Asymptotic Tracking Research Articles

Development of a Resonant Generalized Predictive Controller for Sinusoidal Reference Tracking

Sinusoidal reference tracking is required in important practical applications. Resonant controllers are suitable for that task. However, stable implementation of these controllers in a digital processor is difficult to achieve. On the other hand, quasi-resonant controllers are easier to implement, but they do not guarantee asymptotic reference tracking. This brief proposes a new resonant controller based on Generalized Predictive Control (GPC) and Internal Model Principle (IMP). The first-order and second-order difference operators are applied to create a GPC system whose structure embeds the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Z}$ </tex-math></inline-formula> -transform of the sinusoidal reference. Thus, according to IMP, the proposed controller, named Resonant Generalized Predictive Control (RGPC), asymptotically tracks sinusoidal references. Besides, the proposed RGPC has the advantages of GPC, such as fast response and easy implementation in digital processors. Experimental tests prove that the proposed RGPC has better performance than other controllers for sinusoidal reference tracking.

Adaptive Asymptotic Tracking With Global Performance for Nonlinear Systems With Unknown Control Directions

This article presents a global adaptive asymptotic tracking control method, capable of guaranteeing prescribed transient behavior for uncertain strict-feedback nonlinear systems with arbitrary relative degree and unknown control directions. Unlike most existing funnel controls that are built upon time-varying feedback gains, the proposed method is derived from a tracking error-dependent normalized function and a barrier function, together with a time-varying scaling transformation, leading to an improved prescribed performance control solution with the following features: 1) the developed control is embedded with normalized error based adaptive parameter tuning and is able to ensure asymptotic tracking; 2) given transient performance is guaranteed in that the tracking error preserves in the prescribed boundary for <inline-formula><tex-math notation="LaTeX">$\forall t\geq 0$</tex-math></inline-formula>; and 3) it is able to cope with nonlinear systems with arbitrary relative degree, mismatched uncertainties, and unknown control directions. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

Output tracking of time-delay Hamiltonian descriptor systems under saturation constraints

In this paper, the output tracking problem of Hamiltonian descriptor systems under the influence of saturation and time delay is investigated. In order to achieve fast output tracking and reduce tracking overshoot, an extended composite nonlinear feedback (ECNF) control method is proposed for Hamiltonian descriptor systems. Considering the special form of Hamiltonian descriptor system, based on the method of model transformation, the closed-loop Hamiltonian descriptor system obtained by introducing ECNF controller is replaced by two subsystems without singularity, so as to facilitate the later processing. For two different types of time delays, the criteria of asymptotic output tracking for closed-loop Hamiltonian descriptor systems are obtained respectively. Finally, the control effect of the ECNF method is tested by selecting a practical example and a numerical example.

Event-Triggered, Adaptive, Exponentially Asymptotic Tracking Control of Stochastic Nonlinear Systems

This paper investigates the problem of event-triggered, adaptive, asymptotic tracking control for a class of non-strict feedback stochastic nonlinear systems with symmetrical structures and sensor faults. Based on the negative exponential function, the event-triggered adaptive tracking control strategy deals with the problem of exponentially asymptotic convergence for the first time. The radial basis function neural network (RBFNN) mechanism addresses uncertain factors and unknown external disturbances in the system. The developed strategy ensures that all the signals of the closed-loop system are semi-globally uniformly bounded in probability, and that the tracking error can exponentially converge to zero. Finally, a simulation example demonstrates the effectiveness of the proposed method.

Adaptive dynamic surface tracking control for uncertain full-state constrained nonlinear systems with disturbance compensation

In this paper, an asymptotic adaptive dynamic surface tracking control strategy is investigated for uncertain full-state constrained nonlinear systems subject to parametric uncertainties and external disturbances. A novel disturbance estimator (DE) is firstly used to compensate for external disturbances. The parametric uncertainties are accordingly handled via a synthesized adaptive law. Then, by using the barrier Lyapunov function (BLF) and dynamic surface control (DSC), an appropriate backstepping design framework employing a novel adaptive-gain nonlinear filter is given, which avoids the “explosion of complexity” and relieves the conservatism of filter gain selection. The theoretical analysis reveals the asymptotic tracking performance is assured with the proposed controller. In the end, some simulation cases demonstrate the validity of the proposed controller.

