Unmatched Dynamics Research Articles

Lyapunov stability analysis of an RMRAC‐based adaptive sigmoid super‐twisting sliding mode under matched and unmatched uncertainties

AbstractThis article presents a discrete‐time robust model reference adaptive controller and adaptive sigmoid super‐twisting sliding mode (RMRAC‐ASSTSM) and its stability analysis using Lyapunov stability theory. This control structure is robust to matched and unmatched dynamics. In addition, the chattering phenomenon tends to be suppressed in the steady state due to adaptive super‐twisting sliding mode action using a sigmoid function. The performance of the proposed control structure is corroborated with simulation results, considering a second‐order non‐minimum phase unstable plant, where it can be seen that RMRAC‐ASSTSM regulation errors converge to a finite residual set when the plant presents unmodeled dynamics. A comparison is also presented with a similar RMRAC‐based control structure with an adaptive super‐twisting sliding mode implemented with a sign function.

Continuous-time Lyapunov stability analysis and systematic parametrization of robust adaptive sliding mode controller for systems with matched and unmatched dynamics

Continuous-time Lyapunov stability analysis and systematic parametrization of robust adaptive sliding mode controller for systems with matched and unmatched dynamics

Neuro-Integral Sliding Mode Control for the Perturbed Unicycle Mobile Robot

This work proposes the design of a robust controller for the perturbed kinematic model of the unicycle mobile robot. The controller is based on integral sliding modes (ISMs) and the approximation provided by a differential neural network (DNN) for the tracking error dynamics, represented as an uncertain time-varying linear system. The methodology ensures asymptotic stability for the tracking error despite multiplicative disturbances in the control channel. The ISM compensates for the matched dynamics identified with the DNN. Then, a feedback controller minimizes the effect of unmatched dynamics by solving a set of Linear Matrix Inequalities. Simulation results show the feasibility of the proposed strategy against classical controllers.

A Hybrid Robust Adaptive Sliding Mode Controller for partially modelled systems: Discrete-time Lyapunov stability analysis and application

This work presents a new discrete-time Hybrid Robust Adaptive Sliding Mode Controller, developed from the union of a Robust Model Reference Adaptive Controller, an Adaptive Sliding Mode Controller, and an Adaptive One Sample Ahead Preview Controller in an unique control structure. Robust Model Reference Adaptive Controller is an adequate direct adaptive control strategy to control partially known plants, but can present slow closed-loop response to ensure global stability. Therefore, an adaptive One Sample Ahead Preview controller is incorporated to accelerate transient regimes, once it tries to track reference signal in one sample. Furthermore, an adaptive Sliding Mode Controller is also merged in the controller structure to help controller performance in transient regime and it also improves relevantly the steady state response in a scenario of several unmodelled dynamics Stability analysis of this controller using Lyapunov criterion and its robustness proof are provided, considering the plant subjected to unmodelled dynamics, which provides controller design constraints. These proofs show the controller is globally stable, and the tracking error tends to a residual set in steady state, even in the presence of matched and unmatched dynamics. Numerical simulations of the Hybrid Robust Adaptive Sliding Mode Controller applied on an unstable nonminimum-phase plant are presented, where only part of the overall plant is take into consideration for controller design. Results corroborate the feasibility and robustness of the developed control strategy and the performance superiority when compared to an adaptive One Sample Ahead Preview controller, with a 75% tracking error reduction in a scenario of several unmodelled dynamics.

Lyapunov stability analysis of a robust model reference adaptive PI controller for systems with matched and unmatched dynamics

In this paper, the discrete-time Lyapunov stability analysis of a Robust Model Reference Adaptive PI (Proportional-Integral) Controller is presented. The mathematical development of this controller is grounded on Robust Model Reference Adaptive Control philosophy, which provided boundedness of all closed-loop system signals and ensures its global stability. The resulting controller shows robustness characteristics to matched and unmatched dynamics, it guarantees the convergence of adaptive gains to a solution set and the convergence of tracking error to a residual set on steady state. Besides, to implement it, the only required information about the plant are its relative degree and the signal of its gain. Simulation results of the controller are provided, applying it on an unstable nonminimum-phase plant and in a practical plant. Besides, it was also compared with a Robust Model Reference Adaptive Controller and presented higher performance.

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The tower crane is widely used in construction and transportation engineering. To improve working efficiency and safety, input shaping methods have been applied. Input shaping is a method of reducing residual vibration of flexible systems by convolving a sequence of impulses with unit step command. However, input shaping is based on the linear system theory in which its control performances are degraded, in case of nonlinearity and unmatched dynamics of the control systems. In this paper, a new optimal reference input shape design method based on minimizing cost function is suggested and applied, to a simple cart-pendulum system which is a simplified model of tower cranes. Since pendulum dynamics is nonlinear, analytic solution does not exist. To overcome this problem, in this paper, a machine learning approach is suggested to find optimal reference input shape for the cart position control. The feasibility of the proposed design method is verified through some simulation examples by using MatLab.

