Virtual Control Variables Research Articles

Neuroadaptive Cooperative Fault-Tolerant Control of Heterogeneous Multiagent Systems Based on Fully Actuated System Approaches.

The leader-following cooperative problem in heterogeneous multiagent systems (HMASs) with unmodeled dynamics and actuator faults is investigated in this article. The HMASs, which include unmanned ground vehicles and unmanned aerial vehicles, are first described using a fully actuated system model (FASM). The FASM, as opposed to the first-order state-space model, preserves the physical significance of original systems and makes it feasible to apply the control rule entirely. In order to approximate unknown system dynamics, novel neuroadaptive laws with few learning parameters are then suggested. To counteract the negative effects of actuator faults, the Nussbaum function and adaptive approach are utilized. In addition, a cooperative fault-tolerant protocol is suggested, wherein consensus errors are uniformly ultimately bounded. The lack of virtual control variables in the proposed protocol reduces its complexity. The theoretical results are then validated by numerical simulations.

A novel approach to the FPIBSC strategy for an electric power steering system

The electric power steering system is used to improve comfort and steering feel for the user. In this article, we propose to use an integrated nonlinear control strategy for the electric steering system, which is described based on a complicated dynamic model. This work provides two new contributions. First, this control algorithm combines backstepping and proportional–integral (PI) techniques with parameters adjusted by a fuzzy algorithm, so it is called Fuzzy proportional–integral backstepping control (FPIBSC). The output of the PI algorithm is the input of the backstepping technique, while system stability is evaluated based on the Lyapunov function with virtual control variables. Second, road reaction torque is calculated based on a spatial dynamic model, which considers the influence of many other factors. Numerical simulation methods are used to evaluate the performance of the system. According to research findings, the value of the steering motor angle (controlled object) continuously tracks the desired value with negligible error. Under some specific conditions, the error between signals can be reduced to zero. In addition, other outputs that are obtained from the FPIBSC algorithm also tend to follow the reference signal with high accuracy. The phase difference phenomenon only occurs when using the conventional backstepping algorithm instead of FPIBSC. The assisted torque increases as speed decreases or the driver torque increases. In general, the system’s stability is always guaranteed under many different simulation conditions.

Fixed‐time distributed adaptive optimization for third‐order nonlinear fully heterogeneous vehicular platoon systems

SummaryIn this article, the problem of fixed‐time distributed optimization is researched for third‐order fully heterogeneous nonlinear connected and autonomous vehicles. To address this problem, a fixed‐time distributed optimization algorithm is proposed via a two‐step strategy. First, an optimization algorithm is proposed to generate a virtual reference signal that can converge to the optimal solution. Then, we further construct an adaptive tracking controller to track the virtual signal based on the first step. In the design process of the controller, the virtual control variables and the actual control input are obtained by using the backstepping technique. Furthermore, a fast fixed‐time filter is introduced to avoid the issue of discontinuous gradient functions. Fuzzy logic systems are employed to address the unknown part of the nonlinear function. By using tools from the fixed‐time stability criterion, convex optimization theory, and Lyapunov stability theory, it can be demonstrated that the provided strategy drives all optimization variables to the optimal solution within a fixed time and guarantees the closed‐loop system signals are bounded. Finally, the effectiveness of control strategy is verified via a numerical simulation.

Event-Triggered Tracking Control for a Class of Nonlinear Systems: A Dynamic Gain Approach

This note presents a dynamic gain approach to the event-triggered tracking control for a class of strict-feedback nonlinear systems. A novel shifting function is designed to make the initial tracking error arbitrarily bounded, which significantly relaxes the requirement on the initial tracking error. To achieve the objective that the tracking error does not exceed the constraint after the pre-specified finite time, a barrier Lyapunov function and a new reduced-order observer are constructed by using the shifting function and the desired tracking signal. Based on the proposed dynamic gain approach, an event-triggered output feedback tracking controller is designed. It is proved that the developed control scheme guarantees that all the closed-loop signals are bounded and the tracking error constraint is strictly obeyed after a specified finite time. Compared with the celebrated backstepping method, the dynamic gain approach does not involve any virtual control variables, which avoids the complicated iterative procedure. The effectiveness of the proposed approach is verified by an example.