Neural-network-based adaptive robust precision motion control of linear motors with asymptotic tracking performance

Neural-network-based adaptive robust precision motion control of linear motors with asymptotic tracking performance

Trajectory tracking for a class of switched nonlinear systems: Application to PMSM

This paper proposes a state-dependent switching control for a class of switched nonlinear systems, whose model describes a permanent magnet synchronous machine (PMSM) fed by a three-phase voltage source inverter. Due to its high torque density, high efficiency and wide velocity range, this electrical drive is widely used for traction and several applications in robotics, aerospace, electric vehicles among others. The proposed design conditions are based on a non-quadratic Lyapunov function, dependent on the machine shaft displacement, and assure asymptotic tracking of a pre-specified time-varying rotational velocity profile with guaranteed performance. Properties of the nonlinear system under consideration are used to derive design conditions expressed in terms of linear matrix inequalities that can be solved efficiently. Special cases involving asymptotic stability toward step and ramp velocity profiles are presented. Experimental results are used to validate the proposed technique.

Asymptotic Tracking Control for Nonaffine Systems With Disturbances

This brief intends to address an adaptive asymptotic tracking control with prescribed performance function for a class of nonaffine systems with unknown disturbances. First, the nonaffine system is transformed into an affine system by using a set of alternative state variables. Subsequently, a prescribed performance function with predefined convergence rate, maximum overshoot and steady-state error is introduced. To achieve the asymptotic tracking control performance, the robust integral of the sign of the error (RISE) feedback term is utilized in the control design to reject the unknown external disturbances and NN approximation errors. Finally, an adaptive controller is presented so that the asymptotic tracking performance with guaranteed prescribed performance is achieved. Comparative experiments are provided to show the effectiveness of the proposed control scheme.

A Bound Estimation Method for Robust Adaptive Fuzzy Asymptotic Tracking of Switched Nonlinear Systems with Its Application

A Bound Estimation Method for Robust Adaptive Fuzzy Asymptotic Tracking of Switched Nonlinear Systems with Its Application

Adaptive output-Feedback asymptotic tracking control for a class of nonlinear systems with actuator failure

This study deals with the output-feedback asymptotic tracking control problem for a class of nonlinear strict-feedback systems with actuator loss of effectiveness failure. To handle with the output-feedback control issue in the presences of nonlinearities, a new reduced-order observer design is presented, by utilizing the dynamic gain technique, which not only eliminates the limitation that the Lipchitz coefficients are required to be known in the existing output-feedback results, but makes full use of the measurable information. Furthermore, a new failure compensation mechanism is proposed to erase the effect of actuator failure, by introducing a cubic absolute-value Lyapunov function method and a novel (σ,σf)-modification technique. Compared with the existing output-feedback failure compensation results, our proposed method can not only relax the assumption requirement on nonlinear function, i.e., the nonlinear function with respect to output y can be extended to the nonlinear one with respect to state variable χ¯i in the means of asymptotic tracking, but also avoid the issue that the estimate for actuator efficiency indicator drifts to a large value suddenly. Further, within the framework of backstepping design, a new high-gain reduced-order observer based adaptive output-feedback failure compensation control is developed. Then, with the aid of Lyapunov analysis method, it is shown that all the signals in the closed-loop system are globally bounded, and the system output can asymptotically track a given reference signal. Finally, a simulation example is given to illustrate the efficiency of the proposed techniques.

DC 모터 속도 제어시스템을 위한 내부모델 원리 기반 제어기와 외란 관측기 기반 제어기의 등가 조건

Asymptotic tracking of a reference model and nonlinear disturbance rejection are two of the most important attributes of an effective control system. A DOB-based controller, which is designed based on an augmented system model including the disturbance dynamics, relies mainly on the disturbance estimation to provide robust reference tracking performance. While IMP-based controller design technique achieves the same result by including a dynamic model of the reference and disturbance in the control system model. However, the similarity of these two control techniques extends beyond basic design consideration. This paper presents an analytical study that reaches an equivalent condition between the two classes of controllers for a DC motor speed control problem. Based on the obtained condition, it is proposed that the DOB-based controller can be designed such that it shows the same performance as the IMP-based controller. This has been further verified through a simulation which shows the same robust performance in both cases.

