Time Delay Estimation Error Research Articles

An Adaptive Sliding Mode Control Using a Novel Adaptive Law Based on Quasi-Convex Functions and Average Sliding Variables for Robot Manipulators

This paper proposes a novel adaptive law that uses a quasi-convex function and a novel sliding variable in an adaptive sliding mode control (ASMC) scheme for robot manipulators. Since the dynamic equations of robot manipulators inevitably include model uncertainties and disturbances, time-delay estimation (TDE) errors occur when using the time-delay control (TDC) approach. Further, the ASMC method used to compensate for TDE errors naturally causes a chattering phenomenon. To improve tracking performance while reducing or maintaining chattering, this paper proposes an adaptive law based on a quasi-convex function that is convex at the origin and concave at the gain switching point, respectively. We also adopt a novel sliding variable that uses previously sampled tracking errors and their time derivatives. Further, this paper proves that the sliding variable of the robot manipulator controlled by the proposed ASMC satisfies uniformly ultimately bounded stability. The simulation and experimental results illustrate the effectiveness of the proposed methods in terms of tracking performance.

Path-following control of an underactuated stratospheric airship with unknown dynamics and external disturbances using time-delay control

In this paper, the path-following problem for an underactuated stratospheric airship with unknown dynamics and external disturbances has been studied. Vector field guidance is employed to fix the underactuated issue and generate desired heading. Time-delay control (TDC) is utilised to track desired states and estimate the model uncertain and disturbances using simple delayed states. To compensate time-delay estimation (TDE) errors, terminal sliding-mode is utilised and combined with TDC. The stability of the proposed controller is provided by using Lyapunov function. A numerical simulation is demonstrated to prove the performance of the proposed control algorithm.

Model-Free RBF Neural Network Intelligent-PID Control Applying Adaptive Robust Term for Quadrotor System

This paper proposes a quadrotor system control scheme using an intelligent–proportional–integral–differential control (I-PID)-based controller augmented with a radial basis neural network (RBF neural network) and the proposed adaptive robust term. The I-PID controller, similar to the widely utilized PID controller in quadrotor systems, demonstrates notable robustness. To enhance this robustness further, the time-delay estimation error was compensated with an RBF neural network. Additionally, an adaptive robust term was proposed to address the shortcomings of the neural network system, thereby constructing a more robust controller. This supplementary control input integrated an adaptation term to address significant signal changes and was amalgamated with a reverse saturation filter to remove unnecessary control input during a steady state. The adaptive law of the proposed controller was designed based on Lyapunov stability to satisfy control system stability. To verify the control system, simulations were conducted on a quadrotor system maneuvering along a spiral path in a disturbed environment. The simulation results demonstrate that the proposed controller achieves high tracking performance across all six axes. Therefore, the controller proposed in this paper can be configured similarly to the previous PID controller and shows satisfactory performance.

A model free adaptive‐robust design for control of robot manipulators: Time delay estimation approach

SummaryThis paper addresses a new robust control scheme for tracking control of the robot manipulators. This algorithm employs time delay estimation (TDE) technique in combination with backstepping control strategy. The suggested control scheme has no dependency on the robot dynamic model and knowing the bound of the inertia matrix is enough to develop this controller. To develop the idea, at first the boundedness of the TDE errors is analyzed by Lyapunov‐Krasovskii approach. Next, the proposed TDE based adaptive backstepping nonsingular terminal sliding mode control (ABNTSMC) algorithm is developed. In this way, a novel adaptive‐robust term is employed to defeat the chattering phenomenon. Moreover, the closed‐loop stability of the system is proven through Lyapunov second approach. Fast transient response, supreme robustness, and chattering‐free as the premier specifications are gained employing the proposed control algorithm. The efficiency of the suggested control scheme is illustrated through some simulations on an industrial robot and the results are compared with some other control algorithms. Finally, the practical effectiveness of the proposed TDE based control algorithm is verified through some experiments on a parallelogram robot manipulator.