Shifting and state transformations-based adaptive tracking control for deferred full state-constrained uncertain nonlinear systems

This paper concerns the tracking control problem of a class of uncertain nonlinear systems subject to deferred time-varying state constraints and external disturbances. The states of the system are free in the initial phase and are restricted by some time-varying constraints after a particular time. A class of novel shifting functions are defined, which make any initial states that beyond the constraint region move to the desired position (such as zero). Thereafter, a new state transformation is implemented for the shifted state, which transforms the state constraint problem into the boundedness of a new variable. Compared with the existing BLF method, this approach avoids feasibility test for virtual control variables. Adaptive backstepping control and dynamic surface control are used in system controller design and stability analysis, and the ideal tracking performance is achieved. Finally, simulation example and comparative studies are carried out to illustrate the effectiveness and outstanding characteristics of the proposed approach. Simulation results show that the proposed control scheme broadens the scope of application, shortens running time and improves control efficiency compared with the existing control strategies.

Integral back-stepping active disturbance rejection control for piezoelectric stick-slip drive nanopositioning stage

Piezoelectric stick-slip driven nanopositioning stage (PSSNS) with nanometer resolution has been widely used in the field of micro-operation. However, it is difficult to achieve nanopositioning over large travel, and its positioning accuracy is affected by the hysteresis characteristics of the piezoelectric elements, external uncertain disturbances, and other nonlinear factors. To overcome the above-mentioned problems, a composite control strategy combining stepping mode and scanning mode is proposed in this paper, and an integral back-stepping linear active disturbance rejection control (IB-LADRC) strategy is proposed in the scanning mode control phase. First, the transfer function model of the system in the micromotion part was established, and then the unmodeled part of the system and the external disturbance were treated as the total disturbance and extended to a new system state variable. Second, a linear extended state observer was used as the core of the active disturbance rejection technique to estimate displacement, velocity, and total disturbance in real time. In addition, by introducing virtual control variables, a new control law was designed to replace the original linear control law and improve the positioning accuracy and robustness of the system. Furthermore, the effectiveness of the IB-LADRC algorithm was verified by simulation comparison experiments and experimentally validated on a PSSNS. Finally, experimental results show that the IB-LADRC is a practical solution for a controller capable of handling disturbances during the positioning of a PSSNS with a positioning accuracy of less than 20 nm, which essentially remains constant under load.

Attitude tracking backstepping control for small unmanned helicopters based on adaptive neural network under unknown environment disturbances

To solve the attitude tracking control problem of small unmanned helicopters under unknown bounded disturbances, an attitude tracking backstepping controller based on adaptive radial basis function (RBF) neural network disturbance compensation is proposed in this paper. The unknown disturbance is estimated online and in real time through RBF neural network with a novel gradient descent weight update rate. A novel attitude tracking backstepping controller based on virtual control variables is designed, and the system stability is analyzed using the Lyapunov method. The experimental verification of the backstepping controller is carried out on the three-degrees-of-freedom helicopter. The experiments show the effectiveness and advancedness of the proposed adaptive neural network backstepping controller in suppressing unknown external disturbances compared with the robust adaptive integral backstepping.

Stability Enhancement of Modular Multilevel Converter - High Voltage Direct Current Systems Interacted with Weak Power Grid Based on Current-mode Virtual Inertia Control

The extensive growth of large-scale flexible high voltage direct current (HVDC) transmission systems compromises the strength of the alternating current (AC) power grid. Sub-synchronous oscillations will likely arise within such flexible HVDC systems, which would significantly threaten the grand electric power system’s stable operation. A current-type enhanced virtual inertia control is proposed to suppress the sub-synchronous oscillations induced by a weak AC power grid in the modular multilevel converter (MMC)-based HVDC systems. Firstly, a small signal model of MMC is established to study the stability of the system under a weak power grid. Focally, a current-mode virtual inertial control is proposed to suppress the AC power grid’s sub-synchronous oscillation by directly taking the grid current as the virtual inertia control variable. Finally, the proposed virtual inertia control approach is verified using both offline and real-time simulation based on the Chongqing-Hubei flexible MMC-HVDC transmission system. The simulation results demonstrate that the proposed current-mode virtual inertia control strategy can efficiently suppress sub-synchronous oscillations in the MMC-HVDC system interacting with a weak AC grid, which enhances the stability and reliability of the power system.

