Robust Control Design Research Articles

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System

This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.

Optimal robust control of nonlinear systems: inter-sample optimisation in sampled-data control

A methodology is presented for the design and implementation of robust controllers that optimise inter-sample performance for a broad range of nonlinear systems operated within a sampled-data environment. The methodology applies to nonlinear continuous-time systems described by state equations, and it allows for modelling uncertainties and constraints on maximal control effort. It is shown that there exist optimal robust state-feedback controllers that minimise inter-sample tracking errors for such systems, as long as an appropriate controllability requirement is met. A relatively simple design and implementation procedure for such controllers is described.

Modeling and Adaptive Control for Tendon Sheath Artificial Muscle Actuated Bending-Tip Systems With Unknown Parameters and Input Hysteresis: An Experimental Research

Due to the flexible structure and extension capacity, the tendon-sheath artificial muscle (TSAM) actuated bending-tip (TAB) system has attracted increasing efforts in the field of rehabilitation and surgical robots. However, the TAB system usually suffers from unknown input hysteresis, unidentifiable parameters, and unexpected external disturbance, which bring great challenges for precise dynamic modeling and robust controller design. So far, there is still no available strategy to deal with these complicated nonlinearities for the TAB system. In this paper, the Euler-Lagrange dynamics is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> established for the TAB system based on rigorous energy analysis. Then, a novel adaptive controller is developed based on the original dynamics <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any approximation, which can suppress the unavoidable effects of unknown parameters and input hysteresis, and achieve high-precision tracking performance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> . Specially, the proposed adaptive method can also weaken the widely-used constant curvature assumption. By utilizing the Lyapunov-based technique, the stability of the closed-loop system is proven. Finally, to further validate the effectiveness and the robustness of the proposed controller, a series of hardware experiments are carried out on a self-built flexible ureteroscopy robot.

Cooperative Game Theory based robust shared lateral control for Driver Vehicle Interactions

Extensive manual driving is liable to attention lapses and driver exhaustion resulting in lane offset errors, driver comfort minimization and degradation in vehicle stability. On the contrary, apart from being expensive, autonomous vehicles suffer from the issue of trust, ethics and traffic mapping. In order to address the above limitations, this paper deals with the design of a Game Theoretic based Shared Control (GTSC) framework that enables an interaction between the human and the machine. The novelty lies in the generation of automatic driver automation relative weights based on the vehicle’s lateral position relative to the maximum admissible lateral offset. The interaction between the human driver and automated system based on the cooperative game theory is utilized to develop a robust shared control framework. The driver model parameters have been estimated using the experimentally obtained driver steering torque and steering wheel angle respectively through an inverse modelling procedure. The lateral dynamics of the vehicle model in the presence of crosswinds and yaw moment as disturbances are considered for the design. A higher order sliding mode observer is designed to ensure robust estimation of the unknown states. Unlike the existing studies that primarily concentrates on the robust game theoretic shared controller design, this new study broadens its focus. The study introduces an observer-based robust design for GTSC and establishes the stability of the closed-loop system. The effectiveness of this proposed framework is verified through simulations in Carsim as well as real-world testing on a Hardware-in-the-loop (HIL) platform with a human driver. The study also addresses the challenge of obstacle avoidance using the GTSC framework. Comparisons have been performed with the state-of-the-art shared control studies while considering factors like crosswinds, variation in the longitudinal velocities and alterations in the reference path to evaluate the effectiveness of the proposed shared control study. The results demonstrate the improvement in the lateral offset, driver comfort and the vehicle stability compared to the manual control of the vehicle.