Adaptive hybrid-mode assist-as-needed control of upper limb exoskeleton for rehabilitation training

In this paper, a novel adaptive hybrid-mode assist-as-needed (AHMAAN) control algorithm is designed for the exoskeleton-assisted upper limb rehabilitation training. The overall control framework includes an outer control loop to calculate the required interaction force, and an inner control loop to drive the exoskeleton track subject’s motion, and provide specific target interaction force obtained from the outer control loop. In the outer control loop, a hybrid control mode is proposed, which consists of resistive mode and assistive mode. In this regard, a virtual tunnel is firstly established around the defined training task path, and the training mode is switched according to the deviation between the subject’s position and the boundary of the virtual tunnel. Furthermore, for tuning the strength of the resistance or assistance to the subjects with different motor capabilities, two adjustable gain factors are designed, whose values are adaptively adjusted according to the subject’s training performance by using a fuzzy logic. Then, for the inner control loop, a barrier Lyapunov function-based controller is designed to constrain exoskeleton tracking errors within the defined boundary. Meanwhile, time delay estimation (TDE) technology is used to estimate the uncertain terms of the system, and a robust adaption law is developed to compensate TDE error. Experimental tests have been performed on an upper limb exoskeleton with three healthy subjects to evaluate the effectiveness of the developed method. The results show that the proposed control scheme can be effectively applied in a variety of rehabilitation requirements and achieves better training performance than classical hybrid-mode assist-as-needed control method.

X-ray pulsar observation signals simulation method at the spacecraft in near-Earth space

The near-Earth space holds significant strategic value, and X-ray pulsar-based navigation in this region can diversify navigation methods, enhancing the safety and autonomy of spacecraft. Due to the challenges and high costs associated with obtaining actual measurements of pulsars in near-Earth space, the simulation technology for X-ray pulsar signals in this region can provide input for demonstrating the feasibility of technical solutions and experiments related to the application of X-ray pulsar-based navigation in near-Earth space. Therefore, this paper proposes a method for simulating X-ray signals in near-Earth space. Firstly, a scale transforming method is employed to generate a photon arrival time sequence at the spacecraft that includes energy information. Subsequently, the atmospheric transmittance model is utilized for photon selection, obtaining a sequence of photons that have passed through the atmosphere after absorption. Finally, experimental validation of the proposed algorithm is conducted using Crab pulsar data measured by the Insight-HXMT. The similarity between the simulated data and the measured data is evaluated in terms of profiles, phases, and energy spectra. Simulation experiments demonstrate that the time delay estimation error caused by the simulation algorithm is less than 17.17 us. When the observation tangent point altitude is in the range of 160 km to 180 km, the Pearson correlation coefficient of the profiles between simulated and measured data is 73.74 %. The Pearson residuals of the energy spectra are evenly distributed between −0.2 and 0.2, indicating a good level of similarity between the two.

An Improved Adaptive Sliding Mode Control Based on Time-Delay Control for Robot Manipulators

This paper proposes a new adaptive sliding mode control (ASMC) scheme for robot manipulators not only by designing a sliding variable and an adaptive law but also by compensating a time-delay estimation (TDE) error induced by time-delay control (TDC). Based on the operating cycle, because TDC utilizes the previous angular acceleration and input torque for the estimation of the dynamics of the manipulators, TDC produces an inevitable TDE error and this paper compensates the present TDE error by using the previous TDE error. For the ASMC, this paper constructs the sliding variable by additionally utilizing the previous error and its derivative. Also, this paper proposes an adaptive law, which guarantees the positive condition of the adaptive parameter, by using the current adaptive parameter value and the sampling period. For the stability analysis, this paper shows uniformly ultimately bounded (UUB) stability of the sliding variable for the manipulators controlled by the proposed ASMC scheme. The simulation and experimental results present the effectiveness of the proposed control schemes.

