Gain-scheduled Controller Research Articles

An improved real-time temperature control for pulsed laser cutting of non-oriented electrical steel

An improved method based on fuzzy gain scheduling (FGS) control is developed in this study to tune the PID parameters and precisely control the working temperature in situ during laser cutting of non-oriented electrical steel sheets. Experiments on laser cutting of thin electrical steel sheets are performed to compare the cutting quality of kerf features using an open loop controller with a constant power, a conventional PID controller, and the proposed FGS controller. An unstable and inconsistent cutting quality of kerf with a larger heat affected zone (HAZ) and dross attachment is observed under open loop control due to a significant variation of working temperature and kerf width along the cutting path. The FGS controller shows better cutting performance and tracking response than the conventional PID controller by reducing the settling time as well as enhancing the control stability in the steady period. A better quality of finer and uniform kerf width with parallel kerf edges of a smaller HAZ and dross attachment are thus produced by the improved FGS control through real-time tuning of control parameters. Finally, the average kerf width is well correlated with the set-point temperature in FGS control by a linear equation.

Design and Experimental Validation of Robust Self-Scheduled Fault-Tolerant Control Laws for a Multicopter UAV

In recent years, multicopter unmanned aerial vehicles (UAV) have been widely used in many commercial and military applications. Due to the increasing requirement for high autonomy and safety, UAVs should possess a fault-tolerant ability to accommodate malfunctions during flight. This article presents two fault-tolerant control (FTC) designs for a multicopter UAV subject to actuator faults. The proposed FTC approach is based on gain-scheduling (GS) control in the framework of structured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> synthesis. The scheduled gains of the first controller are parameterized as polynomial functions of the loss of actuator effectiveness, given by an appropriate fault detection and diagnosis system. In order to facilitate the tuning process, the second controller uses the loss of virtual control effectiveness as the GS variable. Experimental results performed on an hexacopter UAV show the effectiveness and the robustness of these methods subject to multiple critical actuator faults.

Affine linear parameter‐varying embedding of non‐linear models with improved accuracy and minimal overbounding

In this study, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behaviour of non-linear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and the minimisation of the conservativeness of the resulting embedding. The LPV state-space model is synthesised with affine scheduling dependency, while the scheduling variables themselves are non-linear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the non-linear system model and also it can be used to minimise the complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a three degrees of freedom (3DOF) control moment gyroscope is converted by the proposed method to an LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

Improved Gain Scheduling Control and Its Application to Aero-Engine LPV Synthesis

Issues of gain scheduling control for aero-engines are addressed in this paper. An aero-engine is a system with high nonlinearity, and the requirement on controlling performance is high. Linear Parameter Varying (LPV) synthesis is commonly used to satisfy the requirements. However, the designing procedure of an LPV synthesis controller is complex, and may lead to undesirable design results when the variation rate of scheduling parameter is relatively fast. In this paper, an improved gain scheduling design procedure that can guarantee reliable stability and performance is developed. The method allows arbitrary variation of scheduling parameters, and is a modification for conventional LPV synthesis control. Special cases where traditional LPV synthesis control can still work are also discussed. The modified design procedure is evaluated on a small turbofan engine. Simulations show that for conditions where conventional scheduling fail to stabilize the plant, the proposed modification can ensure reliability and achieve desired performance.

Design of gain scheduled fuzzy PID controller for multi-link robot manipulators

Gain Scheduling (GS) controller is one of the most popular approaches to nonlinear control design. Commonly, Gain Scheduling (GS) controllers have better performance than robust ones. In this paper, the structure of a proposed gain scheduled PID fuzzy controller (GS-PIDF) designed and analyzed. The Fuzzy PID controller gains weighted through gain scheduling designed system to grantee both the stability and the best performance of a multi links robot manipulator system. The overall designed controller system is applied to two links robot manipulator system, which is subject to modelling using Lagrangian dynamics method and simulation vie MatLab and Simulink package to minimize the vibration and acquire best performance.