An Energy Efficient Control Strategy for Electric Vehicle Driven by In-Wheel-Motors Based on Discrete Adaptive Sliding Mode Control

This paper presents an energy-efficient control strategy for electric vehicles (EVs) driven by in-wheel-motors (IWMs) based on discrete adaptive sliding mode control (DASMC). The nonlinear vehicle model, tire model and IWM model are established at first to represent the operation mechanism of the whole system. Based on the modeling, two virtual control variables are used to represent the longitudinal and yaw control efforts to coordinate the vehicle motion control. Then DASMC method is applied to calculate the required total driving torque and yaw moment, which can improve the tracking performance as well as the system robustness. According to the vehicle nonlinear model, the additional yaw moment can be expressed as a function of longitudinal and lateral tire forces. For further control scheme development, a tire force estimator using an unscented Kalman filter is designed to estimate real-time tire forces. On these bases, energy efficient torque allocation method is developed to distribute the total driving torque and differential torque to each IWM, considering the motor energy consumption, the tire slip energy consumption, and the brake energy recovery. Simulation results of the proposed control strategy using the co-platform of Matlab/Simulink and CarSim® demonstrate that it can accomplish vehicle motion control in a coordinated and economic way.

Prescribed Performance Control for Electro-hydraulic Servo System of the Ammunition Manipulator

There are stochastic initial disturbances which lead to unexpected tracking errors of the ammunition manipulator during the starting stage. In this paper, a prescribed performance control strategy is proposed for the steady constraint control of the ammunition coordinator. In order to keep the position errors of the ammunition coordinator in the whole tracking control process within the prescribed constraint range, the prescribed performance control theory is adopted to convert the system original error into a new error form that can be restrained through error transformation, and the performance function is designed to constrain the error boundary. The second-order command filter is used to reduce the derivation calculation error of the virtual control variables during the backstepping iteration and the corresponding filtering error compensation algorithm is designed to improve the control accuracy. In addition, adaptive laws are well-designed to compensate the uncertainty of system parameters. The simulation analysis shows that the designed prescribed performance controller obtains good control performance. The convergence and stability of the tracking error of the ammunition manipulator are achieved, and the prescribed performance function prevents the violation of tracking error performance constraints.

Neuro-adaptive control for searching generalized Nash equilibrium of multi-agent games: A two-stage design approach

This paper investigates the generalized Nash equilibrium searching problem of multi-agent games over weight-unbalanced directed networks. In this problem, the feasible action set of each agent is not only constrained by private convex sets and shared coupling equality, but also constrained by its own uncertain dynamics. Moreover, the local cost function is related to both his own actions and others, and each agent is only allowed access to neighbor information. To address this problem, we propose a neuro-adaptive control strategy based on two-stage design. In the first stage of design process, an approximator with adaptive-gain is designed to generate a virtual trajectory that converges to a necessary Nash equilibrium, the compensator based on consensus-tracking is used to obtain non-neighbor information and several auxiliary state variables are used to exchange information with local neighborhoods on a digraphs to deal with equality constraints. In the second stage of the strategy, we further developed a neuro-adaptive tracking controller based on one-step design for tracking the virtual trajectory. In the controller design, the virtual control variables and the actual control laws are obtained in a collective way, without repeating the design process. We introduce a variable called the minimum learning parameter to reduce the number of online learning parameters of the neural network. By using tools from variational inequality theory and Lyapunov stability theory, we prove that the proposed control strategy can drive all agents reach Nash equilibrium. Finally, the effectiveness of control strategy is verified by simulation example.

Adaptive finite-time fuzzy control for hybrid levitation system of maglev trains with active anti-lock constraints

The great risk of the suspension contact tremendously restricts the practical public service of hybrid maglev trains. If an operational train contacts to the guideway resulting in the “lock” state, it would cut down its lifetime or even endanger passenger safety. To address the deadlock problem of hybrid maglev trains, a novel adaptive finite-time fuzzy control with active anti-lock constraints is proposed in this paper. First, an efficient fuzzy-logic system is applied to approximate the hybrid levitation dynamics, not only precisely describing the system but also reducing computation burden. Moreover, by a novel nonlinear coordinate transformation, an anti-lock levitation controller is designed to prevent suspension contact between trains and guideways via the back-stepping technique. In the process, command filtering is utilized to circumvent the derivatives of virtual control variables and to address practical input constraints. Differing from the barrier Lyapunov function technique, the proposed nonlinear transformation helps to directly address both positive lower and upper boundaries. In addition, finite time convergence is achieved by the proposed scheme, which enjoys the characteristics of a fast and quantifiable response. Numerical simulations verify the theoretical results.

