Virtual Control Signals Research Articles

Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation

This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.

Active anti-disturbance control of a quadrotor unmanned aerial vehicle using the command-filtering backstepping approach

In this paper, a backstepping-based nonlinear controller is developed to control the quadrotor in the presence of constant and time-varying disturbances. The control law is derived based on Lyapunov stability arguments. The controller is integrated with a disturbance observer to estimate and attenuate the effect of the disturbing forces and moments influencing the quadrotor. In this approach, no disturbance model is required for the disturbance observer. Discontinuous terms are added to the control law to ensure the negative definiteness of the Lyapunov function derivative without neglecting the disturbance observer estimation errors. Command filtering is used to compute the derivatives of the virtual control signals to avoid the complex analytic derivation of these derivatives, and to avoid differentiating the discontinuous terms existing in the controller. The effectiveness of the developed controller is investigated in simulations against disturbances due to partial actuator failure, wind, and unmodeled rotor dynamics.

Robust Control Allocation for Spacecraft Attitude Tracking Under Actuator Faults

This brief addresses attitude tracking problems for an over-actuated spacecraft in the presence of actuator faults, imprecise fault estimation, and external disturbances. First, a model reference adaptive control technique is used to design a high-level controller to produce the three-axis virtual control torque. Then, taking fault estimation uncertainties into account, a robust control allocation (RobCA) strategy is proposed to redistribute virtual control signals to the remaining actuators when an actuator fault occurs. The RobCA is formulated as a min–max optimization problem, which deals with actuator faults directly without reconfiguring the controller and ensures some robustness of system performances. Finally, simulation results are provided to show the effectiveness of the overall control strategy.

Terminal Sliding Mode Control Allocation for Nonlinear Systems

In this paper, the problem of tracking control is studied for a class of nonlinear systems with actuator faults/failures. The control strategy has two steps. In the first step, a virtual control input is found using terminal sliding mode control which can easily tackle the output tracking control problem in a finite time. In the second step, control allocation (CA) transforms the virtual control signals to the real-control inputs. The CA problem is solved using a neural network which satisfies control constraints and during faults or failures redistributes the control signals to the healthy actuators. The effectiveness of the proposed control approach is demonstrated by the simulation results of the near space vehicle system.

Adaptive decentralized fault-tolerant tracking control of a class of uncertain large-scale nonlinear systems with actuator faults

We are concerned with the fault-tolerant tracking control affair for a class of large-scale multi-input and multi-output (MIMO) nonlinear systems suffering from actuator failures. Taking advantage of the mean-value theory and the implicit function theorem, the non-affine subsystems are transformed into affine forms. Neural networks (NNs) are utilized to approximate unknown virtual control signals, and then an adaptive NN-based decentralized tracking control strategy is exploited recursively by combining backstepping methods as well as the dynamic surface control (DSC) methodology. In theory, the stability of the resulting whole system is rigorously analysed, where it is proven that all signals remain uniformly ultimately bounded (UUB) and the designed strategy can guarantee the convergence of tracking errors via a suitable choice of control parameters. Finally, two simulation examples, both practical and numerical examples, are illustrated to verify the feasibility of the theoretical claims.

Direct Adaptive Fuzzy Tracking Control of Marine Vehicles With Fully Unknown Parametric Dynamics and Uncertainties

In this brief, a novel direct adaptive fuzzy tracking control (DAFTC) scheme for marine vehicles with fully unknown parametric dynamics and uncertainties is proposed. The significant contributions of the DAFTC approach are as follows. First, in the backstepping framework, fully unknown parametric dynamics and uncertainties are encapsulated into a lumped nonlinearity function encompassing system states and virtual control signals. Second, the integrated nonlinearity function is further identified online by an adaptive fuzzy approximator that synthesizes a model-free control scheme (termed DAFTC) without requiring any a priori knowledge of the model. Third, tracking errors are proven to be uniformly ultimately bounded (UUB) and can converge to an arbitrarily small neighborhood of zero in a finite time. Simulation studies and comprehensive comparisons demonstrate that the proposed DAFTC scheme has remarkable performance and is superior in both tracking accuracy and unknown parametric dynamics compensation.

