Linear Parameter-varying Control Research Articles

Controlling neural activity: LPV modelling of optogenetically actuated Wilson–Cowan model * *This work was supported by ANPCyT, Ministry of Science & Technology, Argentina Grant PICT2017-2417. Demián García-Violini is supported by the Agencia I+D+i, Ministry of Science & Technology, Argentina, under PICT-2021-I-INVI-00190.

Objective. This paper aims to bridge the gap between neurophysiology and automatic control methodologies by redefining the Wilson–Cowan (WC) model as a control-oriented linear parameter-varying (LPV) system. A novel approach is presented that allows for the application of a control strategy to modulate and track neural activity. Approach. The WC model is redefined as a control-oriented LPV system in this study. The LPV modelling framework is leveraged to design an LPV controller, which is used to regulate and manipulate neural dynamics. Main results. Promising outcomes, in understanding and controlling neural processes through the synergistic combination of control-oriented modelling and estimation, are obtained in this study. An LPV controller demonstrates to be effective in regulating neural activity. Significance. The presented methodology effectively induces neural patterns, taking into account optogenetic actuation. The combination of control strategies with neurophysiology provides valuable insights into neural dynamics. The proposed approach opens up new possibilities for using control techniques to study and influence brain functions, which can have key implications in neuroscience and medicine. By means of a model-based controller which accounts for non-linearities, noise and uncertainty, neural signals can be induced on brain structures.

Multi‐variable and multi‐objective gain‐scheduled control based on Youla‐Kucera parameterization: Application to autonomous vehicles

AbstractThis paper presents a Youla‐Kucera based interpolation between a set of Linear Parameter‐Varying (LPV) controllers, each one being a gain‐scheduled of Linear Time‐Invariant (LTI) controllers designed separately for different operating points. The gain‐scheduling is achieved based on Youla‐Kucera (YK) parameterization. A generalized LPV‐YK control structure is designed to interpolate between various LPV controllers. The closed‐loop system is proved to guarantee the quadratic stability for any continuous/discontinuous interpolating signals in terms of a set of Linear Matrix Inequalities (LMIs). The proposed method can help multi‐variable and multi‐objective systems to achieve high performances at different operating conditions and different critical situations regardless of the interpolation rate. A numerical example is simulated to show the importance of the proposed method to achieve different objectives for lateral control of autonomous vehicles. In addition, the approach has been tested on a real Renault ZOE vehicle to validate its real performance, and compare it with a standard polytopic LPV controller.

Switching Polytopic Linear Parameter-varying Control for Hypersonic Vehicles in Full Envelope

Switching Polytopic Linear Parameter-varying Control for Hypersonic Vehicles in Full Envelope

An improved linear parameter-varying modeling, model order reduction, and control design process for flexible aircraft

This paper presents an improved process for the modeling, model order reduction (MOR), and control design of a flexible flying wing unmanned aerial vehicle based on the linear parameter-varying (LPV) technology. By applying the Lagrangian formulation and doublet lattice method, the aeroservoelastic (ASE) model of the flexible aircraft is first derived and then rewritten as an airspeed-dependent LPV system, which consists of rigid-body states, structural modes, aerodynamic states, etc. This leads to a high-order LPV model, and the stability of the system varies from stable to unstable when the speed of the aircraft exceeds the critical flutter speed. To facilitate the control design, an oblique projection-based MOR method is then adopted to reduce the order of the plant. Different from previous studies, the MOR method is improved to systematically generate a reduced-order LPV model with consistent states for both the stable and unstable dynamics parts. Finally, an output-feedback LPV controller is designed to simultaneously achieve the body freedom flutter suppression and longitudinal attitude control. Numerical simulation results show the effectiveness of the improved LPV-based ASE modeling, order reduction, and control design process for the flexible aircraft.

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.

