Gain-scheduled Controller Design Research Articles

Design a Robust Proportional-Derivative Gain-Scheduling Control for a Magnetic Levitation System

This study focuses on the design of a robust PD gain-scheduling controller (PD-GS-C) for an unstable SISO (single-input, single-output) magnetic levitation system with two electromagnets (MLS2EM). Magnetic levitation systems offer various advantages, including friction-free, reliable, fast, and cost-effective operations. However, due to their unstable and highly nonlinear nature, these systems require sophisticated feedback control techniques to ensure optimal performance and functionality. To address these challenges, in this study, we derive the nonlinear state-space mathematical model of the MLS2EM and linearize it around five different operating points. The PD-GS-C controller aims to stabilize the system and improve steady-state control error. The strategy for obtaining the PD controller gains involves a parameter space technique, which specifies performance requirements. This technique results in ranges of proportional (KP) and derivative (KD) gains that are used by the PD-GS-C structure. To optimize the controller’s performance further, we utilize the big bang–big crunch optimization technique (BB-BC) to determine the optimal PD gains within the specified ranges. The optimization process focuses on achieving optimal performance in terms of a specific performance index function. This function quantifies the system’s time-domain step response criteria, which include minimizing overshoot percentage, settling time, and rising time. The index function is inversely proportional to the desired performance criteria, meaning that the goal is to maximize the index function to optimize the system’s performance. To validate the effectiveness and viability of the proposed strategy, we conducts MATLAB simulations and real-time experiments. The simulations and experimental findings serve to demonstrate the controller’s performance and verify its capabilities in stabilizing the MLS2EM magnetic levitation system.

Dynamic gain scheduling control design for linear multiagent systems subject to input saturation

This paper considers the finite-time bipartite consensus problem governed by linear multiagent systems subject to input saturation under directed interaction topology. Due to the existence of input saturation, the dynamic performance of linear multiagent systems degrades significantly. For the improvement of the dynamic performance of systems, a dynamic gain scheduling control approach is proposed to design a dynamic Laplacian-like feedback controller, which can be obtained from the analytical solution of a parametric Lyapunov equation. Suppose that each agent is asymptotically null controllable with bounded control, and that the corresponding interaction topology of the signed directed graph with a spanning tree is structurally balanced. Then the dynamic Laplacian-like feedback control can ensure that linear multiagent systems will achieve the finite time bipartite consensus. The dynamic gain scheduling control can better improve the bipartite consensus performance of the linear multiagent systems than the static gain scheduling control. Finally, two examples are provided to show the effectiveness of the proposed control design method.

Noniterative Data-Driven Gain-Scheduled Controller Design Based on Fictitious Reference Signal

Noniterative Data-Driven Gain-Scheduled Controller Design Based on Fictitious Reference Signal

Discrete gain scheduling control approach to elliptical orbit rendezvous system with actuator saturation

AbstractThis paper studies the discrete gain scheduling control design problem of elliptical orbit spacecraft rendezvous system with actuator saturation. Due to the presence of actuator saturation, the dynamic performance of the spacecraft rendezvous system degrades significantly. In order to improve the dynamic performance of the system, a discrete gain scheduling control approach is adopted to construct a group of time‐invariant ellipsoidal invariant sets, which can be used to determine the switching points of the discrete gain scheduling control. By choosing some discrete parameter values, the discrete gain scheduling control is obtained from a solution of a periodic Riccati matrix differential equation. Under the control obtained, the dynamic performance of the system is much improved while accomplishing successfully the rendezvous mission of the spacecraft. Finally, a practical example is provided to show the effectiveness of the proposed control design approach.

Robust H2 switching gain-scheduled controller design for switched uncertain LPV systems

Robust H2 switching gain-scheduled controller design for switched uncertain LPV systems

Systematic mitigation of gain scheduling induced windup phenomena

Abstract In this paper, we discuss the systematic design of gain scheduling controllers for nonlinear systems. We discuss control signal blending induced windup phenomena and employ an extended Model-Recovery Anti-Windup (MRAW) scheme to mitigate them. Combining control signal blending with MRAW allows to build gain scheduling controllers without imposing the common slow variation assumption regarding the scheduling vectors. In addition, the approach offers a higher flexibility in the choice of the sub-controllers compared to classical approaches and convex optimization allows for a very efficient design of the anti-windup networks.

From Impractical LPV Controllers to Practical and “Implementable” LPV Controllers: Verification with Research Airplane

We first give a brief review of classical Gain-Scheduled (GS) controllers with our design example of Stability/Control Augmentation System (S/CAS) for Quad-Tilt-Wing UAV (QTWUAV), and we clarify the issues to be overcome from the S/CAS design example. Then, a brief review of Linear Parameter-Varying (LPV) GS controller design, which has been proposed to overcome the issues in classical GS controller design, is given from the viewpoint of the practicality. Finally, several methods, which have been proposed by the author, are briefly reviewed with some verification results using JAXA's research airplane MuPAL-α. This paper ends with concluding remarks and future research topics related to LPV GS controllers.