Robust stability region analysis of time‐delayed load frequency control systems with EVs aggregator using Kharitonov theorem

AbstractThis study focuses on analyzing the robust stability regions and robustness margin of a time‐delayed load frequency control (LFC) system with Electric Vehicles (EVs) using the Kharitonov Theorem. Communication time delays in LFC systems can jeopardize stability and reliability, leading to suboptimal controller performance. Integrating EVs into LFC systems enhances dynamical stability but introduces additional complexity. Therefore, it is crucial to employ robust analysis and controller design techniques to ensure system stability. In this study, we utilize the Kharitonov Theorem to determine the robust stability regions and stability boundaries in the parameter plane of the Proportional‐Integral (PI) controller. By considering communication time delays and parametric uncertainties in the LFC system with EVs (LFC‐EVs), the robust PI controller gains using these methods are efficiently computed. To evaluate the performance of the theoretically computed robust controller parameters, time‐domain simulations are conducted.

Stochastic Analysis of Control Systems Subject to Communication and Computation Faults

Control theory allows one to design controllers that are robust to external disturbances, model simplification, and modelling inaccuracy. Researchers have investigated whether the robustness carries on to the controller’s digital implementation, mostly looking at how the controller reacts to either communication or computational problems. Communication problems are typically modelled using random variables (i.e., estimating the probability that a fault will occur during a transmission), while computational problems are modelled using deterministic guarantees on the number of deadlines that the control task has to meet. These fault models allow the engineer to both design robust controllers and assess the controllers’ behaviour in the presence of isolated faults. Despite being very relevant for the real-world implementations of control system, the question of what happens when these faults occur simultaneously does not yet have a proper answer. In this paper, we answer this question in the stochastic setting, using the theory of Markov Jump Linear Systems to provide stability contracts with almost sure guarantees of convergence. For linear time-invariant Markov jump linear systems, mean square stability implies almost sure convergence – a property that is central to our investigation. Our research primarily emphasises the validation of this property for closed-loop systems that are subject to packet losses and computational overruns, potentially occurring simultaneously. We apply our method to two case studies from the recent literature and show their robustness to a comprehensive set of faults. We employ closed-loop system simulations to empirically derive performance metrics that elucidate the quality of the controller implementation, such as the system settling time and the integral absolute error.

Adaptive controller design and disturbance attenuation for minimum phase multiple‐input multiple‐output linear systems with noisy output measurements and with measured disturbances

SummaryIn this paper, we present a systematic procedure for robust adaptive control design for minimum phase uncertain multiple‐input multiple‐output linear systems that are right invertible and can be dynamically extended to a linear system with vector relative degree using a dynamic compensator that is known. For this class of systems, it is always possible to dynamically extend them, and/or integrate a select set of output channels, and/or padding dummy state variables to arrive at a system model that admits uniform vector relative degree and uniform observability indices that is further minimum phase according to Reference 13. We assume that the uniform vector relative degree is known and an upper bound for the uniform observability indices is known. We also assume that the unknown parameter vector lies in a convex compact set such that the high frequency gain matrix remains invertible for any parameter vector value in the set. These are the assumptions that allow for a successful design of a robust adaptive controller. A numerical example is included to fully illustrate the controller design and the effectiveness of the controller.

Robust control design for suspension system in LIGO

In this article, we present a relatively new state-space methodology, called synthesis, to design a robust controller for a subsystem of the Laser Interferometer Gravitational Wave Observatory. In particular, we examine the quadruple pendulum subsystem, which is simplified for the purpose of the study to a two wire simple pendulum system. Structured and unstructured uncertainties are considered in the modelling, though the structured ones are incorporated in the unstructured framework based on a design philosophy presented in the literature. Incorporating weighting functions that emphasize the spectral band of the uncertainties as well as the band in which disturbances are to be attenuated, we design a robust control law using the coprime factorization technique of the paradigm.

Robust Controller Design for a Generic Helicopter Model: An AI-Aided Application for Terrain Avoidance

This paper focuses on robust controller design for a generic helicopter model and terrain avoidance problem via artificial intelligence (AI). The helicopter model is presented as a hybrid system that covers hover and forward dynamics. By defining a set of easily accessible parameters, it can be used to simulate the motion of different helicopter types. A robust control structure based on reinforcement learning is proposed to ensure the system is robust against model parameter uncertainties. The developed generic model can be utilized in many helicopter applications that have been attempted to be solved with sampling-based algorithms or reinforcement learning approaches that take the dynamical constraints into consideration. This study also focuses on the helicopter terrain avoidance problem to illustrate how the model can be useful in these types of applications and provide an artificial intelligence-aided solution to terrain avoidance.

