Linear Parameter-varying Control Methods Research Articles

Linear Parameter Varying and Reinforcement Learning Approaches for Trajectory Tracking Controller of Autonomous Vehicles

This research focuses on controlling the motion trajectory of autonomous vehicles by using a combination of two high-performance control methods: Linear Parameter Varying (LPV) and Reinforcement Learning (RL). First, a single-track motion model is researched and developed with coordinate systems to determine the car's motion trajectory through signals from GPS. Then, the LPV control method is used to design a controller to control the car's motion trajectory. Reinforcement learning method with detailed training procedures is used to combine with the advantages of LPV controller. Finally, the simulation results are evaluated in the time domain through the use of specialized CarSim software, which clearly demonstrates the superiority of the research method.

A Full Envelope Robust Linear Parameter-Varying Control Method for Aircraft Engines

In order to solve the problem of full flight envelope control for aircraft engines, the design of a linear parameter-varying (LPV) controller is described in this paper. First, according to the nonlinear aerodynamic model of the aircraft engine, the LPV engine model for the controller design is obtained through the Jacobian linearization and fitting technique. Then, the flight envelope is divided into several sub-regions, and the intersection of adjacent sub-regions is not empty. The sub-region LPV controller is designed using the parameter-dependent Lyapunov function (PDLF)-based LPV synthesis method, while eliminating the dependence of the LPV controller on scheduling parameter derivatives. In order to ensure the stability and performance of the aircraft engine across the full flight envelope, a mixing LPV control method is proposed to design the LPV controller in the overall region. The effectiveness of the proposed method is verified by simulating a dual-spool turbofan engine on a nonlinear component level model and comparing the proposed method with the gain scheduling based on PI and H∞ point design.

Finite-time switched LPV control of quadrotors with guaranteed performance

This paper presents a novel finite-time switched linear parameter-varying (LPV) control method for quadrotors subject to large attitude angles and external disturbances. For controller design purpose, both the nonlinear attitude and position dynamics are modeled as a switched LPV system without the idealized assumption of linear approximation. A family of polytopic LPV controllers are designed and each of them is available for a specific parameter subspace of the quadrotor system. The persistent dwell time (PDT) switching logic is adopted to govern the switching behavior among these controllers, which is capable of addressing more general parameter variations than typically used dwell time or average dwell time. By applying an extended cost function, the established switched LPV control method ensures a guaranteed finite-time H∞/LQR performance for the error-tracking system of quadrotors. The advantages of the proposed method are demonstrated via simulations.

Nonlinear parameter‐varying state‐feedback design for a gyroscope using virtual control contraction metrics

AbstractIn this article, we present a virtual control contraction metric (VCCM) based nonlinear parameter‐varying approach to design a state‐feedback controller for a control moment gyroscope (CMG) to track a user‐defined trajectory set. This VCCM based nonlinear (NL) stabilization and performance synthesis approach, which is similar to linear parameter‐varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and ‐gain performance on NL systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully‐ and under‐actuated operating modes of the CMG show effectiveness of this approach compared with standard LPV control methods.

A Linear Parameter Varying Control Approach for DC/DC Converters in All-Electric Boats

Utilization of renewable energies in association with energy storage is increased in different applications such as electrical vehicles (EVs), electric boats (EBs), and smart grids. A robust controller strategy plays a significant role to optimally utilize the energy resources available in a power system. In this paper, a suitable controller for the energy resources of an EB which consists of a 5 kW solar power plant, 5 kW fuel cell, and 2 kW battery package is designed based on the linear parameter varying (LPV) controller design approach. Initially, all component dynamics are augmented, and by exploiting the sector-nonlinearity approach, the LPV representation is derived. Then, the LPV control method determines the suitable gains of the states’ feedbacks to provide the required pulse commands of the boost converters of the energy resources to regulate the DC-link voltage and supply the power of EB loads. Comparing with the state-of-the-art nonlinear control methods, the developed control approach assures the stability of the overall system, as it considers all component dynamics in the design procedure. The real-time simulation results demonstrate the performance of the designed controller in the creation of a constant DC-link voltage.

