Discrete-time Adaptive Control Research Articles

Discrete-Time Adaptive Control for Three-Phase PWM Rectifier.

This paper proposes a dual-loop discrete-time adaptive control (DDAC) method for three-phase PWM rectifiers, which considers inductance-parameter-mismatched and DC load disturbances. A discrete-time model of the three-phase PWM rectifier is established using the forward Euler discretization method, and a dual-loop discrete-time feedback linearization control (DDFLC) is given. Based on the DDFLC, the DDAC is designed. Firstly, an adaptive inductance disturbance observer (AIDO) based on the gradient descent method is proposed in the current control loop. The AIDO is used to estimate lump disturbances caused by mismatched inductance parameters and then compensate for these disturbances in the current controller, ensuring its strong robustness to inductance parameters. Secondly, a load parameter adaptive law (LPAL) based on the discrete-time Lyapunov theory is proposed for the voltage control loop. The LPAL estimates the DC load parameter in real time and subsequently adjusts it in the voltage controller, achieving DC load adaptability. Finally, simulation and experimental results show that the DDAC exhibits better steady and dynamic performances, less current harmonic content than the DDFLC and the dual-loop discrete-time PI control (DDPIC), and a stronger robustness to inductance parameters and DC load disturbances.

Multiple estimation models for discrete-time adaptive iterative learning control

ABSTRACT This article focuses on making discrete-time Adaptive Iterative Learning Control more effective using multiple estimation models. Existing strategies use the tracking error to adjust the parametric estimates. Our strategy uses the last component of the identification error to tune these estimates of the model parameters. We prove that this strategy results in bounded estimates of the parameters, and bounded and convergent identification and tracking errors. We emphasise that the proof does not use the Key Technical Lemma. Rather, it uses the properties of square-summable sequences. We extend this strategy to include multiple estimation models and show that all the signals are bounded, and the errors converge. It is also shown that this works whether we switch between the models at every instant and every iteration or at the end of every iteration. Simulation results demonstrate the efficacy of the proposed method with a faster convergence using multiple estimation models.

Disturbance rejection based on discrete-time adaptive preview control for unmanned aerial vehicle shipboard landing under structure damage

This article studies the shipboard landing control problem for unmanned aerial vehicle with external disturbance and structure damage. A novel discrete-time adaptive preview architecture is presented, where the model reference adaptive control is improved by introducing the preview control method, so that both the uncertainties (caused by the airwake and structure damage) and the control lag could be well compensated simultaneously. The proposed scheme guarantees a more rapid, accurate, and robust performance. For application, the reference input signal is generated by fusing the deck motion prediction information and glide path command. The effectiveness of the algorithm is validated by a longitudinal landing simulation.

Discrete-Time Adaptive Control for Uncertain Scalar Multiagent Systems with Coupled Dynamics: A Lyapunov-Based Approach

Discrete-time architectures offer a distinct advantage over their continuous counterparts, as they can be seamlessly implemented on embedded hardware without the necessity for discretization processes. Yet, because of the difficulty of ensuring Lyapunov difference expressions, their designs, which are based on quadratic Lyapunov-based frameworks, are highly complex. As a result, various existing continuous-time results using adaptive control methods to deal with system uncertainties and coupled dynamics in agents of a multiagent system cannot be directly applied to the discrete-time context. Furthermore, compared to their continuous-time equivalent, discrete-time information exchange based on periodic time intervals is more practical in the control of multiagent systems. Motivated by these standpoints, in this paper, we first introduce a discrete-time adaptive control architecture designed for uncertain scalar multiagent systems without coupled dynamics as a preliminary result. We then introduce another discrete-time adaptive control approach for uncertain multiagent systems in the presence of coupled dynamics. Our approach incorporates observer dynamics to manage unmeasurable coupled dynamics, along with a user-assigned Laplacian matrix to induce cooperative behaviors among multiple agents. Our solution includes Lyapunov analysis with logarithmic and quadratic Lyapunov functions for guaranteeing asymptotic stability with both controllers. To demonstrate the effectiveness of the proposed control architectures, we provide an illustrative example. The illustrative numerical example shows that the standard discrete-time adaptive control in the absence of observer dynamics cannot guarantee the reference state vector tracking, while the proposed discrete-time adaptive control can ensure the tracking objective.