Design of continuous-time model reference adaptive and super-twisting sliding mode controller

This paper presents a continuous-time Robust Model Reference Adaptive and Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The controller law is composed by two control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main benefit of this novel control algorithm is to present, simultaneously, high robustness and fast dynamic response, which are conflicting with each other in conventional adaptive algorithms. Furthermore, as the STSM Controller is also adaptive, the dynamic response has relevant chattering mitigation without additional efforts on controller design, implementation, or execution. Besides, the union of the STSM with RMRAC also improved sliding accuracy in steady state. Thereby, in steady state, the STSM control contribution is almost zero, which avoids the chattering phenomenon, once it acts only in the transient regimes. The stability and robustness analysis of the control structure are presented, in continuous-time, considering the overall plant, that is, in presence of matched and unmatched dynamics. The continuous-time stability analysis is important in an adaptive system, since it features an intermediary step for control system stability analysis in discrete-time and its application in real plants. In addition, to present the feasibility and benefits of the proposed controller, simulations results of two case studies are presented: one is the controller application in an unstable non-minimum phase plant, and the second is its application for current regulation of a single-phase grid-tied power converter with an LCL filter. Moreover, to corroborate the robustness and tracking performance of the proposed controller a comparison with an adaptive first order Sliding Mode is also presented.

A Robust Adaptive Super-Twisting Sliding Mode Controller applied on grid-tied power converter with an LCL filter

This paper presents a new robust adaptive controller, totally developed on discrete-time. This controller is composed by two control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller, constituting a new control structure, nominated Robust Adaptive STSM Controller. The main advantage of this new control proposal is its high adaptability and robust performance, with fast reference tracking without chattering. The stability and robustness analysis, in discrete time, are presented, considering the overall plant, that is, in presence of matched and unmatched dynamics. To evaluate its robustness performance, the proposed controller is designed for grid-injected current control of three-phase grid-tied power converter with an LCL filter under weak grid. To validate it, the plant was partially modeled as a first order transfer function, neglecting capacitor dynamics and considering it as an additive dynamics on control design. Experimental results are presented to corroborate the controller performance and the stability analysis by means of Lyapunov Theory is provided.

Lyapunov stability analysis of discrete-time robust adaptive super-twisting sliding mode controller

This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation.

3D Space Trajectory Tracking of Underactuated AUVs using Back-Stepping Control and Time Delay Estimation

Abstract In this paper, a robust controller using the back-stepping approach and the time delay estimation(TDE) is proposed for the 3D space motion control of torpedo-like autonomous underwater vehicles(AUVs). Due to the lack of control inputs, the vehicle dynamics does not satisfy the matching condition and has nonlinear dynamics including rigid dynamics and hydrodynamics. By utilizing a relevant coordinate transform, it is shown that the tracking error dynamics of the vehicles can be represented as a strict-feedback form. Using the error dynamics, the back-stepping controller is designed to gain robustness against the unmatched dynamics. The nonlinear dynamics of the vehicle is compensated by using the TDE which estimates the dynamics robustly utilizing the system inputs and outputs. By combining the back-stepping scheme and the TDE, the proposed controller has robust tracking performance against model uncertainties and disturbances. Owing simplicity of the TDE, moreover, the proposed controller can be implemented without necessity of whole dynamic model of the vehicles. The simulation results using the REMUS model demonstrates the robustness of the proposed controller against the model uncertainties and disturbances.

Extended-state-observer-based output feedback adaptive control of hydraulic system with continuous friction compensation

This paper presents an extended state observer-based output feedback adaptive controller with a continuous LuGre friction compensation for a hydraulic servo control system. A continuous approximation of the LuGre friction model is employed, which preserves the main physical characteristics of the original model without increasing the complexity of the system stability analysis. By this way, continuous friction compensation is used to eliminate the majority of nonlinear dynamics in hydraulic servo system. Besides, with the development of a new parameter adaption law, the problems of parametric uncertainties are overcome so that more accurate friction compensation is realized. For another, the developed adaption law is driven by tracking errors and observation errors simultaneously. Thus, the burden of extended state observer to solve the remaining uncertainties is alleviated greatly and high gain feedback is avoided, which means better tracking performance and robustness are achieved. The designed controller handles not only matched uncertainties but also unmatched dynamics with requiring little system information, more importantly, it is based on output feedback method, in other words, the synthesized controller only relies on input signal and position output signal of the system, which greatly reduces the effects caused by signal pollution, measurement noise and other unexpected dynamics. Lyapunov-based analysis has proved this strategy presents a prescribed tracking transient performance and final tracking accuracy while obtaining asymptotic tracking performance in the presence of parametric uncertainties only. Finally, comparative experiments are conducted on a hydraulic servo platform to verify the high tracking performance of the proposed control strategy.