A novel disturbance observer-based backstepping controller with command filtered compensation for a MIMO system

This paper presents a novel disturbance observer-based trajectory tracking controller based on the integral backstepping approach. To avoid the complexity of analytically calculating derivatives of virtual control signals in the standard backstepping technique, a command filtered backstepping approach is utilized. The proposed control approach is formulated for a class of nonlinear MIMO systems and provides robustness against external disturbances. This approach is applied on an aerodynamic laboratory setup known as the twin rotor MIMO system (TRMS). Stability analysis of the proposed controller is presented using Lyapunov stability arguments and singular perturbation theory. Simulation studies show that the proposed controller successfully allows the system outputs to track arbitrary reference trajectories and reject arbitrary constant disturbances that may occur due to partial actuator failure. The reliability and effectiveness of the approach is validated experimentally by implementation of the proposed controller on a hardware-in-the-loop system.

Three-dimensional formation control based on filter backstepping method for multiple underactuated underwater vehicles

SUMMARYThis paper proposes a leader following formation tracking controller for multiple underactuated underwater vehicles (UUVs) which move in three dimensional space. In order to avoid the derivative of the virtual control signals, a control method based on filter backstepping is proposed. The method can significantly simplify the design process of the backstepping controller through the use of a filter rather than the analytic derivation directly to the virtual control variable. Furthermore, the influence of measurement noise is obviously weakened. The stability of the formation system of multiple UUVs has been proved based on Lyapunov stability theory. Simulation results illustrate that the designed controller can track a three-dimensional formation trajectory accurately.

Online optimisation‐based backstepping control design with application to quadrotor

In backstepping implementation, the derivatives of virtual control signals are required at each step. This study provides a novel way to solve this problem by combining online optimisation with backstepping design in an outer and inner loop manner. The properties of differential flatness and the B-spline polynomial function are exploited to transform the optimal control problem into a computationally efficient form. The optimisation process generates not only the optimised states, but also their finite order derivatives which can be used to analytically calculate the derivatives of virtual control signal required in backstepping design. In addition, the online optimisation repeatedly performed in a receding horizon fashion can also realise local motion planning for obstacle avoidance. The stability of the receding horizon control scheme is analysed via Lyapunov method which is guaranteed by adding a parameterised terminal condition in the online optimisation. Numerical simulations and flight experiments of a quadrotor unmanned air vehicle are given to demonstrate the effectiveness of the proposed composite control method.

On reduction of control effort in feedback linearization GPC strategy applied to a solar furnace

SummaryIn this paper, the temperature control of a solar furnace is addressed by taking into account physical and safety constraints. In particular, the use of a feedback linearization generalized predictive control strategy is proposed where the fictitious model providing a virtual control signal is suitably selected to reduce the control effort by considering both the reference tracking task and the compensation of disturbances, represented by the variation of the input energy provided by the Sun, mainly because of the solar daily cycle and passing clouds. Simulation and experimental results show the effectiveness of the methodology in comparison with other approaches helping this technology to become an inexpensive alternative option for the material treatment and testing in the industrial context. Copyright © 2015 John Wiley & Sons, Ltd.

A biologically inspired approach to tracking control of underactuated surface vessels subject to unknown dynamics

In this paper, a novel biologically inspired approach is proposed for the tracking control of an underactuated surface vessel subject to unknown dynamics. The tracking control algorithm is first derived from the error dynamics analysis of the vessel using backstepping. Then, three shunting neural dynamics derived from biological membrane equation are employed to avoid the inherent complexity of numerical derivatives of virtual control signals in the backstepping design. A single-layer neural network (NN) is finally used to approximate the unknown dynamics including uncertain model parameters and hydrodynamics coefficients. Unlike some existing tracking methods for surface vessel whose control algorithms suffer from requiring high computational effort, the proposed tracking control algorithm is computationally efficient as no derivative calculations on virtual controls are required. In addition, it is capable of tracking any smooth trajectories without any prior knowledge of the dynamics parameters. The effectiveness and efficiency of the proposed control approach are demonstrated by simulation and comparison studies.