Discrete-time adaptive distributed output observer for time-varying formation tracking of heterogeneous multi-agent systems

This paper presents discrete-time distributed algorithms to achieve time-varying output formation tracking of heterogeneous linear multi-agent systems subject to time-varying faults and directed graphs. To overcome the impacts caused by unknown faults and directed graphs, a discrete-time adaptive distributed output observer-based control architecture is established to guarantee time-varying output formation tracking exponentially. In particular, several distributed leader observers are firstly given to estimate and reconstruct the leader’s state over a directed graph. The new discrete-time adaptive distributed output observer is presented to remove the need of having fully access to the leader’s system matrices and to reduce the dimension and information exchange in the developed distributed observers. In terms of this estimated information from the adaptive distributed output observer, a distributed output feedback controller integrated with an observer-based scheme is developed to compensate for the impact of unknown faults such that time-varying output formation tracking is achieved with a global exponential convergence. Two examples and simulation results are provided to validate the effectiveness of the proposed designs.

Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.

Signal-parametric discrete-time adaptive controller for pneumatically actuated Stewart platform

The paper is devoted to the adaptive control of pneumatic drives for the Stewart platform with six degrees of freedom. Based on the approach known as the method of the implicit reference model, the synthesis of parametric and signal-parametric adaptive controllers is carried out. The use of both a group of pneumatic valves and a spool valve in the control system is considered. The effect of quantization on the level of the control process when using pneumatic valves is studied. In addition, the discretization of the control process and the effect of load changes on the pneumatic drive are considered. The results of comparative simulations are presented, demonstrating the system’s robustness to the plant parameters and the efficacy of the proposed signal-parametric adaptive controller.

Discrete time adaptive neural network control for WME and compression refrigeration systems

In this paper, we study the discrete-time control problem for the refrigeration system with unmodeled dynamics. This paper proposes discrete adaptive neural network controllers for two refrigeration systems, including the water membrane evaporator cooling and compression refrigeration systems. The influence of model uncertainty on system performance can be eliminated effectively by designing the neural network and the corresponding discrete-time adaptive updating strategy. Thus, the model parameters in the refrigeration system are not required in our control algorithms. Simulation results show that the proposed strategy can effectively adjust the refrigeration system temperatures. Compared with the traditional PID control strategy, the system response overshoot under our method can be reduced by 0.3%, and the system settling time is reduced by at least 94.3%.

Discrete-Time Adaptive Neural Tracking Control and Its Experiments for Quadrotor Unmanned Aerial Vehicle Systems

For the control of a quadrotor unmanned aerial vehicle, the strong nonlinearities, coupling, and underactuated problem in both positioning and attitude systems of the quadrotor are major challenging issues to be solved. In this article, a discrete-time adaptive dynamic surface control (DSC) scheme for the quadrotor is proposed to obtain a satisfactory tracking performance. The nonlinearities and couplings are overcome by employing the designed robust adaptive DSC nonlinear control method. The underactuated problem is overcome by solving the designed adaptive neural control equations. Also, different from the continuous-time control scheme, the discrete-time control is more suitable for the computer and network control in practicable cases. Furthermore, the digital first-order low-pass filters are constructed to predict the future virtual control signal in the backstepping method, leading to the avoidance of the model transformation problem in the discrete-time backstepping method.

Discrete-Time Adaptive Fractional Nonlinear Control Using Fuzzy Rules Emulating Networks

AbstractThe goal of this paper is to design a robust controller that relies only on input–output data to enforce robust tracking, when considering a large class of uncertain nonlinear system. The discrete-time controller is based on an adaptation approach that relies on a fractional reaching law. The feedback gain is adapted through a fuzzy inference system that emulates a neural network, providing interesting capabilities to compensate a large sort of uncertainties and unmodeled effects. The uniform ultimate boundedness of the tracking error is analyzed in the Lyapunov framework. Finally, an experimental assessment is studied to highlight the reliability of the proposed scheme.

Discrete-Time Adaptive PID Current Controller for Wind Boost Converter

This paper proposes an adaptive controller for a dc-dc boost converter to regulate the output current levels of a 400 W small wind turbine based on a permanent magnet synchronous generator with a three-phase diode rectifier. Despite the stochastic nature of wind, this discrete-time adaptive PID controller regulates the current levels without large overshoots and oscillations to attain the maximum power point of the wind system. The adaptive mechanism algorithm operating with two electrical measurements adjusts the controller parameters, and is designed with an approach consisting of the integration of the variable operation point of the small wind turbine into the discrete-time model of the dc-dc boost converter and the Bode stability criteria. The mechanism algorithm features a low computational complexity for controller parameters estimation and therefor a practical implementation in a low-end microcontroller (small size, low cost, and low energy consumption) is possible. Furthermore, the results based on the processor-in-the-loop simulation approach show that controlling the current levels and the maximum power point of the wind system via the proposed adaptive controller is more effective than a controller tuned around a particular fixed operating point.