Model-free adaptive robust control based on TDE for robot with disturbance and input saturation

AbstractA model-free adaptive robust control based on time delay estimation (TDE) is proposed for robot in the presence of disturbance and input saturation. TDE is utilized to estimate the complicated nonlinear terms of the robot including unknown dynamics and disturbance, and a TDE error observer is developed to estimate the inevitable TDE error. When the input torque of the robot exceeds the upper or lower limit of the input saturation, an auxiliary system and a saturation deviation boundary adaptive law are employed to mitigate the negative impact of input saturation on the position tracking. Finally, the robust control law is obtained by backstepping. The stability of the closed-loop system is proved by Lyapunov functions, and the validity of the proposed method is demonstrated by comparative simulations and experiments. Compared with the model-based controllers and other model-free controllers, the proposed method does not necessitate the accurate dynamic model of the complicated system and with lower computation. Moreover, it can guarantee the desired position tracking performance of the robot even subject to disturbance and input saturation simultaneously.

An Enhanced Adaptive Time Delay Control-Based Integral Sliding Mode for Trajectory Tracking of Robot Manipulators

This article proposes an enhanced adaptive time delay controller (ATDC) for robot manipulators subjected to external disturbances. This approach is model-free and uses time delay estimation (TDE) to estimate complex and unknown robot dynamics. First, to remove the reaching phase and improve the robustness of the control, an integral sliding surface (ISS) is used. Second, to speed up the convergence and compensate for the TDE errors and external disturbances, the gains of time delay control and the sliding mode have been made adaptive. In this article, we clearly point out using the Lyapunov method that the position and velocity tracking errors are guaranteed to be uniformly ultimately bounded (UUB). The effectiveness and the robustness of the designed controller over existing methods are experimentally verified on a parallel Delta robot. The novel model-free proposed control is robust and highly accurate, which is appropriate and recommended for industrial robotic applications.

Fast Finite-Time Path-Following Control for Autonomous Vehicle via Complete Model-Free Approach

Without any knowledge of the vehicle model and its parameters, a novel complete model-free path-following control strategy is developed for autonomous vehicles based on the time-delay estimation (TDE) technique. Different from the existing time-delay control (TDC) approaches, an adaptive nonsingular terminal sliding mode (ANTSM) control law is designed to stabilize the path-following errors without any information of the suitable control gain, which is significant in the conventional TDC scheme, and the boundary of the TDE error, which is necessary for the sliding-mode-based control scheme. The proposed model-free control structure can dynamically update the gain of the designed controller and the boundaries of the TDE error, and the practical finite-time convergence of the preview error can be achieved. In the HIL tests, the comparative results demonstrate that the proposed ANTSM model-free control strategy can provide superior comprehensive tracking performance over both the model-based sliding mode controller and the conventional TDC controller, while the autonomous vehicle follows desired paths.

TDE-Based Adaptive Super-Twisting Multivariable Fast Terminal Slide Mode Control for Cable-Driven Manipulators With Safety Constraint of Error

An adaptive super-twisting multivariable fast terminal sliding mode control scheme based on time delay estimation (TDE) and asymmetric error constraints are proposed to guarantee high-precision trajectory tracking control of cable-driven manipulators under complicated unknown uncertainties. The control system is constrained by joint position errors, which are asymmetric and time-varying. First, the error range of the joints is designed to ensure that the deviation of the joint position from the desired profile is not too large while ensuring the safety performance of the manipulator, and the remaining set-total system dynamics are estimated and compensated using time-delay estimation. Secondly, the design analysis of the angular false expectation using safety constraint functions allows the constraints of different cross sections to be handled in a unified system architecture; the problem of robotic arm motion trajectories with output constraints and uncertainties is addressed through rigorous analysis. The super-twisting adaptive control effectively ensures fast, accurate and robust convergence of the algorithm in satisfying all constraints in operation, and the stability of the closed-loop control system is analyzed using the Lyapunov method. Finally, the effectiveness and superiority of the proposed adaptive hyper-torsional non-singular terminal sliding mode control scheme are verified by simulations and experiments in 2-DOF.

