Adaptive finite‐time super‐twisting sliding mode control for robotic manipulators with control backlash

The paper investigates a modified adaptive super-twisting sliding mode control (ASTSMC) for robotic manipulators with input saturation. To avoid singular perturbation while increasing the convergence rate, a modified sliding mode surface (SMS) is developed in this method. Using the proposed SMS, an ASTSMC is developed for robot manipulators, which not only achieves strong robustness but also ensures finite-time convergence. The boundary of lumped uncertainties cannot be easily obtained. A modified adaptive law is developed such that the boundaries of time-varying disturbance and its derivative are not required. Considering input saturation in practical cases, an ASTSMC with saturation compensation is proposed to reduce the effect of input saturation on tracking performances of robot manipulators. The finite-time convergence of the proposed scheme is analyzed. Through comparative simulations against two other sliding mode control schemes, the proposed method has been validated to possess strong adaptability, effectively adjusting control gains; simultaneously, it demonstrates robustness against disturbances and uncertainties.

This paper presents a sliding mode controller for trajectory tracking of robotic manipulators with actuator faults. To achieve finite-time convergence of tracking errors and desirable tracking precision, a fast nonsingular terminal sliding mode controller is designed. The uncertainty caused by actuator faults is transformed into system disturbance which is compensated by introducing the dynamic gain technique. As a result, the prior knowledge about upper bound of system disturbance is not required. Moreover, the sign function is replaced by the saturation function in the control law, so the chattering phenomenon is attenuated. Finally, the designed controller is applied to control a two-link robotic manipulator in simulation, and results validate the effectiveness of the control scheme.

This paper develops a novel non-singular terminal sliding mode control scheme for trajectory tracking of robot manipulators in the presence of external disturbances and uncertainties. Firstly, with the introduction of two nonlinear terms, a newly terminal sliding surface is designed. Then utilizing this sliding surface, a novel non-singular terminal sliding mode controller is proposed to eliminate the reaching interval, singularity issue and subsequently with this controller, the finite time error convergence is also assured. In the proposed controller, radial basis function neural network is employed to approximate highly uncertain nonlinear dynamics of robot manipulators using update laws derived with Lyapunov approach. Meanwhile, the effects of approximation errors are attenuated with $$H_\infty $$ performance criterion by introducing a robust term into the controller. As a result of proposed approach, asymptotic convergence of tracking errors is achieved within finite time and the approximation errors are attenuated to desired levels. The numerical simulation result shows the effectiveness of proposed controller for the case of microbot type robot manipulator.

This paper intends to design and develop an adaptive fuzzy sliding mode controller (SMC) for robotic manipulator. Since it is not viable to pair the SMC operations with the system model every time, this paper adopts a Fuzzy Inference System (FIS) to replace the system model. It effectively achieves the experimentation in two phases. Accordingly, in the first phase, it attains the accurate features of the system model based on varied samples to characterize the robotic manipulator. In the second stage, it represents the derived fuzzy rules based on adaptive fuzzy membership functions. Moreover, it establishes the self-adaptiveness using Grey Wolf Optimization (GWO) to attain the adaptive fuzzy membership functions. The analysis distinguishes the efficiency of the adopted technique with the optimal investigational scheme and the traditional schemes such as SMC, Fuzzy SMC (FSMC) and GWO-SMC. Moreover, the comparative analysis is also performed by including the noise and validates the effectiveness of the proposed and conventional models. Index Terms : Sliding Mode Control, Robot manipulators, Controller, Noise.

Ahstract-This paper introduces a sliding mode control (SMC) strategy for robotic manipulators subject to uncertainties, disturbances, and input and output quantization. A continuous SMC method is proposed and a hysteretic quantizer with sector-bounded quantization errors is utilized to quantize the control input signal. Furthermore, a super-twisting algorithm (STA) based observer is adopted to estimate the unmeasured states by using quantized values of output signals. It is demonstrated that under the proposed SMC, the sliding variable can converge to a quasi sliding mode. Finally, a networked two-link robotic manipulator is used to verify the effectiveness of the proposed control method.

A sliding mode control based on motor angular speed control has been presented for a robot manipulator grasping a payload with mass variation. In order to guarantee the continuity of the control signals applied to the actuators of the robot manipulator, a sliding mode control with integral compensation is adopted. Improvement of robustness of the control system against payload mass variation is obtained by introducing a sliding mode feedforward signal. The control scheme is applied to a three joint robot manipulator, control performance both with payload torque compensation and without payload torque compensation are investigated. Simulation results show that the control scheme presented, is robust against payload mass variation and has satisfactory control performance.

