Robust Feedback Control Research Articles

Robust Adaptive Contact Force Control of Pantograph–Catenary System: An Accelerated Output Feedback Approach

The pantograph-catenary system plays the crucial role in high-speed electric trains for electrical power collection, where continuity and smoothness of the contact between the pantograph and the catenary is one of the key factors ensuring high-quality power collection essential for safe and reliable train operation. In this article, a nonlinear and highly coupled model for the pantograph-catenary system is established, and an accelerated robust adaptive output feedback control method based on a high-gain observer is proposed to solve the contact force tracking control problem of the pantograph-catenary system using output information only. It is shown that, with the proposed method, the tracking error of the contact force is ensured to be ultimately uniformly bounded with an accelerated preassignable decay rate, resulting in smooth contact force and good-quality current collection. Both theoretical analysis and numerical simulation confirm the effectiveness and benefits of the method.

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

This study addresses the non-fragile controller design of a class of fractional-order (FO) linear delayed systems assumed to have structured uncertainties in both the plant and the controller. By using the linear matrix inequality method, singular value decomposition and FO Razumikhin theorem, the delay-dependent and order-dependent robust non-fragile state feedback controller and non-fragile observer-based robust state feedback controller are synthesised, respectively, based on whether the states are available or not. Three examples are presented to verify the effectiveness of the proposed schemes.

Structural vibration control using delayed state feedback via LMI approach: with application to chatter stability problems

This paper considers the problem of active vibration control in machining processes to prevent dynamic instability and chatter. A method for robust delayed-state feedback control is presented based on Lyapunov–Krasovskii functionals (LKFs). For fast computation and realizability, a partial state feedback approach based on a reduced order model of structural vibration is considered that matches available sensors and captures the main vibratory modes that impact on stability limits. Robustness to neglected dynamics and other model errors are accounted for by a frequency domain description of model uncertainty, augmented with the basic LKF stability condition. The controller synthesis problem is formulated as a set of linear matrix inequality equations that can be solved numerically using convex optimization methods. Evaluations on a hardware-in-the-loop flexible structure test-bed show that feedback controllers optimized via the LKF stability condition provide significant improvements in stability regions compared with optimized PD control and quadratic regulation. The results confirm the methodology as a useful approach for robust chatter control based on combined flexible structure and cutting process models.

Robust optimal feedback control design for uncertain systems based on artificial neural network approximation of the Bellman’s value function

In this study, a local approximated solution for the Hamilton–Jacobi–Bellman equation based on differential neural networks is proposed. The approximated Value function is used to obtain a feedback control law for a class of uncertain dynamical systems. The approach to deal with the uncertainties of the dynamical system is a min–max method that yields obtaining a robust-like solution for an optimal control problem. The proposed cost functional is presented in the Bolza form and the necessary and sufficient conditions for getting the min–max optimal solution with the designed robust version of the dynamic programming approach are provided. Moreover, the effect of the neural network approximation is studied. All the analysis considers a smoothness assumption regarding the Value function. The practical stability of the system with the neural network feedback optimal control is formally demonstrated by means of the Lyapunov method. Finally, the performance of the control law is compared in simulation with a classical optimal controller. The proposed controller overcomes the results produced by the classical controller, which is confirmed by the functional evaluation.

Feedforward Plus Feedback Control of an Electro-Hydraulic Valve System Using a Proportional Control Valve

The output feedback signal of the electro-hydraulic valve system (EHVS) affects the activation of its right or left envelope function; thus, even weak measurement noise can cause high-frequency switching between the two envelope functions, leading to chattering in the control input. Consequently, feedforward and feedback controllers in a cascaded configuration generate undesirable chattering in the output signal. We propose a practical and reliable control approach for an EHVS actuated by a proportional control valve. The proposed controller has a parallel structure comprising an inverse generalized Prandtl–Ishlinskii (P–I) model-based feedforward controller, with both hydraulic dead-zone and flow saturation limits, for compensating asymmetric hysteretic behavior. Further, the proposed controller comprises a robust proportional-integral-derivative (PID) feedback controller for achieving robustness against disturbances and noises. The proposed parallel structure is independent of the output feedback of the EHVS. Moreover, the proposed robust PID feedback controller guarantees EHVS stability by precisely selecting the cutoff frequency for the sensitivity and complementary sensitivity functions based on the amplitude spectrum of the inverse-model-based feedforward compensation error. The results verify the high reliability of the proposed EHVS control scheme for the precise control of an EHVS actuated by a proportional control valve in practice.

Robust l2−l∞ dynamic output feedback control design for uncertain discrete‐time switched systems with random time‐varying delay

SummaryThis article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.