Modified adaptive discrete-time incremental nonlinear dynamic inversion control for quad-rotors in the presence of motor faults

Unmanned air vehicles are intrinsically non-linear, unstable, uncertain, and prone to a variety of faults, most commonly the motor faults. The main objective of this paper is to develop a fault-tolerant control algorithm for the quadrotors with the motor faults. Accordingly, a novel adaptive modified incremental nonlinear dynamic inversion (MINDI) control is proposed to stabilize and control the quad-rotor with partial motor faults. The controller consists of a MINDI controller augmented with a discrete-time nonlinear adaptive algorithm. Since the incremental nonlinear dynamic inversion (INDI) algorithm is essentially based on the sensor measurements, it necessitates the angular rates differentiation and therefore amplifies the high-frequency noises produced by the gyroscopes. The application of derivative filters causes unavoidable internal state delays in the INDI structure. Henceforth, the performance of the controller developed for the unstable and uncertain quadrotors degrades considerably. To address this drawback, this paper proposes the MINDI controller which basically derives the angular accelerations from the angular moment estimations. Furthermore, to increase the robustness of the MINDI against motor faults, a discrete-time adaptive controller has been incorporated. The performance of the proposed controllers is verified both through the nonlinear simulations and testbed experiments. The results are compared with a recent efficient algorithm, which had been implemented on a quad-rotor model.

Stability and hidden oscillations analysis of the spacecraft attitude control system using reaction wheels

The paper is devoted to the problem of spacecraft attitude control using reaction wheels. The control system should ensure switching between less accurate to more accurate flight modes, resistance to external environmental influences, and, in some cases, the survival of the spacecraft. In these modes, the reaction wheel drives can reach their maximum performance, which introduces a saturation effect into the control loop. Its appearance can lead to self-excited attitude oscillations and significantly degrade positioning accuracy. In the paper, by the example of the DEMETER satellite, taking into account the flexibility of the appendices, attached to the spacecraft, the hidden oscillations in the PID-controlled spacecraft orientation system under the conditions of an actuator saturation were localized, and their parameters were found. The algorithms for the spacecraft attitude control were derived and a comparative study of their oscillatory attractors areas was given. To ensure asymptotic stability of the spacecraft orientation system the anti-windup correction was introduced, preventing hidden oscillations of the spacecraft attitude in the practically meaningful region of the initial conditions. Special attention is paid to the uncertainty of the satellite model parameters, which are not initially known with good precision and are varying along the satellite's orbit. For ensuring the attitude control system robustness in the face of the parametric uncertainty, in the paper the discrete-time adaptive controller with the Implicit Reference Model and anti-windup correction is proposed, and its efficiency is demonstrated by intensive simulation research.

Discrete-Time Adaptive Decentralized Control for Interconnected Multi-Machine Power Systems with Input Quantization

This study contrives a discrete-time adaptive decentralized control algorithm with input quantization for interconnected multi-machine power systems with SVC. First, a dynamic surface scheme is applied to the excitation controller design, in which first-order digital low-pass filters are used to predict the next virtual control law, which overcomes the model conversion problem in backstepping. Therefore, the controller design and structure are simplified. Further, an improved hysteresis quantizer is utilized for amplitude quantization of control input signals; along with the discretization of time, this achieves digital decentralized control. Finally, semi-global uniformly ultimately boundedness (SGUUB) of the whole control system is demonstrated based on the Lyapunov stability theory, and the effectiveness of the proposed control algorithm is verified on the ModelingTech real-time simulation experimental platform for power electronics.

Adaptive discrete-time NN controller design for automobile steer-by-wire systems with angular velocity observer

As one of steering systems, the steer-by-wire (SbW) system plays a significant role in the automobile. This paper investigates the study of the adaptive discrete-time neural network (NN) steering tracking control of the SbW system based on angular velocity observer. First, the continuous second-order SbW system is discretized by the Euler approximation approach. Before the control design, an adaptive discrete-time angular velocity observer is constructed to estimate the value of angular velocity signal. Then, an adaptive discrete-time control via a backstepping scheme is proposed to achieve the exact steering tracking performance, where the unknown nonlinear function, as well as the control coefficient, are incorporated into the lumped uncertainty and approximated by one NN. The main advantages of the proposed control scheme can be concluded that: (1) without using the exact prior knowledge of system uncertainty and angular position signal, the discrete-time tracking control is achieved and (2) the noncausal problem is overcome without transforming the original system into a predictor form. Finally, the Lyapunov stability theory shows that the tracking error converges to a small neighborhood of zero. Simulations and experiments illustrate the effectiveness and superiority of the proposed adaptive discrete-time NN control.

