Virtual Control Input Research Articles

Fuzzy adaptive nonlinear stochastic control for vehicle suspension with electromagnetic actuator

This work solves the stability problem of a vehicle suspension with stochastic disturbance by designing an adaptive controller. The model of a quarter vehicle subjected to noise excitation is considered. The stochastic perturbance is realized by the roughness of the road and the vehicle moving with constant velocity. In the control design procedure, fuzzy logic systems are used to approximate unknown nonlinear functions. Meanwhile, the mean value theorem is employed to ensure the existence of the affine virtual control variables and control input. The backstepping technique is applied to construct the ideal controller. On the basis of Lyapunov stability theory, the proposed control method proves that the displacement and speed of the vehicle is reduced to a level ascertained by a true “desired” conceptual suspension reference model. Finally, the effectiveness of the proposed method is verified by simulation of electromagnetic actuator servo system.

Global Predefined Time and Accuracy Adaptive Neural Network Control for Uncertain Strict-Feedback Systems With Output Constraint and Dead Zone

This article proposes a global adaptive neural network tracking control method for uncertain strict-feedback nonlinear system with output constraint and dead zone to achieve predefined-time convergence of the tracking error to predefined accuracy. First, an integral-type Barrier Lyapunov function (BLF) is constructed to handle output constraint. Next, radial basis function neural network (RBFNN) control and robust control are used to tackle unknown nonlinear function. The continuous switching function is designed to switch RBFNN control to robust control when the arguments of the unknown function exceed the active region of neural network. Utilizing the property of radial basis function, we derive the upper bound of the term containing the unknown nonlinear function and design adaptive laws to determine the derived upper bound and robust control gain. Then, the predefined time virtual control inputs are obtained and their derivatives are estimated by finite time differentiator. Finally, we use the dead zone inverse technique to obtain the actual control input. Stability analysis shows the presented control scheme achieves global convergence of the errors to predefined accuracy within predefined time. The simulation results verify the effectiveness of the presented control scheme.

Adaptive fuzzy global fast terminal sliding mode control of an over-actuated flying robot

In this paper, the issue of full control (both position and orientation controls) of an over-actuated unmanned flying robot is addressed using an adaptive fuzzy global fast terminal sliding mode control (AF-GFTSMC) scheme in the presence of external disturbances and parametric uncertainties. At the first step, full dynamic equations of motion of a novel over-actuated flying robot are developed taking into account the rotational kinematics. Using the Lyapunov stability theorem, an AF-GFTSMC is designed to suppress the errors between desired references and actual responses of the robot in finite time. Since the number of actuators is more than control forces and torques, considering some constraints on actual control inputs, a control allocation strategy based on the reflective Newton algorithm is employed and formulated in order to compute the actual control inputs according to virtual control inputs. Finally, some simulations are performed in the presence of external disturbances and parametric uncertainties, utilizing different designed control strategies, classical and AF-GFTSMC methods. It is also clearly verified that the designed control approaches are effective and robust through tracking some predefined trajectory in 3D space as well as attenuation of chattering phenomena.

Practical control implementation of tri-tiltRotor flying wing unmanned aerial vehicles based upon active disturbance rejection control

Tilt rotor unmanned aerial vehicles exhibit their effectiveness via a novel and convenient structure. However, the flight control system is a critical problem in need of a robust solution. Focusing on its flight features, which display strong nonlinear and varying dynamics, caused by complexity in the aerodynamic layout and tilting structure, a practical control scheme is proposed to meet such technical issues. This paper first develops the nonlinear model, consisting of the interference between rotors and the wing body, relying on wind tunnel technology. A simplified linear model that decomposes the longitudinal and lateral components is used in order to facilitate controller design. Then, a time-scale separation decoupling control scheme based upon active disturbance rejection control is proposed to cope with control challenges. Introducing the concept of virtual control input, an effective control allocation is obtained by choosing the appropriate bandwidth in the frequency domain. The extended state observer is applied to estimate and compensate for unknown total disturbances and model uncertainties. Finally, robustness verification, successful test-bench experiments, and practical flight tests that show the fast tracking and disturbance rejection of the active disturbance rejection control controller are discussed. The proposed practical coupling rejection control design demonstrates its capability to employ a single input single output method to control a tri-tiltRotor flying wing unmanned aerial vehicle relying on active disturbance rejection control.

Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages

This paper proposes a new method for control of nonlinear multi input – multi output (MIMO) mechanical systems that incorporate viscoelastic dampers (VED) for reducing undesired vibrations of actuators. To this end, a control algorithm is proposed based on considering various characteristics of the described dynamical systems (namely mechanical dynamics, viscoelasticity and actuator dynamics) in generation of control inputs guaranteeing convergence of system response to desired reference signals. This procedure features three consecutive parts within the control loop which are conducted iteratively at each control sample. At each sample, initially necessary forces and moments exerted to mechanical system are calculated as virtual control inputs generated based on a MIMO discrete-time sliding mode control (DSMC) algorithm. As the aim of control model is obtaining a closed-loop system without resulting in notable vibrational effects, undesired chattering effects should be eliminated from inputs generated by DSMC. This objective is attained by calculation of appropriate input bounds. Next, an additional virtual input is assigned corresponding to viscoelastic strain such that virtual mechanical input from previous part of the control loop is generated. To this end, Maxwell model for viscoelastic material is considered. Finally, actual controller input is generated such that all virtual control objectives are satisfied. The effectiveness of control procedure is numerically illustrated for a 3-PRR manipulator.

Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result.

Dynamical analysis of the fractional-order centrifugal flywheel governor system and its accelerated adaptive stabilization with the optimality

This paper investigates the issues of dynamical analysis and accelerated adaptive stabilization of the fractional-order (FO) centrifugal flywheel governor system with optimality. The dynamic behavior of the centrifugal flywheel governor system is revealed and its local stability is discussed in the fractional calculus (FC). A speed function is introduced to accelerate convergence rate within a pre-given time and a hierarchical type-2 fuzzy neural network (HT2FNN) is employed to play an approximating role for unknown nonlinear items. An extended state tracking differentiator which overcomes repetitive differentiation problem is used to approximate the derivative of virtual control input. Then, a stabilization controller is designed by integrating with the speed function, neural network and tracking differentiator in the framework of backstepping. It is proved that the proposed scheme guarantees the boundedness of all signals of the closed-loop system by using the frequency distributed model and makes the predefined cost function smallest. Finally, simulation results verify the effectiveness of the presented scheme.

A Back-Stepping Control Method for Modular Multilevel Converters

In this article, a back-stepping method (BSM) in a–b–c reference is presented to establish the stable operating conditions for modular multilevel converter (MMC). The designed BSM utilizes arm currents, sum of submodule capacitors voltages and MMC input energy as the main variables to form the energy functions. The proposed BSM is designed by well-known dynamic MMC equations to be applicable for both single- and three-phase ones while the control of variables is also guaranteed by BSM. A virtual control input containing input energy error and its dynamics is defined in the second energy function to further enhance the appropriate transient responses of the MMC. The proposed BSM has inherent feature of the circulating current suppression control loops which helps avoiding additional control loops. Moreover, several assessments are presented to show how BSM coefficients contribute to the noticeable decrement in control variables errors of the MMC system. Experimental and simulation results prove an excellent capability of BSM for controlling MMCs compared to the conventional PI linear controller. Moreover, the BSM robustness against the variations of the MMC circuit parameters is validated.

Adaptive NN Backstepping With Considering Integral of Tracking Error

In order to simplify the design procedure of traditional neural network backstepping and improve the robustness and precision of control, an improved scheme is studied for a class of nonlinear systems. To avoid reconstructing virtual control inputs in each recursive step, RBF neural networks are utilized as approximators to estimate the desired feedback control of the whole system only. Meanwhile, the integral action of tracking error is introduced into the backstepping design procedure, which not only participates in updating the neural network weight, but also serves as a component part of the control input. This design may benefit the parameter tuning and make controller perform better sometimes. Based on the Lyapunov synthesis approach, theoretical analysis and simulation results are provided to show the feasibility of the improved scheme.

Super Twisting Disturbance Observer-Based Fixed-Time Sliding Mode Backstepping Control for Air-Breathing Hypersonic Vehicle

This paper investigates the velocity and altitude tracking control problem for air-breathing hypersonic vehicle (AHV) under external disturbances and uncertainties. An improved smooth super-twisting based disturbance observer (SSTDOB) is proposed to estimate the unknown external disturbances. With the assistance of SSTDOB, an effective fixed-time sliding mode backstepping control (FSMBC) is designed to guarantee the tracking errors converge to a small neighbor of the origin. Meanwhile, a fixed-time tracking differentiator (FTD) is employed to estimate the virtual control inputs, which can eliminate the differential explosion problem. The overall stability of the closed-loop system is analyzed by utilizing Lyapunov stability theory. Simulation results demonstrate the effectiveness of the composite method.