Reduced-order model based dynamic tracking for soft manipulators: Data-driven LPV modeling, control design and experimental results

We propose a generic nonlinear reduced-order tracking control method for elastic soft robots. To this end, a new linear parameter varying (LPV) control framework is developed using the data collected from the soft robots. Specifically, for LPV modeling we first derive a nonlinear robot model, which is large-scale by nature, using finite element methods (FEM). Then, a proper orthogonal decomposition (POD) algorithm is used to generate a set of linearized reduced-order models, representing the local behaviors of the soft robot at different operating points within the workspace. Via a unified POD projector, not only the order of these linearized models can be significantly reduced but also their mechanical structure and stability properties can be preserved for LPV modeling and control design. Next, using radial basis function (RBF) networks, we propose an iterative training method to build the LPV robot model by interpolating a subset of selected linearized models with a specified interpolation error. For LPV control design, the equivalent-input-disturbance (EID) concept is exploited to develop a dynamic tracking control scheme, which is composed of three core components: feedforward control, disturbance-estimator control and feedback control. The feedforward control is designed to account for the effects of the trajectory reference and the time-varying affine term, issued from the FEM-based model linearization. The disturbance-estimator control is obtained from a generalized proportional integral LPV observer, which also provides the estimated reduced-order states for feedback control. The observer-based feedback control design is reformulated as a convex optimization problem under linear matrix inequality (LMI) constraints. The globally uniformly ℓ∞ stability of the closed-loop LPV robot model is guaranteed by means of Lyapunov stability theory. Experimental tests are conducted with a soft Trunk robot, inspired by the elephant trunk, under several scenarios with small and large deformations to show the effectiveness of the proposed LPV tracking control framework. A comparative study is also performed with a recent linear EID-based controller and an iterative learning controller to emphasize the interests this nonlinear control method for soft elastic robots. This paper is complemented with a series of demonstration videos: https://bit.ly/3D8C4Vd.

Frequency-Domain Data-Driven Position-Dependent Controller Synthesis for Cartesian Robots

Cartesian robots have position-dependent dynamics that must be taken into account for high-performance applications. Traditional methods design linear time-invariant (LTI) controllers that are robustly stable with respect to position variations but result in reduced performance. Advanced methods require linear parameter varying (LPV) models and LPV controller design methods that are not well-established in the industry. On the other hand, the classical model-based gain-scheduled technique involves parametric identification, high-performance controller design for each position, interpolation of the controller parameters, and real-time controller validation, making it time-consuming and costly. Our approach uses frequency response at different operating points to design an LPV controller using a convex optimization algorithm based on second-order cone programming. The approach is applied to an industrial three-axis Cartesian robot, showing significant improvements over state-of-the-art control design strategies. Data acquisition and controller design can be performed automatically, reducing significantly the engineering costs for controller synthesis.

Online adjustable linear parameter-varying controller for artificial pancreas systems

The purpose of this article is to present a non-hybrid fully closed-loop controller for the Artificial Pancreas (AP) problem focused on long-term clinical trials and home-use applications. It includes physical activity (PA) and unannounced meals. The controller is based on a robust gain-scheduled algorithm with a Linear Parameter-Varying (LPV) structure. It takes into account the time-varying dynamics of the problem by adapting itself in real-time according to measured glucose levels, and allows online fine-tuning during tests and periodic evaluations without the need of a controller redesign. The proposed fully parameterized LPV control adds several features to our previous results, accounts for the main perturbations of the AP problem and simplifies its implementation. To help in the parameter fine-tuning, a methodology based on clinical information is proposed. In-silico tests show that the achieved performance is similar or better than our previous Automatic Regulation of Glucose (ARG) algorithm, tested in two clinical trials, with the addition of the features mentioned before.