In this paper, radial basis function network (RBFN) with sliding-mode controller (SMC) is designed to the joint position control of two-link robot manipulators for periodic motion and predefined trajectory tracking control. Radial basis function uses curve fitting mode to obtain the nonlinear mapping. The unavoidable learning procedure degrades its transient performance in the existence of disturbance. Sliding-mode control is effective in overcoming uncertainties and has a fast transient response, while the control effort is discontinuous and creates chattering. For this defect, a saturation function is utilized to improve it. The back-propagation (BP) algorithm and Lyapunov stability theorem are used to decide a suitable update law and sliding-mode switch gain, respectively. Thus, the satisfied performance will be obtained, which better than the controller with single RBFN controller, sliding mode controller. The simulated results of a two-link robotic manipulator for the joint frictions, changing link masses and adding external disturbances are provided to show that the effectiveness of the proposed control scheme.

When a permanent magnet synchronous motor runs at low speed, the inverter will output discontinuous current and generate torque ripple; when the motor is runs at high speed, a large amount of stator harmonic current generates, which affects its speed following ability and torque stability. To ensure the fast and smooth switching of a permanent magnet synchronous motor in the full speed domain, this paper proposes the nonsingular terminal sliding mode control of PMSM speed control based on the improved exponential reaching law. Firstly, the improved exponential reaching law is composed of the state variables and power terms of the sliding mode surface functions. The reaching law function is designed in sections to balance the fast dynamic response of the system and chattering control. Secondly, an improved exponential reaching law based on the sliding mode control strategy of the PMSM speed loop is proposed. By designing the initial value of the integral term in the nonsingular terminal sliding mode surface function, the initial state of the system is located on the sliding mode surface. The integral sliding mode surface is used to reduce the system steady-state error, while the proposed sliding mode reaching law is used to increase the arrival speed and suppress system chattering, ultimately affecting modeling error problems, complex working conditions, and uncertainty factors. This paper proposes a sliding mode observer based on an improved exponential reaching law to compensate for the disturbances. Lyapunov stability theory can prove that this system can make the speed tracking error converge to zero in finite time. Hardware-in-the-loop experiments were used to validate the effectiveness of the proposed method.

ABSTRACTIn this article, we give some comments on the article ‘A new terminal sliding mode control for robotic manipulators’. The article presents a new terminal sliding mode control approach for global finite-time tracking of robotic manipulators. We point out a serious error occurred through the article, leading to the ineffectiveness of the proposed approach. A correction is proposed. Comparisons are presented.

In dynamic analysis of constrained multibody systems (MBS), the computer simulation problem essentially reduces to finding a numerical solution to higher-index differential-algebraic equations (DAE). This paper presents a hybrid method composed of multi-input multi-output (MIMO), nonlinear, variable-structure control (VSC) theory and post-stabilization from DAE solution theory for the computer solution of constrained MBS equations. The primary contributions of this paper are: (1) explicit transformation of constrained MBS DAE into a general nonlinear MIMO control problem in canonical form; (2) development of a hybrid numerical method that incorporates benefits of both Sliding Mode Control (SMC) and DAE stabilization methods for the solution of index-2 or index-3 MBS DAE; (3) development of an acceleration-level stabilization method that draws from SMC’s boundary layer dynamics and the DAE literature’s post-stabilization; and (4) presentation of the hybrid numerical method as one way to eliminate chattering commonly found in simulation of SMC systems. The hybrid method presented can be used to simulate constrained MBS systems with either holonomic, nonholonomic, or both types of constraints. In addition, the initial conditions (ICs) may either be consistent or inconsistent. In this paper, MIMO SMC is used to find the control law that will provide two guarantees. First, if the constraints are initially not satisfied (i.e., for inconsistent ICs) the constraints will be driven to satisfaction within finite time using SMC’s stabilization method, urobust,i=−ηisgnsi. Second, once the constraints have been satisfied, the control law, ueq and hybrid stabilization techniques guarantee surface attractiveness and satisfaction for all time. For inconsistent ICs, Hermite-Birkhoff interpolants accurately locate when each surface reaches zero, indicating the transition time from SMC’s stabilization method to those in the DAE literature. [S0022-0434(00)02404-7]

Robotic manipulator is a multi-input multi-output (MIMO), highly nonlinear and coupled system. Controlling this system always has been a challenging task for control engineers. In this paper, sliding mode control (SMC) technique utilizing Proportional and Derivative (PD) surface with different reaching laws has been applied on a two-link planar rigid robotic manipulator. Performance of PD sliding surface has been investigated with three different control laws namely, constant rate, exponential and power rate reaching law. Stability of the studied controller configurations have been demonstrated using Lyapunov theory. One of the major problems in SMC, “chattering” is reduced by introducing boundary layer in the controller. Genetic Algorithm optimization technique is used for tuning of parameters of SMC and boundary layer in all the cases for minimum Integral Absolute Error and chattering. Simulation results revealed that all the investigated laws performed equally for set-point tracking and the constant rate reaching law outperforms the other two laws for noise suppression. Also, all three reaching control laws of SMC offered significantly enhanced trajectory tracking and chattering performance as compared to recent literature.