A robust optimal distributed control design for simultaneous voltage regulation and current sharing in DC microgrid

AbstractIn this article, a robust optimal distributed controller is designed for achieving average voltage regulation and current sharing in a DC microgrid. Each distributed generation unit (DGU) consists of a DC‐DC buck converter that supplies a local constant current load. The proposed controller only utilises output currents of converters and the possible maximum error values in estimation of series resistance in the RLC filter used in each DGU. The proposed controller is formed such that the possible estimation error is considered as an uncertain parameter. In addition to obtaining two main objectives, average voltage regulation, and current sharing, a robust control problem is solved through an optimal control technique to calculate controller parameters such that the stability of the grid is guaranteed. The stability of the closed loop system with parametric uncertainty is proved through Lyapunov analysis. The closed loop system with the suggested controller is tested by simulations and through different scenarios to reveal the reliable and satisfactory performance of the proposed robust optimal control structure.

Sliding mode control design using generalized relative degree approach: Aerospace application

Relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs using the RD alone can fail due both to insufficient control authority in minimum phase systems, and instability of internal/zero dynamics attributed to nonminimum phase systems. A novel definition and a concept of Practical Generalized RD (PGRD) are proposed in this paper and are used in concert with Sliding Mode Control (SMC) to compensate for system perturbations in minimum phase systems. The use of known Generalized Relative Degree (GRD) in nonminimum phase systems allows for the elimination of internal dynamics. However, instability that emerges in the corresponding control dynamic extension is defeating any output tracking controller design. A novel methodology of using GRD for designing continuous SMC in nonminimum phase systems is presented. An algorithm for generating a bounded solution of the unstable dynamic extension is proposed and used in concert with SMC, allowing robust control design for nonminimum phase systems. The efficacy of the proposed GRD-based approaches is demonstrated on a minimum and nonminimum phase rocket attitude control problem both analytically and via simulation.

On a neural network approach for solving potential control problem of the semiclassical Schrödinger equation

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schrödinger equation, where the control variable is the potential given by an external field that may contain uncertainties. Inspired by a relevant work Li et al., 2021 [1], we incorporate the sampling-based learning process into the training of networks, while combining with the fast time-splitting spectral method for the Schrödinger equation in the semi-classical regime. The numerical results have shown the efficiency and accuracy of our proposed deep learning approach.

Predefined-time stabilization of brushed direct current motor system affected by matched and unmatched disturbances and stochastic noises

This paper presents the predefined-time convergent robust controller design for a brushed direct current (DC) motor system affected by matched and unmatched deterministic disturbances and stochastic noises, considering both fully measurable and incompletely measurable states. The control algorithm allows the control designer to set the convergence time a priori. The convergence time is independent of initial conditions and disturbances and noises affecting the system. Numerical simulations are conducted to demonstrate efficiency of the designed control algorithm. The obtained results show that the control algorithm counteracts the matched and unmatched disturbances, and noises in case of fully measurable states and mitigates their influence in case of incompletely measurable ones.

Robust control design on Scilab: Hybrid remotely operated vehicle

AbstractThe goal of this work is to demonstrate the advanced features of Scilab/Xcos software in the process of designing robust controllers and to validate them numerically by a multivariable system with high coupled dynamics; it is a hybrid remotely operated vehicle (HROV). The methodology presents five steps which are the nonlinear model representation, the model linearization, the building of augmented plants, the synthesis of robust controllers through the optimization algorithms, and the plotting of the results. Linear models can be obtained straightforwardly at many operation points. The robust controllers are synthesized using the mixed sensitivity approach and tested in Scilab script and in the Xcos block diagram interface. The surge and yaw rate vehicle dynamics are controlled by a centralized controller; obtaining a good settling time, of less than 14 s, without overshooting and mitigating the coupling dynamics. Moreover, the good shaping in sensitivity and complementary sensitivity indicates robustness in performance and stability for the HROV. The proposed methodology includes time and frequency domain analysis, among other advanced features, to overcome the need for commercial software.