Three‐Dimensional Constrained Tracking Control Via Exact Differentiation Estimator of a Quadrotor Helicopter

AbstractIn this paper, a constructive method is presented to design a three dimensional trajectory tracking controller that forces a quadrotor helicopter to track a bounded and sufficiently smooth reference trajectory asymptotically in the presence of constant force disturbances. The quadrotor helicopter under consideration has fewer independent thrusters than degrees of freedom to be controlled. Motivated by the vehicle's steering practices, the roll and pitch angles are regarded as virtual controls along with four control forces to fulfill the task of position and yaw angle reference tracking. To prevent position constraint violation, the barrier Lyapunov function (BLF) is employed in the vectorial backstepping procedure to guarantee that the position and attitude constraints are not violated. The backstepping procedure employs an exact and robust sliding mode differentiator of order two to facilitate the implementation of the attitude command signal without calculating the virtual control signal derivative analytically.

Adaptive Energy-Efficient Control Allocation for Planar Motion Control of Over-Actuated Electric Ground Vehicles

A hierarchical control structure, consisting of a high-level dynamic sliding mode control (SMC) and a low-level adaptive energy-efficient control allocation (A-EECA) scheme, is presented to track the planar motions of an electric ground vehicle with four in-wheel motors while achieving the optimal energy consumption. By explicitly incorporating the efficiency functions and input constraints of in-wheel motors in the low-level A-EECA design, virtual control signals from the high-level dynamic SMC are distributed to four actuators with an adaptive convergence to the energy-optimal operating points. Taking allocation errors between the virtual control efforts and the real actuation realizations as inputs, the input-to-state stability of the overall feedback system is proved. Both simulation and experimental results in different maneuvers are demonstrated to validate the control design. The high-level vehicle tracking performance, low-level torque distributions, and total energy consumptions in the test maneuvers are compared between the proposed A-EECA and a standard pseudoinverse control allocation without considering the power optimization.

Tracking Control System Design Based on Adaptive Neural Network

The implicit function theorem and the mean value theorem non-affine function of the system into an affine form, and then RBF neural network approximation virtual control and actual control signals desired. Finally Lyapunov functional theory and backstepping method are used to design a self-adapt tracking control scheme. The proposed control scheme can guaranteed to achieve better tracking performance, thus avoiding the problems caused by the high-gain control affine term sector caused by design problems and overcome loop controller. In order to solve practical engineering control problems provides a theoretical basis and can learn from the ideas, and finally through numerical examples to demonstrate the effectiveness of the proposed method.

Novel neural control for a class of uncertain pure-feedback systems.

This paper is concerned with the problem of adaptive neural tracking control for a class of uncertain pure-feedback nonlinear systems. Using the implicit function theorem and backstepping technique, a practical robust adaptive neural control scheme is proposed to guarantee that the tracking error converges to an adjusted neighborhood of the origin by choosing appropriate design parameters. In contrast to conventional Lyapunov-based design techniques, an alternative Lyapunov function is constructed for the development of control law and learning algorithms. Differing from the existing results in the literature, the control scheme does not need to compute the derivatives of virtual control signals at each step in backstepping design procedures. Furthermore, the scheme requires the desired trajectory and its first derivative rather than its first n derivatives. In addition, the useful property of the basis function of the radial basis function, which will be used in control design, is explored. Simulation results illustrate the effectiveness of the proposed techniques.

