Feedback Control Gain Research Articles

Nonlinear optimal control for multi‐DOF robotic manipulators with flexible joints

AbstractA main problem in the control of flexible‐joint robots and in the precise positioning of their end‐effector, is synchronization between the turn angles of the robots' joints and the turn angles of the motors that provide actuation to these joints. In this article, a nonlinear optimal (H‐infinity) control method is proposed for multi‐DOF robotic manipulators with flexible joints. The dynamic model of these robotic manipulators is shown to be underactuated and to satisfy differential flatness properties. The state‐space description of these robots undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure makes use of first‐order Taylor‐series expansion and relies on the computation of Jacobian matrices. For the approximately linearized model of these multi‐DOF robotic systems an H‐infinity feedback controller is designed. This controller stands for the solution of the robots' optimal control problem under model uncertainty and external disturbances. The computation of the controller's feedback gain requires the solution of an algebraic Riccati equation, which is performed again at each time‐step of the control algorithm. The stability properties of the control scheme are proven trough Lyapunov analysis. First, it is confirmed that the controller satisfies the H‐infinity tracking performance criterion which ascertains its robustness. Moreover, it is proven that the control loop is globally asymptotically stable. Finally, to implement sensorless control for such robotic systems the H‐infinity Kalman Filter is used as a robust state estimator. The proposed control method for multi‐DOF robotic manipulators with flexible joints retains the advantages of linear optimal control, that is fast and accurate tracking of its reference setpoints under moderate variations of the control inputs.

Robust repetitive control for a class of uncertain nonlinear systems

AbstractThis paper presents an output‐feedback repetitive control method for a class of systems with nonlinearities, unknown state‐dependent uncertainties, and external disturbances. An additive‐state‐decomposition approach is used to decompose the system under study into a primary linear periodic system in charge of repetitive‐control tracking task and a secondary linearized system in charge of robustly stabilization task. Such a treatment not only significantly simplifies system analysis and controller design, but also provides an effective method to cope with the intrinsic constraints between tracking and disturbance rejection. Another attractive point lies in two aspects. On one hand, a periodic term from the nonlinearity in the plant is extracted to be treated in the primary system and the known plant information is used to design controller parameters, which greatly improves the disturbance rejection ability of the system. On the other hand, repetitive control gain, feedback control gain, and the observer gain are optimized through an optimization algorithm by introducing an index to evaluate the overall system performance. System stability criteria and design procedure are developed. Finally, a case study on the tracking control of a chuck‐piece system demonstrates the validity of the proposed method. Comparisons with some existing methods show that the proposed method achieves better performances in both signal tracking and disturbance rejection.

Active tuning of elastic wave propagation in a piezoelectric metamaterial beam

In this paper, an active control strategy is employed to actively tune the vibration and wave propagation properties in a piezoelectric metamaterial beam. The piezoelectric actuator and sensor are periodically arranged along the piezoelectric metamaterial beam. By using the extended Hamilton principle, the governing equations for the fully coupled piezoelectric metamaterial beam are obtained. The negative proportional feedback control strategy is introduced to achieve the periodical active stiffness for the piezoelectric metamaterial beam. The band structures and natural frequencies of the proposed periodic structure are derived by the transfer matrix method, and the spectral element method is applied as numerical validation. The influences of the feedback control gain ratio, length ratio, and the number of the unit cells on natural frequencies and bandgaps are discussed. Results indicate that the natural frequencies of the system are reduced with the increase in the feedback control gain ratio and length ratio. In addition, multiple bandgaps can be generated by using the negative proportional feedback control strategy. It is found that bandwidths can be obviously broadened by selecting the proper feedback control gain ratio and length ratio. The theoretical and numerical results show that the vibration and wave propagation properties of the proposed piezoelectric metamaterial beam can be controlled by using the negative proportional feedback control strategy.