Improved Modal Damping Characterization for Small-Scale Heliogyro Blades

The heliogyro solar sail maneuvers by actuating high-aspect-ratio blades at their root with sinusoidal pitch profiles, producing spin-averaged forces and moments. The lightweight blade material has little inherent damping, requiring active control to attenuate blade vibration caused by maneuvering. Paradoxically, some amount of inherent damping at the blade’s higher-frequency modes is needed to add damping to the larger-magnitude low-frequency modes, and so the control design’s robustness depends on the accuracy of the blade damping model. Therefore, characterization of blade damping is critical for increasing the Technology Readiness Level for the heliogyro. This paper describes damping characterization tests performed on small-scale heliogyro blades hanging in a high-vacuum chamber, the closest analog possible for centrifugally loaded blades in space. Improvements to the measurements and a new modal damping algorithm, which the authors call the incremental and reduced frequency response function method, allowed separate flap and twist damping ratios to be calculated for the first three modes of these lightly damped blades to within ±2% error. This unprecedented precision enables definitive conclusions that the residual air damping is insignificant and that an assumption of a linear viscous torsional blade damping model is insufficient for the design of a robust proximal blade twist feedback controller.

Güvenli Ulaşım Bakış Açısıyla Bir Kayıcı Teknenin Yalpa Hareketi İçin Kontrolcü Dizayni

The issue of safe navigation in the maritime sector is becoming more important day by day. This situation is valid not only in terms of passenger and cargo transportation, but also in different maritime operations. Based on this point, much equipment is used in order to perform safe navigation in ships for different sea states such as wind, wave, etc. This equipment is classified as active and passive systems and can be applied to different types of ships. Active stabilizer systems are frequently used, especially for ship types where speed and maneuverability are high, as instantaneous responses are important. Although there are many active systems used, active roll stabilizer fin systems are the most common. At this point, this paper describes an application of LMI (Linear Matrix Inequality) based robust and saturated H2 state feedback control to roll motion of the planing hull via the fin stabilizer. In the mathematical model, nonlinearities are expressed through damping and restoring terms. Based on the planing hull roll motion mathematical model, we also present a state space model suitable for simulation and control applications. Nondimensional lift coefficients of the fin stabilizer for different angles of attack are calculated with Star CCM+ package software. Both controlled and uncontrolled conditions are examined for the maximum lift coefficient. As a result, the efficiency of the proposed approach for safe transportation was demonstrated with the simulation results and an effective study was carried out by reducing the amplitudes of the roll motion to reasonable levels.

Robust $$H_{\infty }$$ Control of Takagi–Sugeno Systems with Actuator Saturation

The robust static output feedback control for continuous-time Takagi–Sugeno systems subject to actuator saturation is solved here, including $$H_{\infty }$$ performance guarantees. Based on a polytopic model of the saturation, sufficient conditions are proposed for designing these controllers in terms of Linear Matrix Inequalities. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved easily without requiring iterative algorithms or equality constraints, moreover, the output matrix of the considered system does not require to be full row rank. Finally, some examples are presented to show the validity of the proposed methodology.

Non-fragile memory feedback control for uncertain time-varying delay switched fuzzy systems with unknown nonlinear disturbance

Currently, the feedback control rate of most nonlinear systems is realised by the memoryless state feedback controller which cannot affect the impact of time delay on the systems, and the general processing method of the Lyapunov–Krasovskii functional for the time-varying delay switched fuzzy systems (SFS) is more conservative. Therefore, this paper addresses the problem of non-fragile robust and memory state feedback control for switched fuzzy systems with unknown nonlinear disturbance. Non-fragile memory state feedback robust controller which has two controller gains different from each other, and switching law are designed to keep the proposed systems asymptotically stable for all admissible parameter uncertainties. Delay-dependent less conservative sufficient conditions are obtained through using the Lyapunov–Krasovskii functional method and free-weighting matrices depending on Leibniz–Newton, guaranteeing that the SFS can be asymptotically stable. A numerical example is given to illustrate the proposed controller performs better than the classic memoryless state feedback controller.