Neural network based adaptive dynamic surface control for cooperative path following of marine surface vehicles via state and output feedback

This paper addresses the problem of steering a group of marine surface vehicles along given spatial paths, while holding a desired formation pattern subject to dynamical uncertainty and ocean disturbances induced by unknown wind, waves and ocean currents. The control design is categorized into two envelopes. One is to steer individual marine surface vehicle to track a given spatial path. The other is to synchronize the speed of each vehicle along its path and path variables under the constraints of an underlying communication network in order to holding a desired formation pattern. The key features of the developed controllers are that, first, the neural network adaptive technique allows one to handle the dynamical uncertainty and ocean disturbances, without the need for explicit knowledge of the model; second, the proposed dynamic surface control technique simplifies the controller design by introducing the first-order filters and avoids the calculation of derivatives of virtual control signals. Further, this result is extended to the output feedback case, where a high-gain observer based cooperative path following controller is developed without measuring the velocity of each vehicle. Under the proposed controllers, all signals in the closed-loop system are guaranteed to be uniformly ultimately bounded for both state and output feedback cases. Simulation results validate the performance and robustness improvement of the proposed strategy.

Adaptive nonlinear output-feedback dynamic surface control with unknown high-frequency gain sign

In this paper, an adaptive dynamic surface control (DSC) for a class of nonlinear systems with unknown high-frequency gain (HFG) sign is proposed. The novelty of our scheme is that we separate the first virtual control signal from the HFG, which enables us to estimate the HFG directly. As a result, the traditional Nussbaum function (NF) approach is abandoned. By using the proposed DSC, the adaptive laws are needed only at the first design step and the explosion of terms in backstepping control can be eliminated, which greatly reduces the computational burden. In particular, based on an initialisation technique, we prove that the performance of the system tracking error can be guaranteed even when the HFG sign is unknown. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results illustrate that the proposed scheme is more applicable than that of the NF-based backstepping control.

Adaptive dynamic surface control for cooperative path following of underactuated marine surface vehicles via fast learning

This study presents a solution to the problem of cooperative path following of multiple underactuated marine surface vehicles subject to dynamical uncertainties and ocean disturbances. The dedicated control designs are categorised into two envelopes. One is to steer individual underactuated marine surface vehicle to track a given spatial path; and the other is to synchronise the along-path speeds and path variables under the constraints of an underlying communication network in order to hold a desired formation pattern. Within these two formulations, a robust adaptive path-following controller is first designed for individual vehicle based on neural networks and a dynamic surface control (DSC) technique. Then, the along-path speeds and path variables are synchronised to each vehicle owing to the proposed decentralised synchronisation control law building on graph theory and Lyapunov theory. The key features of the developed controllers are that, first, the DSC technique simplifies the controller design by introducing first-order filters and avoids the calculation of derivatives of virtual control signals. Second, the developed controllers with filtering adaptive laws allow for fast learning without generating high-frequency oscillations in control signals. Rigorous theoretical analysis demonstrates that all signals in the closed-loop system are uniformly ultimately bounded. Simulation results are provided to show the efficacy of the proposed method.

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.

Linear system control via saturating dynamic actuators global output‐reference tracking

The problem of controlling cascade systems, involving in series a saturating actuator and a linear plant, is revisited. Presently, the actuator is described with a more realistic model that accounts not only for its saturating nature but also for its dynamics. Furthermore, the considered model emphasises the internal feedback interaction (between saturation and dynamics) that characterises most real-life actuators. The control objective is 2-fold: (i) stabilising the whole actuator-plant association; (ii) and enforcing the plant input de accurately match any bounded reference signal. To this end, a two-loop controller is developed following a backstepping-like design procedure. Accordingly, the outer regulator is first synthesised, to meet the output-reference tracking objective. During this synthesis stage the actuator output is considered as a virtual control signal. The control law obtained at this stage will serve as a reference trajectory for the actuator output. In the second stage, the inner regulator is designed to make the actuator output tracks its reference trajectory. The cascade controller thus developed is formally shown to meet its control objectives, that is, bounded input bounded output (BIBO) stability and perfect asymptotic matching of any reference signal that is compatible with the actuator saturation.