Speed-Sensorless Control of Induction Machines with LC Filter for Geothermal Electric Submersible Pumping Systems

A speed-sensorless state-feedback controller for induction machines (IMs) with LC filter is proposed. The speed and state estimation is based on a speed-adaptive observer, requiring only the measurement of the filter input currents. The motor currents are controlled by a state-feedback controller with prefilter and integral control action, in order to achieve fast and asymptotic set point tracking. Observer and controller gains are calculated offline using linear quadratic regulator (LQR) theory and updated online (gain-scheduling) in order to attain stability and improve controller performance in the whole operation range. Implementation aspects, such as discretization of the control system and reduction of computational effort, are taken into account as well. The proposed control scheme is validated by simulations and experimental results, even for critical operating conditions such as speed zero-crossings. It is shown that the overall control system performs very well under various load- and speed conditions; while its tuning remains simple which makes it attractive for industrial application such as geothermal electric submersible pumping (ESP) systems.

Input constraint control for hydraulic systems with asymptotic tracking

Due to the nonlinearity and various uncertainties, the controller design for hydraulic servo systems with input constraint is more complicated and challenging. This paper first proposes an asymptotic tracking controller for electrohydraulic servomechanisms considering input constraint, parametric uncertainties, and unmodeled disturbances. The core innovation of this controller is to decouple the control input and the input nonlinearity while guaranteeing the nonlinear decoupling term and its derivative to be available and bounded. Meanwhile, the decoupling operation could be skillfully integrated to realize accurate adaptive model-based compensation while remaining the unique feature of asymptotic control for residual disturbances. For this purpose, based on the desired trajectory and the estimated disturbance via an extended state observer (ESO), a desired load pressure signal is constructed to replace the actual load pressure and accomplish the required decoupling operation. In this case, a desired adaptive feedforward compensation in combination with a robust integral of the sign of the error (RISE) feedback is proposed to attenuate parametric uncertainties and residual unmodeled disturbances, respectively. Subsequently, a smooth hyperbolic tangent function is integrated into the controller to handle the input constraint. Theoretical analysis proves that the developed control strategy can achieve semi-global asymptotic tracking performance. Besides, numerical simulations and experimental tests demonstrate that the proposed control scheme can ensure high-precision tracking performance and simultaneously satisfy the preset control input range when encountering the input constraint and modeling uncertainties.

Adaptive prescribed performance asymptotic tracking control for nonlinear systems with time‐varying parameters

AbstractThis study considers the problem of prescribed performance adaptive asymptotic tracking control for a class of nonlinear systems with time‐varying parameters. A novel adaptive tracking control scheme is constructed by using the congelation of variables method and the backstepping method, in which the adaptive laws are designed to approximate the averages of the time‐varying parameters. The normalized function transformation is introduced to achieve the prescribed performance control; meanwhile, the issue of the explosion of complexity is avoided by using the command filtered technique. In addition, the proposed approach guarantees that all signals of the closed‐loop system are bounded and the tracking error can asymptotically converge to zero, while staying within prescribed boundaries. Finally, the effectiveness of the control strategy is shown by two simulation examples.

Adaptive Sliding Mode Control of Robot Manipulators with System Failures

This paper presents a novel adaptive sliding mode controller for a class of robot manipulators with unknown disturbances and system failures, which can well achieve the asymptotic tracking, and avoid some possible singularity problems. A new virtual controller is designed such that the chosen Lyapunov function can be transformed into a non-Lipschitz function, based on which, the system states can arrive at the specified sliding surface within a finite time regardless of the existence of system failures/faults. By fusing an integral fast terminal nonsingular SMC and a robust adaptive technique, the tracking error can be steered into a preset range in a set time and some possible singularity problems are avoided elegantly. With our proposed scheme, the loss coefficient is well estimated, and the stability of the system can be guaranteed even in the presence of the total loss of actuator outputs. The experiment and simulation results are presented to illustrate the effectiveness of the proposed control scheme.

Rapid-Erection Backstepping Tracking Control for Electrohydraulic Lifting Mechanisms of Launcher Systems

Uncertainties and disturbances widely exist in electrohydraulic lifting mechanisms of launcher systems, which may worsen the rapid-erection tracking accuracy and even make the system unstable. To deal with the issue, an asymptotic tracking control framework is developed for electrohydraulic lifting mechanisms of launcher systems. Firstly, the dynamic equations and state-space forms of the electrohydraulic lifting mechanism are modeled. Based on the system model, a nonlinear rapid-erection robust controller is constructed to achieve the improvement of the system control performance, in which a nonlinear feedback term is employed to remove the effects of uncertainties and disturbances on tracking performance. Compared to the existing results, the asymptotic tracking stability of the closed-loop system can be assured based on the Lyapunov theory analysis. In the end, the simulation example of an actual electrohydraulic lifting mechanism of the launcher system is done to validate the effectiveness with the proposed controller.