Low Impedance-Guaranteed Gain-Scheduled GESO for Torque-Controlled VSA With Application of Exoskeleton-Assisted Sit-to-Stand

This article investigates a closed-loop torque-controlled variable stiffness actuator (VSA) combined with a disturbance observer for enhancing low output impedance. We implement the generalized extended state observer (GESO) for conveniently testing the stability of the time-varying VSA system. In our application, the GESO is also required to serve the operation of the low- and high-impedance task. Here, the most important aspect is to consider the influence of the physical stiffness on the output impedance, because the VSA has been regulated with the closed-loop torque control. Through the interaction-torque experiments, we verify that using the fast dynamics GESO with the low-stiffness actuator can achieve low output impedance and stable interaction under the reachable frequency of a human. These properties contribute to perform the low-impedance task. When performing the high-impedance task, where a large torque command is needed, the high-stiffness actuator and the slow dynamics GESO are implemented to achieve high bandwidth and proper tracking performance. The continuously variable observer responses in accordance with the stiffness values are achieved via the gain-scheduling control. Moreover, the present closed-loop linear parameter varying system can be verified to be quadratically stable. The VSA system is then implemented on a knee exoskeleton for a sit-to-stand application. The reference command of the exoskeleton is a joint torque, calculated from the inverse dynamics. This torque signal is also used as the reference command of the stiffness motor of the VSA. The effectiveness of the exoskeleton system is experimentally verified with one healthy volunteer. Subsequently, another two healthy volunteers also successfully experienced the system.

Distributed Control Design for Heterogeneous Interconnected Systems

This article presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular, the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.

LPV-Based Controller Design of a Floating Piston Pneumatic Actuator

The paper presents the modeling and control design of a floating piston pneumatic gearbox actuator using a grid-based Linear Parameter Varying approach. First, the nonlinear model of the pneumatic actuator is presented, then it is transformed into a 6th order Linear Parameter Varying representation with endogenous scheduling parameters. The model is simplified based on empirical considerations to solve the controller synthesis and allow fast controller tuning. The developed Linear Parameter Varying controller is tested in simulations. Moreover, using a balanced truncation-model order reduction method, the minimum order of the controller is determined, which can provide acceptable performance. The simplified controller is implemented in an embedded environment and validated against the real target. Then, the validation results are compared with a gain-scheduled PD controller and a Linear Quadratic Regulator. The results show that by taking the time-varying nature of the scheduling parameters into account, the Linear Parameter Varying controller surpasses the Linear Quadratic Regulator, which cannot handle the high-speed transients around Neutral. Furthermore, the PD controller performs slightly better in two of the four test cases, although the Linear Parameter Varying controller has a higher level of fault tolerance.

Gain-scheduled control for morphing aircraft via switching polytopic linear parameter-varying systems

This paper addresses the gain-scheduled output feedback control for morphing aircraft (MA) in full envelope using switching polytopic linear parameter-varying (SPLPV) theory. The SPLPV model of MA is derived by scheduled parameter interval division and convex decomposition. Considering average dwell time (ADT) and mode-dependent average dwell time (MDADT) switching logics, sufficient conditions to ensure that the SPLPV systems are exponential stable with weighted disturbance attenuation indexes are presented based on the multiple parameter-dependent Lyapunov functions (MPDLFs) technique, and the comprehensive algorithm for the controller solution is obtained. To reduce the computational burden and ease controller implementation, a finite number of linear matrix inequalities (LMIs) are developed for solving controller by proposing the intermediate controller variables are depend affinely on the scheduled parameter. In addition, the control matrix of linear parameter-varying (LPV) system is not limited to be constant, which greatly expands the application scope of the proposed method. The simulation validation is carried out on the SPLPV control for MA.