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator

This article proposes a new incremental model predictive control (IMPC) strategy, which allows for constrained control of a robot manipulator, while the resulting incremental model is derived without a concrete mathematical system model. First, to reduce dependence on the nominal model of robot manipulators, the continuous-time nonlinear system model is approximated by an incremental system using the time-delay estimation (TDE). Then, based on the incremental system, the tracking IMPC is designed in the framework of MPC without terminal ingredients. Thus, compared with existing MPC methods, the nominal mathematical model is not required. Moreover, we investigate reachable reference trajectories and confirm the local input-to-state stability (ISS) of IMPC, considering the bounded TDE error as the disturbance of the incremental system. For reachable reference trajectories, the local ISS of IMPC is analyzed using the continuity of the value function, and the cumulative error bound is not overconservative. Finally, several real-time experiments are conducted to verify the effectiveness of IMPC. Experimental results show that the system can achieve optimal control performance while guaranteeing that input and state constraints are not violated.

Model-free robust adaptive control of overhead cranes with finite-time convergence based on time-delay control

In this paper, a model-free robust adaptive control scheme with finite-time convergence based on time-delay control is proposed for anti-sway and positioning control of two-dimensional underactuated overhead cranes. First, the whole overhead cranes system is simplified to an ultra-local model for time delay estimation (TDE). TDE brings a direct and effective model-free property but also an estimation error. Second, a sliding mode disturbance observer is designed to estimate and compensate for the TDE error. Third, sliding mode control (SMC) is used to enhance the robustness of the controller. An adaptive integral sliding surface is then designed to accelerate the sliding surface convergence rate and shorten the convergence time. To further optimize the selection of parameters, the parameter estimation is integrated to enhance the performance of model-free control. In the final analysis of the simulation, data yield that the introduction of parameter estimation increases the control performance by more than 20% on average, and the above facts verify the effectiveness of the scheme. Finally, the stability of the closed-loop control system is analyzed by using Lyapunov stability theory, and the effectiveness and robustness of the control scheme are verified through computer simulation results.

TDE Based Model-free Control for Rigid Robotic Manipulators under Nonlinear Friction

This paper establishes a model-free finite-time tracking control of nonlinear robotic manipulator systems. The proposed controller incorporates both time delay estimation (TDE) and an enhanced terminal sliding mode control (TSMC). The improved TSMC scheme is devised using fractional-order TSMC (FOTSMC) and proportional-integral-derivative (PID) control to obtain robust tracking and high control performance. The TDE is designed to estimate the unknown nonlinear dynamics of robotic manipulators including the Stribeck friction and the external disturbances. Due to Stribeck friction, the effect of TDE error may fail to obtain the desired error performance; thus, another TDE loop is devised to compensate for TDE error generated by non-smooth frictions. The Lyapunov criterion is used to investigate the finite-time stability to analyze the behavior of the designed approach. Finally, computer simulations of the proposed method on PUMA 560 robotic manipulators are performed in contrast with FOTSMC and adaptive fractional-order nonsingular terminal sliding mode control (AFONTSM).

TDE-Based Adaptive Integral Sliding Mode Control of Space Manipulator for Space-Debris Active Removal

The safe and dependable removal of large-scale space debris has been a long-standing challenge that is critical to the safety of spacecraft and astronauts. In the process of capturing and deorbiting space debris, the space manipulator must achieve extremely high control and precision. However, strong couplings, model uncertainties, and various inevitable unknown disturbances cause many difficulties in coordinated control of the space manipulator. To solve this challenge, this study examines the stabilization control of a space manipulator after capturing non-cooperative large-scale space debris and presents an adaptive integral sliding mode control (AISMC) scheme with time-delay estimation (TDE). The coupling term and lumped uncertainty are estimated by TDE technology, which eliminates the requirement of prior knowledge. Adaptive sliding mode control (ASMC) is used as desired injecting dynamics to compensate TDE errors, and a PID-type integral sliding mode surface is designed to reduce steady-state errors. The Lyapunov criterion is used to prove the global stability of the controller. Simulation results show that the controller has high tracking accuracy and strong robustness.