A road adhesion coefficient-tire cornering stiffness normalization method combining a fractional-order multi-variable gray model with a LSTM network and vehicle direct yaw-moment robust control.

A normalization method of road adhesion coefficient and tire cornering stiffness is proposed to provide the significant information for vehicle direct yaw-moment control (DYC) system design. This method is carried out based on a fractional-order multi-variable gray model (FOMVGM) and a long short-term memory (LSTM) network. A FOMVGM is used to generate training data and testing data for LSTM network, and LSTM network is employed to predict tire cornering stiffness with road adhesion coefficient. In addition to that, tire cornering stiffness represented by road adhesion coefficient can be used to built vehicle lateral dynamic model and participate in DYC robust controller design. Simulations under different driving cycles are carried out to demonstrate the feasibility and effectiveness of the proposed normalization method of road adhesion coefficient and tire cornering stiffness and vehicle DYC robust control system, respectively.

Robust integral controller design based on composite nonlinear feedback in uncertain systems with constrained inputs and external disturbances

AbstractIn this article, to enhance the transient performances in constrained uncertain systems, a control technique based on linear matrix inequality (LMI) is characterized to the robust integral composite nonlinear feedback (CNF) controller design. To achieve this aim, considering the inputs limitations and the uncertainties, the regulation is transformed into a minimization subjected to several LMIs. Solving an optimization in real‐time, the gains of the controller are calculated. So, the regulation and the disturbance rejection are effectively handled employing the presented control law. Compared with the existing integral methodology, the provided simulations validate the applicability of the robust integral CNF control law in uncertain systems.

A data-driven control methodology applied to throttle valves

Electric throttle valves represent a challenge for control design, as their dynamics involves strong nonlinearities, characterized by an asymmetric hysteresis. Large variability in the characteristics of each valve and erratic steady-state behaviors can also be noticed by carrying out experiments on multiple valves, impairing classical model-based control strategies. Nevertheless, local data-driven linear models can be obtained by system identification, and simple proportional–integral (PI) digital controllers can be tuned individually for each valve, providing good tracking performance. As these controllers cannot be transposed from one valve to another, a robust control design is considered. Taking into account the variability of electric throttle valves, a real-time data-driven strategy is then proposed, using identification in closed-loop and controller re-design. This methodology is necessary if control performance is a key issue, and can be embedded on a low-cost controller board (Arduino® Mega 2560). Experimental results going from frequency analysis and linear design to real-time data-driven control illustrate the methodology presented in the paper.

Design of robust path tracking controller using model predictive control based on steady state input

Design of robust path tracking controller using model predictive control based on steady state input

Design of Suboptimal Robust Controllers Based on a Priori and Experimental Data

Design of Suboptimal Robust Controllers Based on a Priori and Experimental Data

Multi-objective optimal design of a fuzzy adaptive robust fractional-order PID controller for a nonlinear unmanned flying system

In this study, a fuzzy adaptive robust fractional-order proportional-integral-derivative (FARFOPID) controller is introduced for stabilization of a nonlinear unmanned flying system. At first, a proportional-integral-derivative scheme improved by the fractional-order technique is employed to control the complicated dynamics of the considered system. An adaptive mechanism based on sliding surfaces is proposed to update the effective gains of the fractional-order PID controller. To improve the performance of the controller in the presence of disturbances and uncertainties, fuzzy systems are used to adjust the parameters of the sliding surfaces. The fuzzy systems, considered in this article, employ the singleton fuzzifier, product inference engine and center average defuzzifier as well as triangular-trapezoidal membership functions. Then, the multi-objective thermal exchange optimization (MOTEO), which has presented a high convergence speed and good performance for global search problems, is utilized to determine the controller parameters in such a way that control efforts and system errors would be minimized, simultaneously. Finally, simulation results clearly depict the effectiveness and efficiency of the proposed approach to handle the regarded unmanned flying system in comparison with other controllers.