Observer-based output feedback robust MPC via zonotopic set-membership state estimation for LPV systems with bounded disturbances and noises

For linear parameter varying (LPV) systems with bounded disturbances and noises, this paper presents a synthesis approach to observer-based output feedback robust model predictive control (RMPC) via the zonotopic set-membership state estimation. In the off-line optimization problem, the state observer sub-gains with a minimal ellipsoidal robust positively invariant (RPI) set for the zonotopic estimation error set are designed. In the on-line control optimization problem, bounds of the current and future zontopic estimation error sets are outer approximated by scaling the minimal ellipsoidal RPI set. Then, an on-line constrained optimization problem that considers bounds of the predicted zonotopic estimation error sets is solved to guarantee robust stability of the closed-loop observer system. In the on-line receding horizon optimization, the zonotopic estimation error set is refreshed based on zonotopic properties, and its outer approximated ellipsoidal set is optimized via the technique of S-procedure. By properly considering the relationship between the zonotopic estimation error set and its outer approximated ellipsoidal set, recursive feasibility of the optimization problem can be ensured. The on-line optimization problem guarantees that the nominal estimation error system and nominal closed-loop observer system converge to the origin. When bounded disturbances and noises are considered, the estimation error system and closed-loop observer system respectively bounded within time-varying RPI sets and robust control invariant (RCI) sets are steered to a neighborhood of the origin such that robust stability of the controlled system is guaranteed. A simulation example is given to illustrate the proposed method.

Robust Adaptive Output Feedback Control for a Class of Underactuated Aerial Vehicles with Input and Output Constraints

This paper addresses the problem of nonlinear robust adaptive output feedback controller for a class of underactuated aerial vehicles with input and output constraints. To solve the problem, the modular design strategy is proposed for the control design. By using the neural networks (NNs) to approximate system uncertainties and observers to reconstruct system states, robust adaptive output feedback controllers are developed. By using a combination of saturation functions and barrier functions, input and output constraints are simultaneously dealt with. The design methodology shows that a cascaded system of an input-to-state stable (ISS) subsystem driven by an ultimate bounded (UB) subsystem enjoys ultimate boundedness property. In addition, the tracking error converges to adjustable neighbourhoods of the origin.

Continuous Phase Control of Vanadium Dioxide Films

Abstract Vanadium dioxide (VO2) undergoes a metal-insulator transition (MIT) at approximately 68 °C, with associated sharp changes in its physical (e.g., optical, electrical, and mechanical) properties. This behavior makes VO2 films of interest in many potential applications, including memory devices, switches, sensors, and optical modulators. For ON/OFF like digital applications, an abrupt switching behavior is ideal. However, to continuously change VO2 metal/insulator phase ratio for analog-like operation, the intrinsic hysteresis characteristic of VO2 MIT renders the phase control becoming a formidable challenge. This paper considers the problem of controlling and tracking desired optical transmittance via continuous phase ratio change. The problem becomes worse while considering the differences of individual thin-film samples and the hysteresis associated with the phase change within a narrow temperature range. This paper reports a robust feedback controller using an optical transmittance measurement and based on an uncertainty and disturbance estimator (UDE) architecture. The proposed controller is capable of mitigating the adverse effect of hysteresis, while also compensating for various uncertainties. The effectiveness of the proposed methodology is demonstrated with experimental validation.

Output Feedback Robust Control with Anti-Windup Applied to the 3SSC Boost Converter

This paper deals with the problem of synthesizing an anti-windup compensator with the robust output feedback model predictive control (MPC) for uncertain systems using linear matrix inequalities (LMI) by incorporating Lyapunov functions. The proposed control is applied in the polytope modeling of three-state switching cell (3SSC) DC-DC converter. The approach involves an off-line design of a robust state observer. And the results shown in this study prove the effectiveness of the proposal MPC with anti-windup and the conditions guarantee the stability of the closed-loop system.

Robust guaranteed‐cost output feedback control of blood glucose in type 1 diabetes patient with intrapatient variability

SummaryDealing with the interpatient and the intrapatient variability in type 1 diabetes mellitus (T1DM) patient are the prominent control challenges in the development of the artificial pancreas system (APS). An APS consider a nonlinear patient model that has many state variables, but the reality is that out of the many states only glucose concentration is measurable till date without any complication and undue high cost. In the present work, the philosophy is to evolve a control technique that can address the above‐cited challenges or issues. In the sequel, a robust observer is first designed based on the attractive ellipsoid method (AEM) for norm‐bounded uncertainty structure. The information of the estimated states is then used to design a guaranteed‐cost robust output feedback control. The design methodology approximates the nonlinearity present in the model as quasi‐one‐sided Lipschitz thus including more information of nonlinearity in the design as well as the control problem is recast into a linear matrix inequality (LMI) framework. Numerical simulations of 200 virtual T1DM patients are carried out which reveal that there are no cases of hypoglycemia and postprandial hyperglycemia in the presence of bounded parametric variability and high uncertainty in exogenous meal disturbance. The proposed method is simple, efficient and optimal closed‐loop solution for blood glucose regulation in T1DM patients in a robust nonlinear framework.