Model‐free incremental adaptive dynamic programming based approximate robust optimal regulation

AbstractThis article presents a new formulation for model‐free robust optimal regulation of continuous‐time nonlinear systems. The proposed reinforcement learning based approach, referred to as incremental adaptive dynamic programming (IADP), utilizes measured input‐state data to allow the design of the approximate optimal incremental control strategy, stabilizing the controlled system incrementally under model uncertainties, environmental disturbances, and input saturation. By leveraging the time delay estimation (TDE) technique, we first use sensor data to reduce the requirement of a complete dynamics, where input‐state data is adopted to construct an incremental dynamics which reflects the system evolution in an incremental form. Then, the resulting incremental dynamics serves to design the approximate optimal incremental control strategy based on adaptive dynamic programming, which is implemented as a simplified single critic structure to get the approximate solution to the value function of the Hamilton–Jacobi–Bellman equation. Furthermore, for the critic neural network, experience data are used to design an off‐policy weight update law with guaranteed weight convergence. Rather importantly, we incorporate a TDE error bound related term into the cost function, whereby the unintentionally introduced TDE error is attenuated during the optimization process. The proofs of system stability and weight convergence are provided. Numerical simulations are conducted to validate the effectiveness and superiority of our proposed IADP, especially regarding the reduced control energy expenditure and the enhanced robustness.

Simultaneous Fault and Input Time Delay Estimation for an Actuator System: Theory and Flight Data Validation

This letter proposes a first order sliding mode observer for the purpose of simultaneously estimating the unknown input time delay and reconstructing the loss of effectiveness in a model of an actuator. The adaptive algorithm is driven by the `equivalent output error injection' signal associated with the sliding motion. Sufficient conditions are given to ensure finite time convergence of the state estimation error system, ensuring both the time delay estimation error and the estimation error associated with the actuator fault converge to a small region around zero. The efficacy of the approach has been evaluated via both a numerical simulation and flight data validation.

Adaptive incremental sliding mode control for a robot manipulator

An adaptive incremental sliding mode control (AISMC) scheme for a robot manipulator is presented in this paper. Firstly, an incremental backstepping (IBS) controller is designed using time-delay estimation (TDE) to reduce dependence on the mathematical model. After substituting IBS controller into the nonlinear system, a linear system w.r.t. tracking errors is obtained while TDE error is the disturbance. Then, the AISMC scheme, including a nominal controller and an SMC, is developed for the resulted linear system to improve control performance. According to the equivalent control method, the SMC in the AISMC scheme is to handle TDE error. To receive optimal control performance at the sliding manifold, an LQR controller is selected as the nominal controller. The SMC is designed based on positive semi-definite barrier function (PSDBF) since it prevents switching gains from being over/under-estimated, and two practical problems are addressed in this paper: A new PSDBF is designed and conservative (large) setting bounds affecting tracking precision and/or system stability are avoided; An improved PSDBF based SMC is developed where the PSDBF and an adaptive parameter are used simultaneously to regulate switching gains, and the system is still stable when sliding variable occasionally exceeds the predefined vicinity. Moreover, finite-time convergence property of the sliding variable is strictly analyzed. Finally, real-time experiments are conducted to verify the effectiveness of the proposed control method.

Adaptive sliding mode control of modular self-reconfigurable spacecraft with time-delay estimation

The reconstruction control of modular self-reconfigurable spacecraft (MSRS) is addressed using an adaptive sliding mode control (ASMC) scheme based on time-delay estimation (TDE) technology. In contrast to the ground, the base of the MSRS is floating when assembled in orbit, resulting in a strong dynamic coupling effect. A TED-based ASMC technique with exponential reaching law is designed to achieve high-precision coordinated control between the spacecraft base and the robotic arm. TDE technology is used by the controller to compensate for coupling terms and uncertainties, while ASMC can augment and improve TDE’s robustness. To suppress TDE errors and eliminate chattering, a new adaptive law is created to modify gain parameters online, ensuring quick dynamic response and high tracking accuracy. The Lyapunov approach shows that the tracking errors are uniformly ultimately bounded (UUB). Finally, the on-orbit assembly process of MSRS is simulated to validate the efficacy of the proposed control scheme. The simulation results show that the proposed control method can accurately complete the target module’s on-orbit assembly, with minimal perturbations to the spacecraft’s attitude. Meanwhile, it has a high level of robustness and can effectively eliminate chattering.