Robust H2 output-feedback bumpless transfer control of polytopic uncertain LPV systems

The problem of Robust Switching Gain-Scheduled Output-Feedback (RSGSOF) H2 controller synthesis with control bumps limitation is tackled in this paper for polytopic uncertain continuous-time linear parameter varying (LPV) systems. The presented robust switching gain-scheduled control design scheme overcomes the limitation of existing methods based on single quadratic Lyapunov function. However, in practice, RSGSOF controller leads to expressive discontinuities at switching instants. Hence, we aim to investigate of H2 output-feedback Bumpless Transfer Controller (BTC) design problem. In this study, not only stability and an upper bound on the H2-norm performance of the closed-loop system can be guaranteed but also solvability conditions are incorporated in the synthesis procedure to reduce control bumps. The proposed BTC composes multiple LPV controllers with the bumps limitation objective and a Lyapunov-based min-switching rule governing the switching among these controllers. Numerical studies demonstrate the effectiveness of the proposed approach.

Network-based gain-scheduled control for preview path tracking of autonomous electric vehicles subject to communication delays

The preview path tracking problem of autonomous electric vehicles with event-triggered transmission and bounded communication delays is addressed using polytope modelling and asynchronous gain-scheduled control methods. By finding a polytope with as few vertices as possible to wrap the curve composed of all time-varying parameters, a new polytope modelling method is proposed to describe the vehicle lateral dynamics, which can not only reduce the modelling complexity greatly but also keep the modelling accuracy. Based on the polytope system model, a network-based gain-scheduled controller that operates asynchronously with the polytope system is constructed, where the scheduling parameters are driven by transmitted longitudinal velocity. By computing the deviation bounds of scheduling parameters and utilising the deviation-bound-dependent method, an asynchronous gain-scheduled control design method is presented. The feasibility and advantages of the proposed methods are shown by numerical verification.

Event‐triggered and self‐triggered gain scheduling control of input constrained systems with applications to the spacecraft rendezvous

AbstractThis article studies event‐triggered and self‐triggered gain scheduling control design for semi‐global stabilization of input constrained linear systems. Using the parametric Lyapunov equation (PLE), a event‐triggered gain scheduling control, which can increase the convergence rate of the closed‐loop systems by designing a gain scheduling scheme and save the communication resources by building an event generator, is designed. In order to avoid continuously monitoring the system states, the self‐triggered gain scheduling control algorithms are also designed. The non‐occurrence of the Zeno phenomenon and the boundedness of the parameter in the PLE are proved. The impact of the parameter on the minimal inter‐event time is analyzed, which allows us to find easily a trade‐off between the inter‐event times and the control performance. Another advantage of the designed methods is that the controller is linear. Finally, the proposed control algorithms are applied to stabilize the spacecraft rendezvous control system and the numerical simulation result shows the efficacy of the control algorithms.

Local Sampled-Data Gain-Scheduling Control of quasi-LPV Systems

Abstract This paper deals with the problem of sampled-data gain-scheduling control design for affine quasi-LPV systems. As the control implementation is based on sample-data and its update occurs only at specific sampling instants, the state-dependent scheduling functions of the controller are piecewise continuous. This characteristic causes a mismatch between the system model and the controller parameters, namely asynchronous scheduling functions of the controller with respect to the plant during the inter-sampling behavior. To cope with this phenomenon, a polytopic description of the inter-sampling is constructed based on bounding assumptions on the scheduling functions and their time derivatives. Then, regarding a time-delay approach, a constructive and numerically implementable LMI-based synthesis condition is derived, and a convex procedure is proposed for enlarging the estimate of the region of attraction of the origin of the closed-loop system. The time-derivative bounds of the scheduling functions are explicitly accounted into the local analysis to ensure the method’s implementation. A numerical example is provided to illustrate the proposed methodology.

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.

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.