LMIs-Based LPV Control of Quadrotor with Time-Varying Payload

Applications of a quadrotor with payload, particularly for chemical spraying, have increased in recent times. The variation in payload mass over time causes a change in the moments of inertia (MOI). Moreover, large tilt angles are required for fast reference tracking and external disturbance rejection. These variations in plant parameters (i.e., mass and inertia) and large tilt angles can degrade the control scheme’s performance and stability. This article proposes a linear matrix inequalities (LMIs)-based linear parameter varying (LPV) control scheme for a quadrotor subject to time-varying mass, time-varying inertia, mass flow rate, and large tilt angles. The control strategy is designed by solving LMIs derived from quadratic H∞ performance and D-stability. The robust stability and quadratic H∞ performance are assessed by LMIs. The efficacy of the proposed methodology is established using numerical simulations, and its performance is compared to the linear time-invariant (LTI) H∞ design with pole placement constraints. The results obtained show that the LPV control scheme gives better tracking performance in the presence of time-varying parameters, noise, and external disturbances without actuator saturation. In comparison to the LTI design technique, the proposed LPV scheme improves the rise time (tr), settling time (ts), and mean squared error (MSE) by up to 14%, 15%, and 30%, respectively. Moreover, smooth transitions are observed in the tilt angles and control signals with the LPV scheme, contrary to the LTI controller, which exhibits significant oscillations.

Self-Scheduled LPV Control of Asymmetric Variable-Span Morphing UAV

In this study, a novel framework for the flight control of a morphing unmanned aerial vehicle (UAV) based on linear parameter-varying (LPV) methods is proposed. A high-fidelity nonlinear model and LPV model of an asymmetric variable-span morphing UAV were obtained using the NASA generic transport model. The left and right wing span variation ratios were decomposed into symmetric and asymmetric morphing parameters, which were then used as the scheduling parameter and the control input, respectively. LPV-based control augmentation systems were designed to track the normal acceleration, angle of sideslip, and roll rate commands. The span morphing strategy was investigated considering the effects of morphing on various factors to aid the intended maneuver. Autopilots were designed using LPV methods to track commands for airspeed, altitude, angle of sideslip, and roll angle. A nonlinear guidance law was coupled with the autopilots for three-dimensional trajectory tracking. A numerical simulation was performed to demonstrate the effectiveness of the proposed scheme.

Intelligent Road-Adaptive Semi-Active Suspension and Integrated Cruise Control

The availability of road and vehicle data enables the control of road vehicles to adapt for different road irregularities. Vision-based or stored road data inform the vehicle regarding the road ahead and surface conditions. Due to these abilities, the vehicle can be controlled efficiently to deal with different road irregularities in order to improve driving comfort and stability performances. The present paper proposes an integration method for an intelligent, road-adaptive, semi-active suspension control and cruise control system. The road-adaptive, semi-active suspension controller is designed through the linear parameter-varying (LPV) method, and road adaptation is performed with a road adaptivity algorithm that considers road irregularities and vehicle velocity. The road adaptivity algorithm calculates a dedicated scheduling variable that modifies the operating mode of the LPV controller. This modification of operation mode provides a trade-off between driving comfort and vehicle stability performances. Regarding the cruise control, the velocity design of the vehicle is based on the ISO 2631-1 standard, the created database, and the look-ahead road information. For each road irregularity, the velocity of the vehicle is designed according to previous measurements and the table of ISO 2631-1 standard. The comfort level must be selected in order to calculate dedicated velocity for road irregularity. The designed velocity is tracked by the velocity-tracking controller evaluated with the LPV control framework. The designed controllers are integrated, and the operation of the integrated method is validated in a TruckSim simulation environment.

Research on turboprop engine control method based on linear parameter varying model

Abstract Starting from a component-level nonlinear model of a turboprop engine, the high-pressure turbine speed and power turbine speed output data at six steady-state operating points are linearized and fitted, and a turboprop engine state variable model is established. Based on these state variable models, the Proportional Integral Derivative (PID) control method, the augmented Linear Quadratic Regulator (LQR) control method and the Linear Quadratic Gaussian/Loop Transfer Recover (LQG/LTR) control method are used to design the controllers respectively, and the relative converted speed of the high-pressure turbine is selected as the scheduling parameter of the Linear Parameter Varying (LPV) model, and the controller is called to control the turboprop engine’s non-linear speed. Linear model for large envelope control. Finally, the control effects of the above three control methods are compared and analyzed, and their advantages and disadvantages are compared. The simulation results show that the LPV controller designed based on the LQG/LTR method is more effective than the controllers designed by the other two control methods on the nonlinear turboprop model.