Off-equilibrium linearisation-based nonlinear control of turbojet enginese with sum-of-squares programming

ABSTRACTIn conventional linear parameter-varying (LPV) modelling and gain scheduling control design for turbojet engines, the linearisation is performed at a set of equilibrium points, and the validity of such LPV models is ensured near the equilibria. However, the linear model can only provide an approximate description of the engine’s state when the system operates away from equilibrium. In this paper, it is suggested that such linearisation should be carried out not only at equilibrium states but also in transient (off-equilibrium) operating regimes. This will result in a global approximation to the system states whether equilibrium or off-equilibrium. Theoretically, the transient control performance can be improved by introducing such an off-equilibrium linearisation-based control procedure. Subsequently, a gain scheduling control procedure based on off-equilibrium linearisation models is proposed by using sum-of-squares (SOS) programming, which, compared with many convex programming methods, can provide less conservative results. The resulting off-equilibrium linearisation-based nonlinear control procedure with SOS programming can capture a wide range of transient engine dynamics with better accuracy, and further achieve better control performance.

Robust speed controller design for permanent magnet synchronous motor based on gain-scheduled control method via LMI approach

In recent years, permanent magnet synchronous motors (PMSMs) have received more attention in industries due to their higher efficiency in comparison to induction motors. Moreover, they play a growingly important role in applications where variable speeds are necessary. This paper is concerned with the speed control of PMSMs, and the controller design procedure is developed in two steps. Firstly, a novel robust controller is designed via linear matrix inequalities (LMIs) approach in order to guarantee the robustness of the speed control under the load variation and uncertainty. The design of the main LMI, uncertainty, and disturbance elimination LMI involves several steps which are presented in the paper. For comparison, classic state feedback controller and proportional–integral–derivative controller with parameters optimized by genetic algorithm are implemented in different scenarios. Secondly, a gain-scheduled controller is designed and simulated. The controller design conditions are derived in terms of LMIs, which can be solved via convex optimization in MATLAB using YALMIP toolbox. It is observed that instead of using one robust controller for all operating points, several ones can be used, and by measuring the speed feedbacks, the control system opt for the appropriate controller. The suggested gain-scheduled control method via LMI approach gives excellent performance over the complete operational range, and the results validate the robustness and effectiveness of the proposed method.

Gain‐scheduling control of dynamic lateral lane change for automated and connected vehicles based on the multipoint preview

Dynamic lateral lane change (DLLC) control of automated and connected vehicles (ACVs) is challenging because of the time-varying and complex properties of the traffic environment. This study proposes a DLLC control strategy combining dynamic trajectory planning and tracking. According to the real-time longitudinal accelerations and velocities of multiple surrounding vehicles, as well as the real-time states of the ACVs, the safe trajectory reference of DLLC is obtained by solving a case-dependent constrained optimisation problem. The lane changing efficiency, vehicle stability and passenger comfort are considered jointly in the trajectory planning. Then, the dynamic trajectory reference is tracked through a gain-scheduling control algorithm combining previewed trajectory feed-forward and ACVs states feedback. Gain-scheduling control algorithm based on a linear time-varying form is utilised to achieve the precise control of the different velocities and improve the real-time ability of the algorithm. The proposed strategy is tested through software and hardware-in-loop experiments, and in different test scenarios. The results of simulations and experiments show that the proposed control strategy can achieve a satisfactory performance of DLLC. The lane changing efficiency, safety, passenger comfort and vehicle stability are verified in complex traffic environments.

Synthesis of Memory Gain-Scheduled Controllers for Discrete-Time LPV Systems

This paper considers synthesis of discrete-time gain-scheduled controllers for linear parameter varying systems based on linear matrix inequalities (LMIs). Unlike most of the previous results, gain...

Hypersurface normalised gain-scheduled controller for a non-linear 6-DOF fast jet

This paper describes a novel approach for improving the dynamic response of a bank-to-turn autopilot for a non-linear six degree-of-freedom (6-DoF) aircraft model. The autopilot consists of a series of gain-scheduled (GS) proportional, integral and derivative (PID) controllers that govern the aircraft's angular velocities for roll, pitch and yaw. The controller gains have been optimised for localised trim points and applied continuously to the controllers using linear interpolation to form a hypersurface. Our novel solution has been achieved by implementing a set of scheduled gains for near-zero reference signals and integrating this with a set of gains that are normalised to the reference signal. The proposed approach has been compared to conventional gain scheduling techniques using a series of step input simulated manoeuvres, applied individually to the roll and pitch controllers. The results show improved rise and fall times, steady state errors, as well as reduced controller effort.