Virtual and physical prototyping of a beam-based variable stiffness actuator for safe human-machine interaction

Abstract This paper reports about the virtual and physical prototyping of an antagonistic Variable Stiffness Actuator (VSA) to be used on robotic arms specifically realized for physical human-robot interaction. Such antagonistic actuation system, which comprises purposely conceived Compliant Transmission Elements (CTEs) characterized by a nonlinear relation between the deflection and the applied torque, allows to simultaneously control both the joint’s position and stiffness. The CTE’s beams geometry, namely slender spline beams, has been defined by means of an automatic routine leveraging on Matlab and ANSYS and allowing for the shape optimization of complex flexures. The synthesized springs are characterized by a predefined quadratic torque-deflection characteristic, which is shown to guarantee a precise stiffness modulation while avoiding the need for a joint’s position sensor. After shape optimization, the CTE is fabricated via additive manufacturing and subsequently tested. The acquired data show a very good consistency with the numerical results, although highlighting a non-negligible hysteresis due to material damping. Therefore, in order to cope with such unavoidable effect along with other parameter uncertainties and unmodeled effects (e.g. static friction), a robust feedback controller is proposed, allowing for the simultaneous and decoupled regulation of joint position and stiffness. Finally, a VSA prototype is produced and tested. Experimental results confirm that the VSA behaves as expected.

Robust super-twisting sliding mode controller with state observer for position tracking of ionic polymer–metal composite actuators

To date, a novel class of smart materials, known as ionic polymer–metal composites, have been intensively studied because of their huge potential applications in robotics, microelectromechanical systems, biomedical devices, and artificial muscles. The position tracking control of the ionic polymer–metal composite actuators is one of the challenging tasks due to the highly nonlinear, uncertain, and unmodeled dynamics. These inaccurate and unmodeled dynamics cause the unwanted disturbances which reduce the control performance. Therefore, a robust feedback controller for position tracking of the ionic polymer–metal composite actuators is necessary. To address this issue, this article presents a super-twisting sliding mode controller combined with integral-chain differentiator as state observer. The main advantage of the proposed method is its potential to estimate the states of the system continuously. As a result, the controller not only eliminates the parameter uncertainties and external disturbance but also it can overcome the chattering problem. The results confirm the feasibility and efficiency of the proposed method both in simulation and experiment.

Vibration control of a flexible beam structure utilizing dynamic Green’s function

The paper deals with designing a control force to create nodal point(s) having zero displacement and/or zero slope at selected locations in a harmonically excited vibrating structure. It is shown that the steady state vibrations at desired points can be eliminated using feedback control forces. These control forces are constructed from displacement and/or velocity measurements using sensors located either at the control force position or at some other location. A simple and exact closed form expression for the control force is derived using dynamic Green’s function. In a certain condition, this control force can be generated using passive elements such as springs and dampers. The design of robust feedback control with respect to excitation frequency variations is carried out and stability of the feedback control system is investigated. The effectiveness of the proposed method is demonstrated on various cases using Numerical examples.

Robust Feedback Control for Nonminimum Phase, Delayed, or Unstable Systems with Multiple Inputs

This paper presents a feedback control solution that achieves robust stability and disturbance rejection in systems with multiple manipulated inputs and a single measurable output. The uncertain plant models may exhibit either nonminimum phase, or delay, or unstable phenomena, which makes it not easy to take full advantage of the frequency response of each plant. In the framework of quantitative feedback theory (QFT), a methodology is proposed to decide the best control bandwidth distribution among inputs and to design the set of parallel controllers with as small as possible gain at each frequency. The temperature regulation in a continuous stirred-tank reactor (CSTR) illustrates the benefits of a quantitative frequency distribution of the dynamic controllability between the jacket flow and the feed flow. The main challenge is that the feed flow exhibits a higher temperature regulation capacity and also produces a temporary decrease in the reactor temperature (nonminimum phase behaviour).

Security Control for LPV System With Deception Attacks via Model Predictive Control: A Dynamic Output Feedback Approach

This article considers security control under the network environment for a system with deception attacks, polytopic uncertainty, and persistent bounded disturbance. Since the state is immeasurable and the physical constraint is considered, the output feedback robust model predictive control (MPC) is utilized. The previous results on the output feedback robust MPC are extended to address the deception attacks. The mean-square quadratic boundedness is defined in order to characterize the closed-loop stability. An optimization problem is proposed, which can be solved by linear matrix inequality techniques. By a simple refreshment of the state estimation error set, the optimization problem is shown to be recursively feasible, and the augmented state converges to the neighborhood of equilibrium point. The effectiveness of the proposed theoretical approach is demonstrated by a numerical simulation example.