Frequency domain LPV controller synthesis for a positioning system with uncertain scheduling parameters

Ever-increasing demands from the industry require better performance out of the same system to achieve a competitive advantage. In systems functioning at different operating points, a fundamental trade-off between robustness and performance can limit the achieved performance. Linear Parameter Varying (LPV) controller synthesis can overcome this issue by adapting the controller parameters with the operating points. This requires a parametric LPV model of the system, which in many cases is difficult or costly to obtain. Recently, LPV controller design methods based on the frequency-domain data in different operating points have shown to result in great performance without the need of a parametric LPV model. In these approaches, however, the scheduling parameters are assumed to be measured exactly. In this paper, a new approach is proposed to design LPV controllers with slowly varying uncertain scheduling parameters, using only the frequency response data of a SISO system around different operating points. The proposed approach is applied on a rotary table, a machine used in the manufacturing industry. The dynamics of the rotary table depend on the inertia of the object mounted on-top which cannot be directly measured. Since the scheduling parameter cannot be measured, it is estimated using a short sequence of data that leads to an inexact estimation with interval uncertainty. For the system considered, the LPV controller designed by the proposed approach shows clear improvement over the state-of-the-art robust controller synthesis approaches.

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.

Uneven Grid-based Linear Parameter-Varying Controller Design for Guided Projectiles

This paper proposes a Linear Parameter-Varying (LPV) controller design for the pitch channel dynamics of a new class of Long Range Guided Projectiles (LRGP). The grid-based approach is preferred since it provides advantages in terms of performance and conservatism. Differently from standard aerospace applications that limit the scheduling vector to the variation of the altitude and the Mach number, the investigated flight envelope is parameterized through a 3D grid, which includes the variation of the angle-of-attack, crucial for range optimization purposes. Thus, an extensive investigation of the grid design is required to minimize the computational complexity of the controller synthesis. The performances of the LPV controller are assessed by employing a nonlinear reference tracking simulation scenario.

H∞ Loop Shaping Using Polytopic Weights and Pole Assignment to Missile Autopilot

Modern missiles must deal with stringent performance requirements and ensure robustness across a wide range of operating conditions during flight time. Classic gain-scheduling designs have been successful in practice, but do not provide theoretically ensured bounds on both performance and robustness. Controllers are interpolated at intermediate operating conditions and switching them may cause instability. On the other hand, polytopic linear parameter-varying (LPV) controllers avert this switching and use real-time information about the plant, in order to smooth out the gain scheduling. We hereby propose a novel procedure to yield an output feedback LPV controller that ensures robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> performance to a missile longitudinal autopilot. Our novel approach considers the four-block loop-shaping <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> control theory with polytopic LPV weights that use polytopic coordinates of the LPV plant. One is capable of adjusting the singular values of the open-loop plant individually at the polytope vertices, and benefits from a trade-off between linear matrix inequalities (LMI) based optimization tools and the designer experience. This can be construed as a natural extension of the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> loop-shaping method that uses linear time-invariant (LTI) weights. Assuming the scheduling variables are frozen, we also include LMI conditions for assigning closed-loop poles and hence circumvent controller order reduction. Nonlinear simulations assess the proposed autopilot, and results show an improved robust stability margin, in addition to an improved response to the acceleration command, concerning the LTI-based approach.