Distributed active disturbance rejection formation containment control for multiple autonomous underwater vehicles with prescribed performance

In this paper, a distributed formation containment control (FCC) issue is studied for multiple autonomous underwater vehicles (MAUVs) system with prescribed performance based on the active disturbance rejection control (ADRC) method in three-dimensional space. The unknown nonlinearities and external disturbances of the MAUVs system are approximated in real time by means of extended state observers (ESOs). Furthermore, tracking differentiators (TDs) are introduced for the sake of refraining from the explosion of complexity induced by the derivatives of the virtual control variables of autonomous underwater vehicles. Applying funnel variables, our designed control strategy ensures the formation tracking errors and containment errors to keep within the specified ranges, hence enhancing the control performance of the MAUVs system. Then, a FCC-ADRC scheme for MAUVs system is proposed. Compared with the traditional FCC scheme, the proposed FCC-ADRC scheme not only does not depend on the specific system configuration, but also can deal with any bounded disturbances, thus obtaining a more general, effective and robust disturbance rejection FCC strategies. Additionally, the stability of MAUVs system is verified through Lyapunov stability analysis. At last, the error curves and time-varying formation containment trajectories obtained by simulation confirm the feasibility and effectiveness of our method.

Sliding mode disturbance observer and sliding mode controller for quadrotor UAV

The dynamics of quadrotor UAV is described considering internal uncertainty and external disturbance. The control system of quadrotor UAV is divided into inner loop attitude control system and outer loop position control system, In order to solve the problem of underactuated character. Three virtual control variables are introduced to decouple the position dynamics. Three sliding mode disturbance observers (SMDOs) are designed to estimate the total disturbances in the position dynamics. Then three sliding mode controllers (SMCs) are designed to drive the trajectory tracking errors to zero asymptotically. The simulation example is carried out to test the effectiveness of SMDOs and SMCs. Simulation results validate that the designed SMDOs and SMCs provide both fast exact tracking capability and strong disturbance rejection capability for the quadrotor UAV.

USV Application Scenario Expansion Based on Motion Control, Path Following and Velocity Planning

The ability of unmanned surface vehicles (USV) on motion control and the accurate following of preset paths is the embodiment of its autonomy and intelligence, while there is extensive room for improvement when expanding its application scenarios. In this paper, a model fusion of USV and preset path was carried out through the Serret-Frenet coordinate system. Control strategies were then scrupulously designed with the help of Lyapunov stability theory, including resultant velocity control in the presence of drift angle, course control based on the nonlinear backstepping method, and reference point velocity control as a virtual control variable. Specifically, based on USV resultant velocity control, this paper proposes respective solutions for two common scenarios through velocity planning. In a derailment correction scenario, an adaptive reference velocity was designed according to the position and attitude of USV, which promoted its maneuverability remarkably. In a dynamic obstacle avoidance scenario, an appropriate velocity curve was searched by dynamic programming on ST graph and optimized by quadratic programming, which enabled USV to evade obstacles without changing the original path. Simulation results proved the convergence and reliability of the motion control strategies and path following algorithm. Furthermore, velocity planning was verified to perform effectively in both scenarios.

Nelinearna strategija kontrole pametnih tankih ploča sa kubnom nelinearnostima primenom tehnike aproksimacije funkcijama (TAF)

The current work introduces three nonlinear control solutions for the regulation of a vibrating nonlinear plate considering model uncertainty. These solutions are feedback linearization control (FBL), virtual velocity error-based control (VVEC), and backstepping control (BSC). In the FBL control, a nonlinear control law is designed with linear closed-loop dynamics such that dynamic stability is ensured. Whereas, by the VVEC (or so-called passivity-based approach in the robotics community) the limitations of the feedback linearization are overcome. On the other side, the BSC selects virtual control variables with stabilized intermediate control laws based on Lyapunov theory. Systematic modeling for the target vibrating plate with piezo patches is described. In effect, considering the nonlinear influence makes the resulted mode shapes for the vibrating structure are highly coupled and careful control design is required. Using the Galerkin approach, the partial differential equation for the smart plate is transformed into definite ordinary differential equations; the multi-input multi-output model is established. The aforementioned control strategies are evaluated and investigated in detail. In essence, they are powerful tools for dealing with nonlinear dynamic systems, however, the VVEC could be considered superior in comparison with the FBL control and the BSC since the designed control structure does not include inertia inverse matrix and modal coordinate acceleration that could make computational problems. As a result, simulation experiments were focused on the VVEC strategy, and the latter was implemented on a simply supported thin plate structure with collocated piezo-patches. The results show the validity of the proposed control architecture.