Semi-active vibration control of a semi-submersible offshore wind turbine using a tuned liquid multi-column damper

In this paper, a control system is proposed for the vibration suppression of a semi-submersible offshore wind turbine equipped with a tuned liquid multi-column damper (TLMCD). The TLMCD consists of three columns of liquid integrated into the superstructure of the semi-submersible platform. To improve the vibration suppression performance of the TLMCD, unlike previous works, the TLMCD is operated in a semi-active mode by introducing three flow control valves that allow liquid to transfer between columns. Since the rotor dynamics may greatly affect the platform vibrations, it has been included in the derived nonlinear dynamic model. In the proposed control loop, the closed-loop performance objectives of platform stabilization and rotor speed regulation are accomplished by two distinct controllers. For the platform stabilization purpose, three controller design methods of displacement-based ground-hook, velocity-based ground-hook, and bang–bang are investigated. Meanwhile, to achieve the rated rotor speed, two methods of the H∞ and gain-scheduling control schemes are attempted. The closed-loop performance is investigated through numerical simulations. Realistic wind profiles along with a wave disturbance are implemented in the numerical simulations. The results show that the gain-scheduling control scheme for the rotor speed regulation and the velocity-based ground-hook method for the platform stabilization outperform other methods. Furthermore, to study the effect of the design parameters of the TLMCD on the closed-loop performance, several cases with different values of the design parameters are examined and compared.

Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains.

An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.

A Control-Oriented Linear Parameter-Varying Model of a Commercial Vehicle Air Brake System

This paper presents a control-oriented LPV (Linear Parameter-Varying) model for commercial vehicle air brake systems, where a pneumatic valve actuator is used to control the brake chamber pressure. To improve the brake system response time and reduce the vehicle stopping distance, the traditional treadle valves used in the air brake system are replaced by electro-pneumatic valves. Also, to develop the model-based brake control strategy, a nonlinear mathematical model is developed based on Newton’s second law, fluid dynamics of the orifice, force balance of spool, and solenoid dynamic characteristics. The brake chamber dynamics is also considered during the charging and discharging processes. The developed nonlinear model is calibrated based on both valve actuator geometry and test bench experimental results. It is proposed to model the nonlinear system in the LPV form so that gain-scheduling controllers can be developed. To obtain the LPV model, system identification is conducted using the calibrated nonlinear model to obtain a set of linearized models under different brake chamber pressure levels, and the resulting identified linear models are assembled to form the LPV model with brake chamber pressure as the varying parameters. A linear infinite-horizon continuous-time LQR (Linear Quadratic Regulator) controller was designed for the braking system based on the developed LPV model with the fixed parameter to demonstrate the effectiveness of the developed LPV model.

Fusion of PDF compensation and gain-scheduled control for discrete stochastic systems with randomly occurring nonlinearities

A fusion control strategy, including probability density function (PDF) compensation and gain-scheduled control, is proposed for discrete-time stochastic systems with randomly occurring nonlinearities. Usually, it is difficult to drive the tracking error strictly to zero in a random environment. So the proposed method aims to stabilize the closed-loop system in the exponentially mean square sense and guarantee the distribution of output error as close to the expected PDF as possible. The parameters of the gain-scheduled controller are obtained by solving appropriate linear matrix inequalities, and the parameters of the PDF compensator are updated in real time according to the Kullback–Leibler divergence between the PDF of output error and the desired one. The proposed method has the characteristics of low conservativeness and easy to implement. The effectiveness of the proposed method is shown by two examples.

Robust disturbance rejection for discrete-time systems having Magnitude and rate bounded inputs

The design of a robust controller for uncertain discrete-time systems subject to bounded disturbances and having magnitude and rate bounded actuators is considered. To tackle the problem, the proposed method utilises nested ellipsoids and employs an incremental (velocity) form of the state-space model of the system. By using modified full block S-procedure, the proposed robust control design approach is applicable to any uncertain system with rational parameter dependence which cannot be managed by the existing approaches without introducing some extra conservatism. Finally, an algorithm that allows the method to be used as a gain-scheduling controller is also noted in the study.