Trust-based fault detection and robust fault-tolerant control of uncertain cyber-physical systems against time-delay injection attacks

Control systems need to be able to operate under uncertainty and especially under attacks. To address such challenges, this paper formulates the solution of robust control for uncertain systems under time-varying and unknown time-delay attacks in cyber-physical systems (CPSs). A novel control method able to deal with thwart time-delay attacks on closed-loop control systems is proposed. Using a descriptor model and an appropriate Lyapunov functional, sufficient conditions for closed-loop stability are derived based on linear matrix inequalities (LMIs). A design procedure is proposed to obtain an optimal state feedback control gain such that the uncertain system can be resistant under an injection time-delay attack with variable delay. Furthermore, various fault detection frameworks are proposed by following the dynamics of the measured data at the system's input and output using statistical analysis such as correlation analysis and K-L (Kullback-Leibler) divergence criteria to detect attack's existence and to prevent possible instability. Finally, an example is provided to evaluate the proposed design method's effectiveness.

Control of hygrothermal vibration of viscoelastic magnetostrictive laminates resting on Kerr’s foundation

Many composite structural applications undergo several environmental conditions, so, for the optimal design of the composite structural systems and efficient use of the engineering applications, the accurate vibrational behavior prediction of the composite structures subjected to thermal/hygrothermal environments effect is required. In the current study, vibration response and damping behavior of a multilayered composite plate with viscoelastic faces and homogenous core, resting on three-parameter Kerr’s foundation are analyzed based on a higher-order shear deformation plate theory with an exponential shape function. Simple velocity feedback control and two magnetostrictive (Terfenol-D) actuators are utilized for controlling the vibration of the sandwich plate. The governing system of the vibration problem is formulated using Kelvin-Voigt viscoelastic relation and Hamilton’s principle as well as the system is solved analytically according to Navier’s approach. To assess influences of the significant parameters such as the magnitude of the feedback control gain, the magnetostrictive layer location, the geometric coefficients, the magnetostrictive layer thickness-to-core thickness ratio, the viscoelastic layer thickness-to-core thickness ratio, orientations of the viscoelastic layer’s fiber, the half wave numbers, the lower and upper spring stiffness, the shear layer stiffness, the temperature and moisture concentrations on frequencies and deflection of the structure, comprehensive parametric examples are discussed. Findings of the study indicate that control systems of the structural applications can be improved excellently by combining the passive and active strategies for vibration damping of the structures.

Quasi-3D theory for the vibration and deflection of a magnetostrictive composite plate resting on a viscoelastic medium

In this study, the vibration and deflection of a multilayered composite plate are investigated based on simple and refined sinusoidal shear deformation plate theories. The plate’s core is made of a homogeneous material. Hamilton’s principle is used to derive the dynamic system of equations. The interaction between the smart composite sandwich plate and the surrounding medium is simulated by the visco-elastic foundations model. The analytical solution for the vibration problem of the simply supported plate is obtained by Navier’s approach. Influence of the magnitude of feedback control gain, magnetostrictive layer location, half-wave numbers, lamination schemes, thickness ratios, aspect ratios, core-thickness ratios, magnetostrictive-thickness ratio, and viscoelastic foundations on eigenfrequency values and deflections of the sandwich plate are discussed. Numerical results illustrate that the vibration behavior of the smart sandwich plate is dependent on the stiffness of the viscoelastic foundations, the feedback control gain value, and the magnetostrictive-thickness ratio. Also, the vibration suppression process can be improved by changing the location of the smart layers in the structure.

Nonlinear hygrothermal effects on the vibrations of a magnetostrictive viscoelastic laminated sandwich plate resting on an elastic medium

In engineering applications, composite structures supported by elastic foundations are being vastly utilized in various operating environmental conditions. The nonlinear hygrothermal effect on vibration analysis of a magnetostrictive viscoelastic laminated composite sandwich plate rested on two-parameter Pasternak’s foundations is studied in the present article. The material properties of the viscoelastic plate’s layers are considered based on the Kelvin–Voigt model. The governing equation system is derived according to Hamilton’s principle. The analytical solution is obtained to study influences of the hygrothermal change, half wave number, magnitude of the feedback control gain, aspect ratios, thickness ratio, and structural viscoelastic damping coefficients on vibration damping characteristics of the plate including the frequencies, the damping rate, and the deflection. The obtained results indicate that the natural frequency and deflection reduce with increasing the structural viscoelastic damping value. The plate takes a long time for suppressing its vibration due to increasing the hygrothermal factor.

PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage

This paper presents a new scheme of adaptive sliding mode control (ASMC) for a piezoelectric ultrasonic motor driven X–Y stage to meet the demand of precision motion tracking while addressing the problems of unknown nonlinear friction and model uncertainties. The system model with Coulomb friction and unilateral coupling effect is first investigated. Then the controller is designed with adaptive laws synthesized to obtain the unknown model parameters for handling parametric uncertainties and offsetting friction force. The robust control term acts as a high gain feedback control to make the output track the desired trajectory fast for guaranteed robust performance. Based on a PID-type sliding mode, the control scheme has a simple structure to be implemented and the control parameters can be easily tuned. Theoretical stability analysis of the proposed novel ASMC is accomplished using a Lyapunov framework. Furthermore, the proposed control scheme is applied to an X–Y stage and the results prove that the proposed control method is effective in achieving excellent tracking performance.

A new parametrization for static output feedback control of LPV discrete-time systems

This paper deals with the problem of synthesizing static output feedback controllers for linear parameter-varying discrete-time systems with guaranteed ℓ2 gain performance. The proposed method relies on augmenting the matrices related to the control input with a block of zeros and also augmenting the control gain accordingly with some real matrix. In this way, the closed-loop system remains the same, but extra degrees of freedom can be exploited in the proposed synthesis conditions. These conditions are described in terms of optimization problems having Linear Matrix Inequalities as constraints. Unlike other methods in the literature, all system matrices can depend on the scheduling parameter and, furthermore, the proposed approach is capable of determining a static output feedback control gain by with a one-phase one optimization problem. Numerical examples illustrate that the proposed approach is less conservative when compared to other available methods.

Extended dissipativity-based control for persistent dwell-time switched singularly perturbed systems and its application to electronic circuits

In this paper, the extended dissipative control issue is studied for a class of discrete-time persistent dwell-time (PDT) switched singularly perturbed systems (SPSs). The persistent dwell-time switching strategy is employed to describe the fast and slow switching among several subsystems of the SPSs alternately. Based on Lyapunov stability theory and switched system theory, some sufficient conditions are obtained, which can ensure the exponentially stable and extended dissipative performance of the closed-loop systems. In addition, the slow state variables feedback (SSVF) controller gain is obtained by solving a set of linear matrix inequalities (LMIs). And, a convex optimization method is utilized to calculate the upper bound of singular perturbed parameters (SPP). Finally, a numerical example and an electronic circuits model are applied to demonstrate the practicability and effectiveness of the developed proposed technique.

Minimum variance control of chaos in a hyperchaotic memristor based oscillator using online particle swarm optimization

This paper introduces a new hyperchaotic oscillator base on a new boundary-restricted Hewlett-Packard memristor model. Firstly, the complex system is designed based on a memristor-based hyperchaotic real system, and its properties are analyzed by means of Lyapunov exponents, Lyapunov dimension and phase portraits diagrams. Secondly, a simple feedback control based on the minimum variance control technique is designed to stabilize the hyperchaotic oscillator system, which is one of the new developed approaches for controlling the chaos in high-dimensional hyperchaotic systems. In this method, the time series variance is considered for designing and calculating the state feedback control gain. Furthermore, the state feedback control is designed so that to minimize the variance as a cost function, followed by developing an online optimization technique using the particle swarm optimization method in order to calculate the state feedback control based on the minimum variance strategy. Then, the application of this method is examined on a hyperchaotic memristor-based oscillator. Finally, the sensitivity of the proposed method is evaluated in different initial conditions that greatly influence the hyperchaotic dynamics. Considering that the optimization is online, simulation results show highly good effectiveness of the presented technique in controlling the chaos in high-dimensional hyperchaotic oscillators