A Nonlinear Control Design Strategy for Piloting Fixed Wing Aircrafts

Abstract This paper proposes a novel nonlinear feedback control strategy for velocity and attitude control of fixed wing aircrafts. The key feature of the control design strategy is the introduction of a virtual control input in order to deal with the underactuation property of such vehicles and to indirectly control the orientaion of the aircraft. As such, the proposed strategy consists of three control loops each realising a specific task. Simulation results on Jetstream-3102 aircraft show very good performance in terms of convergence towards the desired reference trajectories and in terms of robustness with respect to modeling uncertainties.

Universal Adaptive Fault-Tolerant Control of a Multicopter UAV

Abstract This paper presents a universal adaptive fault-tolerant control (FTC) design for multicopter unmanned aerial vehicles (UAVs). The proposed architecture consists of a two-loop control structure: a fault-tolerant controller generates normalized virtual control inputs to track the desired trajectory subject to actuator faults, and an adaptive augmentation controller deals with system uncertainties and also balances the design requirements for specific platform. The FTC approach is based on gain-scheduling control in the framework of structured H∞ synthesis. In order to implement the overall control system on most types of multicopter UAVs, an adaptive mapping algorithm is proposed. High fidelity simulations and experimental results, performed on various multicopters with different payload and configuration, show the effectiveness and robustness of the proposed approach in accommodating different levels of actuator degradation including total failures of the rotors as well as unknown mass and inertia, all using a single controller with fixed coefficients.

A globally fixed-time solution of distributed formation control for multiple hypersonic gliding vehicles

This paper investigates the distributed formation control problem for multiple hypersonic gliding vehicles (HGVs) under direct communication topology. Based on a formation flight framework of multiple HGVs, a globally fixed-time formation control scheme is proposed by using the fixed-time stability and the hierarchical control theory. Firstly, a fixed-time consensus law is addressed in the three-dimensional formation flight dynamics to generate the virtual control inputs. In order to design appropriate actual control inputs to track the virtual control commands rapidly and accurately, a composite fixed-time feedback control law is then put forward, where a new fixed-time tracking differentiator is designed to obtain the information on the time derivatives of virtual control inputs. Following, the problem of “explosion of complexity” can be resolved effectively. Finally, the globally fixed-time convergence is achieved in spite of the initial conditions of HGV's states, where the upper bound of the settling time can be estimated in advance by only using the control parameters and the direct communication topology. The desired formation configuration can be established within a prescribed convergence time. Extensive numerical simulations are performed to demonstrate the effectiveness and superiority of the proposed formation control strategy.

Adaptive Backstepping Nonsingular Fast Terminal Sliding Mode Control for Hydro-Turbine Governor Design

To investigate a typical large-scale nonlinear hydropower system (HS) with a stochastic water flow, a novel nonlinear adaptive control scheme, which is created by the combination of a backstepping strategy, nonsingular fast terminal sliding mode surface and command filter, is proposed for the hydro-turbine governor design of a HS to not only improve the transient stability of the HS but also increase the energy conversion efficiency and improve the reliability and availability of the electricity supply. In contrast to previous research based on ideal hydro-turbine models with accurate parameters, an adaptive backstepping nonsingular fast terminal sliding mode control (ABNFTSMC) with command filtered (CF) is proposed in which virtual control inputs and error compensations are applied to overcome distribution characteristics resulting from energy losses, while guaranteeing finite-time convergence. In addition, to avoid the requirement of analytic differentiation in Lyapunov stability, a command filter method is used to generate certain compensating signals and their derivatives. In this paper, the Nazi Gorge hydropower station in China is used as our verification model of a hydropower plant with monitored data, where energy losses and random water flow disturbances are considered. Simulation results illustrate that the proposed control strategy for a hydro-turbine governor can significantly increase the stability, reliability, and system performance of a HS even in the presence of uncertainties.

Integrated energy-oriented lateral stability control of a four-wheel-independent-drive electric vehicle

Improving the energy efficiency of an electric vehicle (EV) is an effective approach to extend its driving range. This paper proposes an integrated energy-oriented lateral stability controller (IESC) for a four-wheel independent-drive EV (4WID-EV) to optimize its energy consumption while maintaining vehicular stability during cornering. The IESC is a hierarchical controller with two levels. The high-level decision-making controller determines the virtual control inputs, i.e., the desired additional yaw moment and total wheel torque, while the low-level controller allocates the motor torques according to the virtual control inputs. In the high-level controller, the desired additional yaw moment is first calculated using a linear quadratic regulator (LQR) to minimize the control expenditure. Meanwhile, a stability weighting factor (SWF) based on phase plane analysis is proposed to adjust the additional yaw moment, which can reduce the additional energy consumption caused by the mismatch between the reference model and the actual vehicle. In addition to the yaw moment, the desired total wheel torque is calculated using a proportional-integral (PI) controller to track the desired longitudinal velocity. In the low-level controller, a multi-objective convex-optimization problem is established to optimize the motor torque by minimizing the energy consumption and considering the tire-road frictional limit and motor saturation. A globally optimal solution is obtained by using an active-set method. Finally, double-lane change (DLC) simulations are conducted using CarSim and MATLAB/Simulink. The simulation results demonstrate that the proposed controller achieves great lateral stability control performance and reduces the energy consumption by 5.23% and 2.95% compared with the rule-based control strategy for high- and low-friction DLC maneuvers, respectively.