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

The level of maturity reached by robust control theory techniques nowadays contributes to a considerable minimization of the development time of an end-to-end control design of a spacecraft system. The advantage offered by this framework is twofold: all system uncertainties can be included from the very beginning of the design process; the validation and Verification (V&V) process is improved by fast detection of worst-case configurations that could escape to a classical sample-based Monte Carlo simulation campaign. Before proceeding to the control synthesis and analysis, a proper uncertain plant model has to be available in order to push these techniques to their limits of performance. In this spirit, the Satellite Dynamics Toolbox Library (SDTlib) offers many features to model a spacecraft system in a multi-body fashion on SIMULINK. Parametric models can be easily built in a Linear Fractional Transformation (LFT) form by including uncertainties and varying parameters with minimal number of repetitions. Uncertain Linear Time Invariant (LTI) and uncertain Linear Parameter-Varying (LPV) controllers can then be synthesized and analyzed in a straightforward way. The authors present in this article a tutorial, that can be downloaded at https://nextcloud.isae. fr/index.php/s/XDfRfHntejHTmmp, to show how to deal with an end-to-end robust design of a spacecraft mission and to provide to researchers a benchmark to test their own algorithms.

LPV Three-loop Autopilot using Dynamic Inversion: A Practical Approach

This work presents a linear parameter varying (LPV) three-loop longitudinal autopilot that is derived using the dynamic inversion technique. The conventional three-loop autopilots are traditionally designed at various flight conditions using linearized models and are then scheduled as a function of several parameters such as Mach number, velocity, angle-of-attack, etc., which remains a challenging and time-consuming task till today. In contrast, the proposed three-loop autopilot embeds the parameterized gains, from which the parameterized gain-multipliers are directly obtained in the form of explicit formulae. Exploiting the utility of the proposed autopilot structure, a design methodology for LPV controller design is presented, in which, a linear three-loop autopilot designed at single flight condition can be transformed into an LPV autopilot using the derived parameterized gain-multipliers. Simulation results are also presented to demonstrate the performance of the proposed technique.

Linear Parameter Varying Power Regulation of Variable Speed Pitch Manipulated Wind Turbine in the Full Load Regime

In a wind energy conversion system (WECS), changing the pitch angle of the wind turbine blades is a typical practice to regulate the electrical power generation in the full-load regime. Due to the turbulent nature of the wind and the large variations of the mean wind speed during the day, the rotary elements of the WECS are subjected to significant mechanical stresses and fatigue, resulting in conceivably mechanical failures and higher maintenance costs. Consequently, it is imperative to design a control system capable of handling continuous wind changes. In this work, Linear Parameter Varying (LPV) H∞ controller is used to cope with wind variations and turbulent winds with a turbulence intensity greater than ± 10%. The proposed controller is designed to regulate the rotational rotor speed and generator torque, thus, regulating the output power via pitch angle manipulations. In addition, a PI-Fuzzy control system is designed to be compared with the proposed control system. The closed-loop simulations of both controllers established the robustness and stability of the suggested LPV controller under large wind velocity variations, with minute power fluctuations compared to the PI-Fuzzy controller. The results show that in the presence of turbulent wind speed variations, the proposed LPV controller achieves improved transient and steady-state performance along with reduced mechanical loads in the above-rated wind speed region.

Sample-data output-feedback parameter variable control of glucose for type 1 diabetes mellitus patients

This paper presents a new approach for nonlinear sampled-data output-feedback control of blood glucose concentration (BGC) in patients with type 1 diabetes mellitus (T1DM). The Bergman minimal model (BMM) describing the glucose-insulin regulatory system is framed as a linear parameter-varying (LPV) model that the sampled glucose measurement with the quantized insulin infusion is considered as input delay. The proposed method utilizes the input-delay approach based on a parameter-dependent Lyapunov–Krasovskii functional (LKF) and provides the parameterized matrix inequality conditions for the design of the controller. Using the slack variables, the design conditions are converted to a new form that can achieve feasible solutions by solving a limited number of bilinear matrix inequality. The proposed architecture guarantees stability in a compact set of states for all the trajectories with the parametric uncertainty to address the issue of inter-patient variability. Simulation results confirm that the proposed sampled-data static output-feedback LPV controller with only glucose measurement regulates the BGC despite the parametric uncertainty and meal disturbances in T1DM patients.