Logic-based distributed switching control for agents in power-chained form with multiple unknown control directions

This work studies logic-based distributed switching control for nonlinear agents in power-chained form, where logic-based (switching) control arises from the online estimation of the control directions assumed to be unknown for all agents. Compared to the state-of-the-art logic-based mechanisms, the challenge of power-chained dynamics is that in general asymptotic tracking cannot be obtained, even for a single agent. To address this challenge, a new logic-based mechanism is proposed, which is orchestrated by a dynamic boundary function. The boundary function is decreasing in-between switching instants and monotonically increasing at the switching instants, depending on the jumps of an appropriately designed Lyapunov-like function. To remove chattering (i.e. two or more switching instants occurring consecutively with zero dwell time), a dynamic threshold is proposed, based on selecting the maximum values of the Lyapunov-like function before and after switching.

An Enhanced Sliding Mode Speed Control for Induction Motor Drives

In this paper, an enhanced Integral Sliding Mode Control (ISMC) for mechanical speed of an Induction Motor (IM) is presented and experimentally validated. The design of the proposed controller has been done in the d-q synchronous reference frame and indirect Field Oriented Control (FOC). Global asymptotic speed tracking in the presence of model uncertainties and load torque variations has been guaranteed by using an enhanced ISMC surface. Moreover, this controller provides a faster speed convergence rate compared to the conventional ISMC and the Proportional Integral methods, and it eliminates the steady-state error. Furthermore, the chattering phenomenon is reduced by using a switching sigmoid function. The stability of the proposed controller under parameter uncertainties and load disturbances has been provided by using the Lyapunov stability theory. Finally, the performance of this control method is verified through numerical simulations and experimental tests, getting fast dynamics and good robustness for IM drives.

Adaptive disturbance observer-based control of hydraulic systems with asymptotic stability

As control precision is the most important indices of control precision, this study concerns with high accuracy tracking control of hydraulic systems. We suggest an adaptive disturbance-observer-based asymptotic tracking control strategy to hydraulic systems for achieving our motivation. It is of note that parameter uncertainty and disturbance are challenges in the area of hydraulic system control. In this study, the time-varying disturbance is compensated by model-based feed-forward control terms which are designed by a sign of error-function-based disturbance observer. To avoid the high learning burden of the disturbance, which is resulted from the parameter uncertainty, online adaptive control is integrated with the mentioned disturbance observer. To guarantee the theoretical feasibility of the proposed controller, the stability analysis Xis accomplished by introducing the Lyapunov stability theory. Compared with previous works reported in the literature, the proposed adaptive disturbance observer-based a controller can achieve global asymptotic stability when the considered systems are subjected to mismatched or match disturbance. The comparative experimental results reveal that the proposed method can obtain state-of-the-art tracking performance for hydraulic systems under the influence of parameter uncertainty and time-varying disturbance.

Neural-networks-based adaptive asymptotic tracking control of MIMO stochastic non-strict-feedback nonlinear systems with full state constraints and unknown control gains

The neural-networks-based adaptive asymptotic tracking control problem is considered for a class of multiple input multiple output (MIMO) stochastic non-strict-feedback nonlinear systems with unknown control gains and full state constraints. Firstly, barrier Lyapunov functions (BLFs) are designed to avoid the violation of the state constraints, the dynamic surface control (DSC) method is adopted to ensure the computation burden is greatly reduced, and the introduced auxiliary virtual controllers solve the design obstacle arised from unknown control gains. Then, by introducing a specific gain suppression inequality, a new adaptive asymptotic tracking control scheme is proposed and its correctness and validity are rigorously proved, which can not only effectively guarantee that all the signals of the closed-loop system are bounded in probability, but also makes the tracking error converge to zero in the fourth moment. At the same time, the impact of the full state constraints on the system performance is also tackled. Finally, the feasibility and practicability of the proposed control scheme are verified by the simulation results.