L2‐gain robust trajectory tracking control for quadrotor UAV with unknown disturbance

AbstractIn this paper, the trajectory tracking problem of the position and yaw angle of an underactuated quadrotor UAV is studied. Considering that the quadrotor UAV often encounters unknown disturbance resulted by model parameter perturbations and environmental changes, a new L2‐gain robust control method is presented based on dissipation theory. First, the dynamic model of the quadrotor UAV with disturbances is transformed by introducing three virtual control variables. In this way, the trajectory tracking control can be implemented by the dual loop control, that is, the position control loop and the attitude control loop. Then, based on dissipation inequality, the robust position controller and attitude controller are developed to guarantee the L2‐gain of the system to the unknown disturbance. It is proved that all the tracking errors are uniformly ultimate boundedness. In addition, the controller is further reconstructed by introducing a new class K functions to improve the transient and steady‐state performances of the quadrotor UAV system. In the end, two simulation examples are provided to check the validity of the control method proposed and the convergence of the quadrotor UAV trajectory tracking error.

Analysis of a Fast Control Allocation approach for nonlinear over-actuated systems

Autonomous Robots with multiple directional thrusters are normally over-actuated systems that require nonlinear control allocation methods to map the forces that drive the robot’s dynamics and act as virtual control variables to the actuators. This process demands computational efforts that, sometimes, are not available in small robotic platforms. The present paper introduces a new control allocation approach with fast convergence, high accuracy, and dealing with complex nonlinear problems, especially in embedded systems. The adopted approach divides the desired nonlinear system into coupled linear problems. For that purpose, the Real Actions (RAs) and Virtual Control Variables (VCVs) are broke in two or more sets each. While the RA subsets are designed to linearize the system according to different input subspaces, the VCV is designed to be partially coupled to overlap the output subspaces. This approach generates smaller linear systems with fast and robust convergence used sequentially to solve nonlinear allocation problems. This methodology is assessed in mathematical tutorial cases and over-actuated UAV simulations.

Stability analysis of linear/nonlinear switching active disturbance rejection control based MIMO continuous systems

In this paper, a linear/nonlinear switching active disturbance rejection control (SADRC) based decoupling control approach is proposed to deal with some difficult control problems in a class of multi-input multi-output (MIMO) systems such as multi-variables, disturbances, and coupling, etc. Firstly, the structure and parameter tuning method of SADRC is introduced into this paper. Followed on this, virtual control variables are adopted into the MIMO systems, making the systems decoupled. Then the SADRC controller is designed for every subsystem. After this, a stability analyzed method via the Lyapunov function is proposed for the whole system. Finally, some simulations are presented to demonstrate the anti-disturbance and robustness of SADRC, and results show SADRC has a potential applications in engineering practice.

Synchronous Generator Rectification System Based on Double Closed-Loop Control of Backstepping and Sliding Mode Variable Structure

Low-voltage and high-current direct current (DC) power supplies are essential for aerospace and shipping. However, its robustness and dynamic response need to be optimized further on some special occasions. In this paper, a novel rectification system platform is built with the low-voltage and high-current permanent magnet synchronous generator (PMSG), in which the DC voltage double closed-loop control system is constructed with the backstepping control method and the sliding mode variable structure (SMVS). In the active component control structure of this system, reasonable virtual control variables are set to obtain the overall structural control variable which satisfied the stability requirements of Lyapunov stability theory. Thus, the fast-tracking and the global adjustment of the system are realized and the robustness is improved. Since the reactive component control structure is simple and no subsystem has to be constructed, the SMVS is used to stabilize the system power factor. By building a simulation model and experimental platform of the 5 V/300 A rectification module based on the PMSG, it is verified that the power factor of the system can reach about 98.5%. When the load mutation occurs, the DC output achieves stability again within 0.02 s, and the system fluctuation rate does not exceed 2%.