Discrete-time Adaptive Control of Pneumatic Actuators for 6-DoF Stewart Platform

This paper deals with computer-controlled pneumatic actuators for the Gough-Stewart platform with 6 degrees of freedom. An important feature considered in the paper pneumatic actuator is the use of a group of valves rather than a spool valve to control the pressure in the chambers, which leads to a significant quantization in terms of the level of the control action. In addition, there is a sampling in time in the control loop. The present work is aimed at ensuring the robustness of the pneumatic actuators for the Stewart platforms concerning their parameters and the effect of changing the load on the drive caused by the interdependence of the drives due to the movement of the platform. Two discrete-time (parametric, and signal-parametric) adaptive control algorithms, based on the concept of an implicit reference model with anti-windup correction are proposed. The simulation results are presented, demonstrating the efficiency of the signal-parametric algorithm.

A Projection Operator-Based Discrete-Time Adaptive Architecture for Control of Uncertain Dynamical Systems With Actuator Dynamics

Stability analyses of discrete-time adaptive control algorithms are generally predicated on quadratic Lyapunov-based frameworks that result in unavoidable complexity due to the resulting terms in the Lyapunov difference equations. This prevents generalizations of valuable continuous-time adaptive control results to their discrete-time settings. To this end, one important generalization is the consideration of actuator dynamics, which is present in any uncertain dynamical system. To address this problem, we propose a novel discrete-time adaptive control architecture predicated on the hedging method and a new projection operator. A logarithmic Lyapunov function is used for proving the asymptotic stability of the error between uncertain dynamical system states and hedging-based reference model states. An illustrative numerical example is then presented to demonstrate the efficacy of the proposed architecture.

Convex combination of multiple models for discrete-time adaptive control

The principal drawback of traditional adaptive systems is the possibility of rather poor transient response. In this regard, the multiple-model methodology has been beneficial over the past couple of decades. However, the application of this methodology requires proven indirect model reference adaptive control. Such a gap exists in the case of discrete-time linear time-invariant systems with unknown parameters. The principal contribution of this paper is to fill this void by arriving at proof of global stability of discrete-time adaptive systems that use the prediction error rather than the control error to update the parameters of the prediction model. This proof is based on the theory of Lyapunov and the properties of square-summable sequences. An analysis of the available literature reveals that such a result is not available even for linear time-invariant systems. Therefore, the proof is first provided for adaptive systems with a single prediction model wherein the transfer function of the plant has an arbitrary relative degree. Subsequently, this proof is extended to the case of multiple prediction models in the context of multiple-model methodology with second-level adaptation. Two parameter update algorithms are considered. Simulation studies are included to demonstrate the improvement in transient performance.

Discrete-time adaptive neural network control for steer-by-wire systems with disturbance observer

This paper investigates the design and implementation of the discrete-time adaptive neural network control with disturbance observer (DO) on a steer-by-wire (SbW) system, to simultaneously realize accurate tracking and anti-interference performance. Specifically, to approximate the lumped system uncertainty including the friction torque and self-aligning torque, the neural network is employed. To improve the steering tracking performance, the discrete-time identification model is proposed so that the tracking error and modeling error can be utilized to adjust the neural network updating law. Then, the unknown compound disturbances caused by external disturbance, Euler approximation errors and neural network approximation error are restrained by two DOs. Finally, the Lyapunov stability theory shows that the system tracking error is uniformly ultimately bounded. Both numerical simulations and experiments are implemented to show the superiority of the proposed controller.

Adaptive Control of Multivariable Networked Systems With Uncertain Time Delays

A discrete-time adaptive control approach for uncertain linear multivariable networked systems is proposed. It is capable of dealing with unknown time delays introduced by a communication network between a plant and a controller. Based on the idea of model reference adaptive control, two adaptive laws are presented to reduce the conservativeness that is usually introduced when the time delays are unknown. The stability of the closed-loop system is proven. Simulation examples provide a comparison of the proposed techniques to a nonadaptive algorithm.