Coordinated Time-Varying Low Gain Feedback Control of High-Speed Trains Under a Delayed Communication Network

The coordinated control problem for a multiple high-speed train (HST) system subject to unknown communication delays is systematically investigated in this paper. Taking into consideration the inertial lag of the servo motor, a third-order nonlinear control model is constructed to capture the dynamics of a train in real-world operations. By virtue of the backstepping linearization technique, the coordinated control of trains is formulated as a stabilization problem for a linear multiple-input multiple-output system with an unknown input delay. Distributed control laws with a time-varying low gain parameter are designed, besides solving the stabilization problem, to guarantee a fast convergency rate during the train status adjustment process. Numerical examples are provided to illustrate that the time-varying low gain parameter design achieves better control performance compared with the traditional constant low gain feedback design in terms of the convergency rate and the system overshot, and that the proposed control method is effective in train tracking distance adjustment.

Hygrothermal forced vibration of a viscoelastic laminated plate with magnetostrictive actuators resting on viscoelastic foundations

The article presents a vibration analysis of a laminated composite sandwich plate containing viscoelastic layers in the core and faces of the plate. The sandwich plate includes magnetostrictive actuating layers, rests on a three-parameter viscoelastic medium, and undergoes to hygrothermal environmental conditions and in-plane forces in $$x$$ and $$y$$ directions. The viscoelastic layers are considered as Kelvin–Voigt viscoelastic model. The partial differential equations system is deduced according to the dynamic version of the principle of virtual displacements and is based on a theory that accounts for the exponential distribution of transverse shear deformation. The analytical Navier’s solution type is obtained to investigate the parametric effect of the location of smart layers, lamination schemes, modes, the feedback gain control value, viscoelastic structural damping, thickness ratio, the aspect ratio, viscoelastic layer thickness-to-magnetostrictive layer thickness ratio, foundation, in-plane forces, temperature and moisture on vibration characteristics of the sandwich plate. The outcomes show that the deformation and vibration in the structure can be controlled by changing the smart layer position and value of the feedback gain control parameter as well as the studied system stability can be affected by the value of viscoelastic structural damping and foundation constants. Besides, the absorption of moisture in matrix material increases the deflection of structure and increases the damping time. The results of this study can contribute to the development of the design of smart structural applications, especially those that require foundations to support them and deal with their dynamic response as well as provide a reference framework for studies of the impacts of humid environments on such structures in the presence of in-plane forces, especially, in the applications subjected to various forces and environmental conditions. Many of these systems require foundations to support the structures and deal with their dynamic response such as civil and mechanical structural applications and the aerospace and aeronautical vehicles.

Exponential Stability for a Class of Uncertain Linear Systems with a Single Time-Delay (or Multiple Time-Delays)

This paper investigates the issue of exponential stability for a class of uncertain linear systems with a single time-delay (or multiple time-delays). We consider that the uncertainties are the parameter disturbance and the external disturbance, both of which are stochastic. The external disturbances involve not only the current state x(t) but also the delayed state x(t - τ). By means of the Lyapunov-Krasovskii functional, the sufficient conditions on exponential stability for the uncertain linear systems with a single time-delay (or multiple time-delays) are performed in the form of the linear matrix inequality (LMI). Selecting the suitable matrices P (or ) and Q (or ) and parameter β (or ), we can also get the bounds of the state variables for the single time-delay (or multiple time-delays) systems. In order to stabilize the solution of the single time-delay (or multiple time-delays) systems at the equilibrium point, we designed the state feedback control. Thus, the corresponding stabilization criteria are given. Finally, Numerical simulations show that a small disturbance can make a great change to the state variables of the systems. When the feedback gain control is added, the state variables of the systems can quickly stabilize at the equilibrium point. This also shows the effectiveness of the proposed method.