For the problem of position and force trajectory tracking of flexible joint manipulators whose motion is constrained in the end, a finite-time position/force control strategy is proposed using adaptive terminal sliding mode. Firstly, position control and force control are decoupled according to the coordinate transformation and a reduced dynamic model for the manipulator is obtained. Then a new terminal sliding mode is established and an adaptive position/force control law is designed to overcome the uncertainties of the dynamic model. The system variables can be driven to reach the terminal sliding mode and slide to equilibrium point along the mode in finite time. Unlike previous position/force control strategies, this strategy can make both position and force tracking errors of the manipulator converge to zero in finite time. Simulation results are presented to validate the proposed method.

Many advanced methods proposed for control of robot manipulators are based on the dynamic models of the robot systems. Model-based control design needs a correct dynamic model and precise parameters of the system. Practically speaking, however, every dynamic model has some degrees of incorrectness and every parameter associates with some degrees of identification error. The incorrectness and errors eventually result positioning or trajectory tracking errors, and even cause the system to be unstable. In the past two decades, intensive research activities have been devoted on the design of robust control systems and adaptive control systems for the robot in order to overcome the control system drawback caused by the model errors and uncertain parameters, and a great number of research results have been reported, for example, (Hsia, 1989), (Kou, and Wang, 1989), (Slotine and Li, 1989), ( Spong, 1992), and (Cheah, Liu and Slotine, 2006). However, almost parts of results associate with complicated control system design approaches and difficulties in the control system implementation for industrial robot manipulators. Recently, neural network technology attracts many attentions in the design of robot controllers. It has been pointed out that multi-layered neural network can be used for the approximation of any nonlinear function. Other advantages of the neural networks often cited are parallel distributed structure, and learning ability. They make such the artificial intelligent technology attractive not only in the application areas such as pattern recognition, information and graphics processing, but also in intelligent control of nonlinear and complicated systems such as robot manipulators (Sanger, 1994), (Kim and Lewis, 1999), (Kwan and Lewis, 2000), (Jung and Yim, 2001) (Yu and Wang, 2001). A new field in robot control using neural network technology is beginning to emerge to deal with the issues related to the dynamics in the robot control design. A neural network based dynamics compensation method has been proposed for trajectory control of a robot system (Jung and Hsia, 1996). A combined approach of neural network and sliding mode technology for both feedback linearization and control error compensation has been presented (Barambones and Etxebarria, 2002). Sensitivity of a neural network performance to learning rate in robot control has been investigated (Clark and Mills, 2000). In the following, we present a simple control system consisting of a traditional controller and a neural network controller with parallel structure for trajectory tracking control of 16

To improve the trajectory tracking accuracy of robotic manipulators, an adaptive fast terminal sliding mode control of the robotic arm based on the dynamics feedforward compensation is proposed. The controller consists of two parts: one is a feedforward compensation controller based on the dynamics model for reducing the upper bound value of the uncertainty term, and the other is an adaptive fast terminal sliding mode controller designed based on the Lyapunov method for eliminating the effect of the upper bound of the uncertainty term on the tracking performance, and also for reducing the chattering. The experimental comparison results show that the root mean square error and maximum error of trajectory tracking of our proposed controller are smaller under the working conditions with and without end-effector loads, which can significantly improve the trajectory tracking accuracy of robotic manipulators.

In this study, a proposed three phase quasi Z source inverter (QZSI) using Sliding Mode Control (SMC) method is presented. The two impedance source networks have been implemented to increase the nonlinear of system. These control algorithm and proposed topology have been offered to get fast and dynamic response in robust and stable position even though input voltage, references have been changed. According to the proposed model using SMC method, the design of related inverter has been run and observed the behavior of regarding system during simulation. In power electronics systems have included nonlinear loads such as switches, MOSFETs, diodes etc. These cause to negative effects on performance of related systems. On the other hand, generally both Z source (ZS) and quasi Z source (QZS) topologies are preferred, even if buck-boost inverters are designed. SMC method is one of the most popular control types which has provided to dynamic response in robust and stable position against to nonlinear and unstable changes. During the switching process for all parts of system, control method has overcome unintended output and completed control steps based on design structure. Also, the proposed topology has been simulated at MATLAB/SIMULINK.