Adaptive homography-based visual servo for micro unmanned surface vehicles

In this paper, a novel adaptive homography-based visual servo (AHBVS) scheme is proposed to regulate a micro unmanned surface vehicle (MUSV) to the desired pose in the presence of both unknown image depth and unmatched dynamics. By virtue of homography decomposition technique, the scaled pose errors are directly retrieved from the live and desired images which are captured by a monocular camera. On the basis of the MUSV characteristics, a completely new visual servo system is firstly derived from visual measurements including both kinematics and dynamics. Different from kinematics solutions, the dynamics-level AHBVS controllers adapting to unknown image depth and compensating unmatched dynamics are developed by incorporating backstepping technique and Lyapunov synthesis, and thereby facilitating practical implementations. Lyapunov analysis proves that the proposed AHBVS scheme renders the closed-loop visual servo system globally uniformly asymptotically stable (GUAS). Simulation results demonstrate remarkable performance on a prototype MUSV.

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

SummaryThis paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L2‐norm and Cauchy‐Schwartz inequality. Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent–based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well‐known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3‐DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes.

Reinforcing Transient Response of Adaptive Control Systems Using Modified Command and Reference Model

Although adaptive control has been explored for various aerospace applications, there exists an inherent tradeoff between the convergence of the tracking error and the robustness by using high-gain learning to improve the transient behavior and operation safety. This paper studies novel strategies to enhance the transient response of model reference adaptive control (MRAC) for nonlinear aircraft systems with unmatched dynamics. We first develop a new compensator containing the undesired transient residual error to modify the external command. This can tune the command signal to be tracked to reshape the closed-loop system dynamics, whilst the original tracking objective is retained. Moreover, to diminish the potential high-frequency oscillations induced by the high-gain learning in the adaptive law, we resort to an error feedback term in the reference model to accelerate the convergence of the tracking error. In this new MRAC framework, a higher learning gain could be used to improve the tracking error convergence without triggering oscillations. We prove the closed-loop system stability, analyze the enhanced transient performance and examplify the robustness of the proposed adaptive control system. Two numerical examples with benchmark aircraft models are used to show the effectiveness of the proposed strategies.

Tracking error-based static friction compensation for a bi-axial CNC machine

Abstract Contour errors usually result from unmatched dynamics, limited axial bandwidth and undesirable nonlinearities. For circular contours, friction, especially static friction, deteriorates the circular contouring accuracy at quadrant positions where there is reversal of velocities or motion from standstill. A two-stage tracking error-based static friction compensation scheme is proposed to compensate for static friction during the transition from the presliding regime to the sliding regime. The compensation consists of two phases, which are implemented sequentially in time. The first is a function of tracking error and the second is a function of tracking error and velocity. The compensation signals are then imposed at the input of the velocity control loop. Experimental results show that the two-stage tracking error-based static friction compensation scheme can effectively improve the circular contouring accuracy at quadrant positions without complicated modeling.

Improving contouring accuracy by tuning gains for a bi-axial CNC machine

Contour errors in continuous-path computer numerical control (CNC) systems usually result from unmatched axial dynamics and undesirable nonlinearities. The errors due to unmatched dynamics can be largely reduced by using a simple controller so as to keep the order of axial dynamics low and by tuning appropriately the proportional gains to match the dynamics. Experimental results show that the resulting matched axial dynamics can, on one hand, effectively eliminate the linear contour errors, and, on the other hand, largely reduce the circular contour errors due to unmatched axial dynamics. On the basis of the matched axial dynamics, circular contours will be made circular with accuracies greatly improved. However, because of limitation in the bandwidths of the axial dynamics, there will be radial contour errors. The radial contour error can be further reduced by a simple approach of feedforward compensation. Experiments conducted show the effectiveness of feedforward compensation in improving circular contouring accuracies.

Sympatric Anadromous-Resident Pairs of Threespine Stickleback Species in Young Lakes and Streams at Bering Glacier, Alaska

1. Resident freshwater and anadromous pairs of threespine stickleback species (Gasterosteus aculeatus species complex) have been reported from only a few lakes. 2. We discovered such pairs in four lakes and four streams, including recently deglaciated terrain, near the Bering Glacier, Alaska. 3. Bering Glacier surges are accompanied and ended by massive glacial outburst floods, which create unmatched dynamics in the surrounding lakes and streams. 4. This is the first report of a stickleback species pair in a proglacial lake (Vitus), which did not exist 100 years ago. 5. These species pairs may have arisen through sympatric speciation from an anadromous ancestor, double invasion of anadromous stickleback, or independent colonization by resident and anadromous forms.

Sliding Surface Design with a D-Scaled H∞ Method

Sliding mode control of linear systems with unmatched uncertainties and disturbances is considered in this paper. A constant input/output scaled H∞ method is used to design a sliding surface which guarantees robust stability of the unmatched dynamics. This results in an asymptotically stable output when the unmatched disturbance is zero and results in a bounded output (the bound is specified by the H∞ norm of an augmented system) when the unmatched disturbance is not zero.