On consistency of output-error closed-loop subspace model identification for systems compensated by general LTI controllers

Abstract This paper deals with consistency analysis of a closed-loop subspace model identification method for systems compensated by general linear time-invariant feedback controllers. The results presented here are a straightforward extension from the authors’ recent work for systems compensated with constant gain feedback controllers. It is shown that the estimate of the extended observability matrix, which is obtained from our closed-loop subspace model identification method, is consistent up to a similarity transform.

Robust stability of uncertain fractional order systems of neutral type with distributed delays and control input saturation

Time delay occurs naturally due to the limited bandwidth of any real-world system. However, this problem can deteriorate the system performance and can even result in system instability. Input saturation is also an essential issue due to the energy constraint in real actuators that makes the control design procedure more difficult. This article concerns with the stability of uncertain fractional order (FO) delay systems of neutral type including structured uncertainties, distributed delays and actuator saturation. A Lyapunov–Krasovskii functional allows the formulation of the conditions to insure the asymptotic robust stability of such systems via the linear matrix inequalities (LMI) and to compute the gain of a state feedback controller. In addition, by using the cone complementarity linearization method, we obtain the controller gains that extend the domain of attraction. Several simulations validate the theoretical analysis.

Optimal load frequency control through combined state and control gain estimation for noisy measurements

Combined estimation of state and feed-back gain for optimal load frequency control is proposed. Load frequency control (LFC) addresses the problem of controlling system frequency in response to disturbance, and is one of main research areas in power system operation. A well acknowledged solution to this problem is feedback stabilization, where the Linear Quadratic Regulator (LQR) based controller computes the feedback gain K from the known system parameters and implements the control, assuming the availability of all the state variables. However, this approach restricts control to cases where the state variables are readily available and the system parameters are steady. Alternatively, by estimating the states continuously from available measurements of some of the states, it can accommodate dynamic changes in the system parameters. The paper proposes the technique of augmenting the state variables with controller gains. This introduces a non-linearity to the augmented system and thereby the estimation is performed using an Extended Kalman Filter. This results in producing controller gains that are capable of controlling the system in response to changes in load demand, system parameter variation and measurement noise.

EXPERIMENTAL AND THEORETICAL OPTIMAL REGULATOR CONTROL OF BALANCE ZERO MOMENT POINT FOR BIPEDAL ROBOT

In this paper, the optimal control is analyzed to compare the results of the zero moment point of a bipedal walking robot. Seventeen degrees of freedom bipedal walking robot is manufactured of hard Aluminum sheets. The zero moment point is calculated experimentally and theoretically in the single support phase. MATLAB Simulink is used to simulate the results. The experimental results showed that the lower link takes the settling time is (1) sec, the middle link takes settling time (0.9) sec and the upper link takes (1.1) sec to arrive the desired zero moment point for the bipedal walking robot. The minimum performance index in the experimental parts occurs when the optimal feedback control gain is [35.5 30.4 5 -4]. Hence, the minimum performance index in the theoretical part is [35 31 5.2 -4]. The dimensions of the foot area are (12.3cm×6.3cm), 2.3cm thickness, and 32g weight. Also, the approximate balance area in the double support phase equals the area between the feet of the robot.

Robust local stabilization of discrete time-varying delayed state systems under saturating actuators

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.

Optimal state feedback controller for three tank cylindrical interacting system using Grey Wolf Algorithm

This article presents, optimal state feedback controller for three tank cylindrical interacting system was proposed to maintain set point in the tank. Grey Wolf Optimization Algorithm used to describe the optimal tuning of state feedback controller. Generally, optimal state feedback controller reduces fluctuation state with lowest control energy. Gain of the optimal state feedback controller used to reduce the fluctuation state to minimum value. By adding integrator, the measured value of the tank moves towards set point. Linear quadratic regulator is a multivariable state feedback control and it depends on the state of the system. The controller performance enhanced by suitable range of Q and R value. The proposed technique uses heuristic algorithm for tuning the state feedback gain directly. The results show that the developed control technique given better performance.