불확실한 Strict-Feedback 비선형시스템에 대한 비선형 외란관측기를 갖는 강인한 유한시간 Backsteppping 제어

This paper proposes a robust finite-time backstepping control scheme using a nonlinear disturbance observer for uncertain single-input single-output (SISO) full-order strict-feedback nonlinear systems, in which the dynamics are partially known. To improve the convergence time and robustness of the conventional backstepping control, a new finite-time control method is proposed to estimate uncertainties that appear in each step of the controller design based on the finite-time virtual tracking errors and a nonlinear disturbance observer. The finite-time virtual controls and control input are derived by using the finite-time Lyapunov stability criterion. Simulation results for example of a strict-feedback SISO nonlinear system confirm that the proposed control scheme exhibits better performance than a conventional backstepping control scheme.

불확실한 Strict-Feedback 비선형시스템에 대한 비선형 외란관측기를 갖는 강인한 유한시간 Backsteppping 제어

This paper proposes a robust finite-time backstepping control scheme using a nonlinear disturbance observer for uncertain single-input single-output (SISO) full-order strict-feedback nonlinear systems, in which the dynamics are partially known. To improve the convergence time and robustness of the conventional backstepping control, a new finite-time control method is proposed to estimate uncertainties that appear in each step of the controller design based on the finite-time virtual tracking errors and a nonlinear disturbance observer. The finite-time virtual controls and control input are derived by using the finite-time Lyapunov stability criterion. Simulation results for example of a strict-feedback SISO nonlinear system confirm that the proposed control scheme exhibits better performance than a conventional backstepping control scheme.

A Two-Stage State Feedback Controller Supported by Disturbance-State Observer for Vibration Control of a Flexible-Joint Robot

SUMMARYJoint flexibility introduces additional degrees of freedom and vibration modes, thus limiting the performance of the manipulator. To improve control bandwidth, this paper proposes an enhanced two-stage state feedback (SFB) controller, which combines two parts. The first is a SFB loop, which considers the motor position as a virtual control input for the link side dynamics. The second is a disturbance-state observer, which compensates disturbances and reconstructs indirect measurements. Experimental results show the effectiveness of the proposed controller in terms of position tracking, link vibration, and rejection of the kinematic error from the joint’s harmonic drive reducer.

Adaptive integrated guidance and control for impact angle constrained interception with actuator saturation

ABSTRACTThis paper considers the integrated guidance and control (IGC) problem for impact angle constrained interception against manoeuvring targets with actuator saturation constraint. Based on the backstepping technique, an adaptive IGC law is presented to address this problem, where a fixed-time differentiator is proposed to estimate the derivatives of virtual control inputs to avoid the inherent problem of “explosion of complexity” suffered by the typical backstepping. Furthermore, an auxiliary first-order filter is introduced into the IGC law to cope with the actuator saturation constraint. The stability of the closed-loop system is strictly proved. Finally, the superiority of the proposed IGC law is verified by comparison simulations.

Stabilization of a stock‐loan valuation PDE process using differential flatness theory

AbstractThe article proposes flatness‐based control for stabilization of a stock‐loan valuation process that is described by a partial differential equation. By applying semi‐discretization and the finite differences method, the state‐space model of the stock loan has been obtained. It has been proven that the individual rows of this state‐space model are nonlinear ODEs which can be viewed as differentially flat subsystems. For the local subsystems, into which the stock‐loan PDE is decomposed, it becomes possible to apply boundary feedback control. The controller design proceeds by showing that the state‐space model of the stock loan PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state‐space description, the control input (boundary condition) that is actually applied to the stock loan PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state‐space description. Thus, by tracing the rows of the state‐space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the stock loan PDE system so as to assure that all its state variables will converge to the desirable setpoints.By showing the feasibility of such a control method it is also proven that through selected modification of the PDE boundary conditions the value of the stock loan can be made to converge and stabilize at specific reference values.