LPV robust servo control of aircraft active side-sticks

PurposeThis paper aims to focus on the variable stick force-displacement (SFD) gradience in the active side stick (ASS) servo system for the civil aircraft.Design/methodology/approachThe problem of variable SFD gradience was introduced first, followed by the analysis of its impact on the ASS servo system. To solve this problem, a linear-parameter-varying (LPV) control approach was suggested to process the variable gradience of the SFD. A H∞ robust control method was proposed to deal with the external disturbance.FindingsTo validate the algorithm performance, a linear time-variant system was calculated to be used to worst cases and the SFD gradience was set to linear and non-linear variation to test the algorithm, and some typical examples of pitch angle and side-slip angle tracking control for a large civil aircraft were also used to verify the algorithm. The results showed that the LPV control method had less settling time and less steady tracking errors than H∞ control, even in the variable SFD case.Practical implicationsThis paper presented an ASS servo system using the LPV control method to solve the problem caused by the variable SFD gradience. The motor torque command was calculated by pressure and position feedback without additional hardware support. It was more useful for the electronic hydraulic servo actuator.Originality/valueThis was the research paper that analyzed the impact of the variable SFD gradience in the ASS servo system and presented an LPV control method to solve it. It was applicable for the SFD gradience changing in the linear and non-linear cases.

Quantitative robust linear parameter varying H∞ vibration control of flexible structures for saving the control energy

In this article, a general and systematical quantitative robust linear parameter varying control method is proposed for active vibration control of linear parameter varying flexible structures such that a complete set of control objectives can be considered, especially the reduction of necessarily required control energy and the control input. To achieve this goal, the phase and gain control policies are employed in linear parameter varying H∞ control designs for suitable selection of weighting functions. The designed parameter-dependent H∞ controller allows us to explicitly consider the time-varying parameters of the dynamical models for saving the control energy and achieving other control objectives such as the specification of vibration reduction and qualitative robustness properties to both parametric and dynamic uncertainties. Then, various reliable robustness analyses are conducted to quantitatively verify the robustness properties in both deterministic and probabilistic senses. The design processes and the effectiveness of the proposed control method are illustrated by active vibration control of a non-collocated piezoelectric cantilever beam excited by an external position-varying force which is the disturbance to be rejected. This plant has typical parameter (force position)-dependent dynamics and is modeled as a linear parameter varying system whose time-varying parameter is the actual position of the disturbance. The numerical simulations demonstrate that, compared to the classical H∞ control and the acceleration feedback control, the proposed control method allows us to compute a quantitatively robust force-position-dependent H∞ controller whose benefit is requiring less control energy and smaller control input, while satisfying the same control objectives in the frequency and time domains.

Piloted Simulation Study Comparing Classical, H-infinity, and Linear Parameter-Varying Control Methods

Piloted simulation is often regarded as an intermediate step between traditional desktop analysis and flight test. It is a valuable tool in the assessment of how changes in flight control system parameters affect closed-loop vehicle performance. This paper focuses on the piloted simulation evaluation of classical proportional-integral-derivative, robust H ∞ , and linear parameter-varying control design methods. Three different controllers are designed for the longitudinal flight dynamics of the F-16 variable stability in-flight simulator test aircraft within a defined flight envelope. After assessing the performance of each controller using the desktop analysis and simulation, a piloted simulation study is provided to gather qualitative pilot ratings and comments to validate or refute the results and conclusions which were based on the preliminary desktop analysis. The pilot-in-the-loop flight simulator, simulation test plan, and controller evaluation procedure are described. The data obtained from a two-pilot simulation test are then used to conduct a full-handling-qualities study comparing the performance and robustness of each controller. The paper concludes with the selection of the controller that is best suited for application to a modern, fighter-type aircraft.

Anti-windup controller design using linear parameter-varying control methods

In this paper, we seek to provide a systematic anti-windup control synthesis approach for systems with actuator saturation within a linear parameter-varying (LPV) design framework. The closed-loop induced L2 gain control problem is considered. Different from conventional two-step anti-windup design approaches, the proposed scheme directly utilizes saturation indicator parameters to schedule accordingly the parameter-varying controller. Hence, the synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved very efficiently. The resulting gain-scheduled controller is non-linear in general and would lead to graceful performance degradation in the presence of actuator saturation non-linearities and linear performance recovery. An aircraft longitudinal dynamics control problem with two input saturation non-linearities is used to demonstrate the effectiveness of the proposed LPV anti-windup scheme.