One-shot design of performance scaling matrices and observer-based gain-scheduled controllers depending on inexact scheduling parameters

This paper addresses the design problem of continuous-/discrete-time observer-based Gain-Scheduled Output Feedback (GSOF) controllers for Linear Parameter-Varying (LPV) systems, in which some of the state-space matrices are multi-affine with respect to parameters, with the simultaneous design of scaling matrices for multiple uncertainty blocks under the supposition that inexact scheduling parameters are available. In the design of GSOF controllers for practical systems in induced L2∕l2-norm control framework, the following features are to be incorporated; i) structured and easily-understandable controllers are preferable to enhance the practicality, ii) the scaling matrices related to multiple uncertainty blocks which represent various design specifications are also to be designed to reduce conservatism, and iii) one-shot design is preferable to prevent numerical problems in iterative algorithm. However, in general, neither the design problems of the structured controllers nor the simultaneous design of controllers and the performance scaling matrices are formulated in terms of Linear Matrix Inequalities (LMIs). Under the supposition that the uncertainties in the provided scheduling parameters are bounded (this supposition holds true for proportional uncertainties and for absolute uncertainties as well as for the mixed ones of them), we derive a new tractable one-shot multi-affine condition for our problem via dilated/extended LMI technique under some mild assumptions for LPV systems. A numerical example well illustrates the effectiveness of our method.

Design of gain scheduled rotor thrust controller using airspeed and rotor angular velocity

Design of gain scheduled rotor thrust controller using airspeed and rotor angular velocity

Gain-Scheduled Controller Design for Cooperative Adaptive Cruise Control: Towards Automated Driving

Gain-Scheduled Controller Design for Cooperative Adaptive Cruise Control: Towards Automated Driving

Parameter-Space Based Robust Gain-Scheduling Design of Automated Vehicle Lateral Control

This paper presents a robust gain-scheduling controller design based on the parameter-space approach. The gain-scheduling control is of interest for systems with varying dynamics at different operating conditions. Requirements of robustness of stability and performance are also necessary if the system is subject to other parametric or model uncertainties. The parameter space approach is capable of projecting these requirements to the space of design parameters and facilitate the design of robust gain-scheduling control. This method is applied to automated vehicle lateral control to ensure its tracking accuracy and stability subject to uncertainties in vehicle load, speed and tire saturation. The proportional feedback gain and look-ahead distance are scheduled with respect to speed while sustaining robust stability, mixed sensitivity bound constraint and satisfaction of performance indices. Realistic hardware-in-the-loop (HIL) simulation with a validated vehicle model and road tests are conducted to demonstrate the robust performance of the designed gain-scheduling control in the presence of model uncertainty and disturbances. Another general robust gain-scheduling approach, the linear-matrix-inequality- (LMI-) design is also conducted for benchmarking purposes and the comparisons are discussed.

Robust PI, gain scheduled and PSS controller design using LMI regions: Comparative studies

Abstract This paper considers development of a new design procedure for PI and Gain scheduled robust controller with PSS for turbogenerator using LMI regional regions. The obtained PI+PSS and GSC+PSS robust controllers with output and state derivative feedback for uncertain polytopic turbogenerator model ensure that all closed -loop eigenvalues lay in the prescribed LMI region. The proposed method is to guarantee the less conservativeness with respect to previous methods due to introducing a design procedure based on new auxiliary matrices. The effectiveness of this procedure is illustrated by the examples of two controllers for turbogenerator.

Model-Based Control Design of Series Resonant Converter Based on the Discrete Time Domain Modelling Approach for DC Wind Turbine

This paper focuses on the modelling of the series resonant converter proposed as a DC/DC converter for DC wind turbines. The closed-loop control design based on the discrete time domain modelling technique for the converter (named SRC#) operated in continuous-conduction mode (CCM) is investigated. To facilitate dynamic analysis and design of control structure, the design process includes derivation of linearized state-space equations, design of closed-loop control structure, and design of gain scheduling controller. The analytical results of system are verified in z-domain by comparison of circuit simulator response (in PLECS™) to changes in pulse frequency and disturbances in input and output voltages and show a good agreement. Furthermore, the test results also give enough supporting arguments to proposed control design.

Experimental Validation of a Torque-Controlled Variable Stiffness Actuator Tuned by Gain Scheduling

A variable stiffness actuator (VSA) is an inherently parameter-dependent system due to the controllable stiffness element. Within the torque-controlled framework, the VSA is distinguished from the classical series elastic actuator (SEA). A frozen torque controller can directly determine the SEA performance with a fixed-stiffness spring selection. However, since the VSA operates at a set of operating points, the aim is to achieve an adaptive control approach. For this, we propose a gain-scheduled torque controller. The control performance is expected to recover robustness when stiffness values are varied from smaller to larger ones. Simultaneously the bandwidth is maximized, taking into account hardware limitations. In this way, a good tradeoff between stability and performance can be achieved. A key step in the gain-scheduled controller design is to implement the linear controllers, where the linear quadratic Gaussian (LQG) technique was applied to deal with the multiloop feedback (a cascade control scheme) in the VSA plant. A lever-arm based VSA [i.e., a mechanical-rotary variable impedance actuator (MeRIA)] was used to verify this new controller design approach by the simulations and experiments. The resulting gain-scheduled controller was also evaluated by taking into account the impedance control testing on a motion-supported platform for the knee joint.