed to track desired velocities generated by kinematic controller, which has less dependence on accurate model and exact velocity measurement. Finally, rigorous stability analysis proves the uniform and ultimate boundedness of path following errors. The comparative numerical results also substantiate the efficacy and superiority of designed method.

Missile autopilot design based on robust LPV control

This paper proposes an effective algorithm to work out the linear parameter-varying (LPV) framework autopilot for the air defense missile so as to simultaneously guarantee the closed-loop system properties globally and locally, which evidently reduces the number of unknown variables and hence increases the computational efficiency. The notion of quadratic is inducted to meet the global properties, including the robust stability and robust performance, while the regional pole placement scheme together with the adoption of a model matching structure is involved to satisfy the dynamic performance, including limiting the fast poles. In order to reduce the conservatism, the full block multiplier is employed to depict the properties, with all specifications generalized in integral quadratic constraint frame and finally transformed into linear matrix inequalities for tractable solutions through convex optimization. Simulation results validate the performance of the designed robust LPV autopilot and the proposed framework control method integrating with the full block multiplier approach and the regional pole placement scheme, and demonstrate the efficiency of the algorithm. An efficient algorithm for the air defense missile is proposed to satisfy the required global stability and local dynamical properties by a varying controller according to the flight conditions, and shows sufficient promise in the computational efficiency and the real-time performance of the missile-borne computer system.

Probabilistic robust linear parameter-varying control of a small helicopter using iterative scenario approach

In this paper, we present an iterative scenario approach (ISA) to design robust controllers for complex linear parameter-varying (LPV) systems with uncertainties. The robust controller synthesis problem is transformed to a scenario design problem, with the scenarios generated by identically extracting random samples on both uncertainty parameters and scheduling parameters. An iterative scheme based on the maximum volume ellipsoid cutting-plane method is used to solve the problem. Heuristic logic based on relevance ratio ranking is used to prune the redundant constraints, and thus, to improve the numerical stability of the algorithm. And further, a batching technique is presented to remarkably enhance the computational efficiency. The proposed method is applied to design an output-feedback controller for a small helicopter. Multiple uncertain physical parameters are considered, and simulation studies show that the closed-loop performance is quite good in both aspects of model tracking and dynamic decoupling. For robust LPV control problems, the proposed method is more computationally efficient than the popular stochastic ellipsoid methods.

Probabilistic Robust Linear Parameter-Varying Control of an F-16 Aircraft

O PERATIONAL capability at high angles of attack, especially near and at post stall regimes, is critical for next generation fighter aircrafts and uninhabited aerial vehicles [1]. However, significantly large levels of modeling uncertainty are inevitably encountered inflight control design for those regimes. The sources of uncertainty include variations in mass, inertia, and center of gravity positions, uncertainty in the aerodynamic data, etc. [2]. The maneuverability at high angles of attack poses a challenging control problem that requires guaranteeing both robust stability and robust performance in the presence of large parameter variations. Traditional robust control techniques, like H1 and -synthesis, have been proven to be capable of producing robust uncertaintytolerant controllers for next generation aircrafts [2,3]. However, those techniques focus on deterministic worst-case robust analysis and synthesis, which often lead to overly conservative stability bound estimate and high control effort. Moreover, a large number of conventional deterministic problems in robustness analysis and synthesis are shown to be NP-hard. To reduce conservatism and computational complexity, one approach is to shift the meaning of robustness from its usual deterministic sense to a probabilistic one [4]. In contrast to traditional robust control techniques, only a probabilistic solution is given, and a certain risk-level should be accepted. However, such a system may be viewed as being practically robust from an engineering point of view. Algorithms derived in the probabilistic context are based on uncertainty randomization and usually called randomized algorithms, which may be divided into two families: methods based on statistical learning theory [5], and sequential methods based on subgradient iterations [6–8] or ellipsoid iterations [9,10]. The former can deal with nonconvex synthesis problems; however, it resorts to randomized search over the controller parameters to find a candidate solution. On the other hand, the sequential methods are formulated based on convex problems, thus avoiding the controller randomization issue [4]. The probabilistic robust control approach is still in the stage of algorithm development and improvement, and has not been explored in depth for flight control. The number of implementation of probabilistic techniques is therefore rather restricted. In the late 90s, Marrison and Stengel designed a linear quadratic regulator to control the nonlinear longitudinal dynamics of a hypersonic aircraft [11]. Recently, Wang and Stengel designed a robust flight control system for the high-incidence research model problem by combining stochastic robustness with nonlinear dynamic inversion [12]. Their work was based on statistical learning theory, and controllers were searched by using generic algorithms to minimize stochastic robustness cost functions. In our earlier paper, we applied an ellipsoid algorithm to design anH1 controller for a linearized F-16 longitudinal model [13]. Good stability and performance robustness have been achieved at the chosen flight condition. The motivation for this research is twofold. First, the probabilistic control design method for linear time-invariant plants in [13] is generalized to linear parameter-varying (LPV) systems. This generalization is very important because of the relevance of LPV systems to nonlinear systems. TheLPVcontrol synthesis condition is known to be formulated as a convex problemwith a set of parameterdependent linear matrix inequalities (LMIs) [14–16]. Second, the current state of the art does not allow accurate aerodynamicmodeling in the high angle of attack region. Because of its random nature, uncertainty in the aerodynamic data can be characterized using a statistical model, which can be handled effectively by the promising probabilistic robust control approach. Note that the study in this note focuses on the robustness issue with respect to the aerodynamic uncertainty at high angles of attack, and the results would be easily generalized to other parametric uncertainties, such as variations in mass and inertial properties. Because of the convex formulation of LPV control synthesis, the sequential method is more suitable for dealing with uncertainties and designing probabilistic robust LPV controllers. An ellipsoid algorithm with a stopping rule proposed by Oishi [10] is used to determine feasible solutions to LMI synthesis conditions. The paper is organized as follows. In Sec. II, the ellipsoid algorithm is presented, which either gives a probabilistic solution with high confidence or detects that there is no deterministic solution in an approximated sense. Section III first provides a brief overview of robust control problem of an uncertain LPV system, and then discusses the computational issues when the algorithm is applied to the robust LPV control problem. In Sec. IV, a robust LPV controller is designed for an F-16 aircraft with large aerodynamic uncertainty, and the robust performance is tested through nonlinear simulations. Finally, the paper concludes with a summary in Sec. V.

Robust LPV control of diesel auxiliary power unit for series hybrid electric vehicles

This paper presents a robust gain-scheduling approach for the control of diesel auxiliary power unit (APU) for series hybrid electric vehicles (SHEVs), using the linear parameter-varying (LPV) techniques. An average physical model of the diesel APU is established, which combines the subsystem models including diesel engine, synchronous generator, and three-phase diode rectifier in an elegant way. The nonlinear system model is then formulated as a quasi-LPV form with parametric uncertainty and augmented with performance objectives in a robust control framework. As a solution to this type of control problem, a robust LPV control synthesis method is proposed and its numerical implementation issues are also considered. Simulation results verify the performance of the proposed robust LPV controller.