The application of a optimal controller for the flexible joint robot

This paper presents modeling and sophisticated control of a single Degree Of Freedom (DOF) flexible robotic arm. The derived model is based on Euler-Lagrange approach while the first and second order (super twisting) Sliding Mode Control (SMC) is proposed as a non-linear control strategy. The control laws are subjected to various test inputs including step and sinusoids to demonstrate their tracking efficiency by observing transient and steady state behaviours. Both orders of SMC are then compared to characterize the control performance in terms of robustness, handling external disturbances and chattering. Results dictate that the super twisting SMC is more accurate and robust against the external noise and chattering phenomena compared to the first order SMC.

This paper “describes” the investigation of the stability of a single Degree of Freedom (DOF) flexible robotic arm by the diagrams shown below. The derived model is based on Euler- Lagrange approach. Exploration of a flexible robotic arm with using state-of-the-art controllers is essential for intelligent applications. These robot arms have joints that work independently of each other in order to create a smooth connection between joints. They still ensures the natural properties like a real human arm. The use of polarity assignment method “helps” the system to achieve desired output signals which has not been thoroughtly studied before for this system. The author can also compare the effectiveness of control methods for this system to find the most effective method for control strategies. In particular, ANN ( artificial neural network) is the most modern technique currently applied to this system to investigate the security and stability of the system through this program. This is new and it has never been used before for a system of this type. Neural networks strategy has been implemented in this paper as an application of artificial intelligence. It has successfully performed a mission in re-simulating functions of another control method: Polarity assignment method. Simulation results are done by Matlab.

In this study, a high-order sliding mode controller (HOSMC) is designed for the control of a one degree-of-freedom (DOF) flexible link space robotic arm with payload. The high order sliding mode based controller is developed, which exploit the robustness properties of sliding-mode controllers (SMCs), while also increasing accuracy by reducing chattering effects. Ever increasing demand for high-speed performance and low energy consumption of space robotic systems require low-mass designs. This restriction puts a limitation on the degree of rigidity of space robot manipulators. These manipulators may posses' significant flexibility that needs to be taken consideration in the design of the control systems. Space robot manipulators have highly nonlinear and coupled dynamics. Flexible space robot arms have structural flexibilities and resulting high number of passive degrees-of-freedom. Therefore, the control of such flexible systems has significant challenges due to the highly nonlinear structure. The high performance control of a flexible link space robotic arm requires the full system dynamic structural flexibilities become of increased importance particularly when high speed, high accuracy operation of lightweight structures is aimed. In this study, a high-order sliding mode controller (HOSMC) is designed for the control of a one degree-of-freedom (DOF) flexible link space robotic arm with payload. The high-order sliding mode based controller is developed, which exploit the robustness properties of sliding-mode controllers (SMCs), while also increasing accuracy by reducing chattering effects. In most related literature, the full system dynamic structural flexibilities effects are neglected to avoid increased computational complexity at the expense of compromising the tracking accuracy of the system in the transient and steady-state. As a solution to the problem, in this study, the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order HOSM (2-HOSM) control law is derived by including the structural flexibilities into the control design process. 2-HOSM controller is designed to achieve set-point positioning control. The performance of the designed control method is tested for the precise positioning of a space robotic arm under heavy uncertainties and external disturbances has been evaluated in real-time on an experimental setup. The proposed control method is applied for the set-point control and trajectory control of the system and has resulted in an improved precision and overall performance as demonstrated by experimental results. The improved accuracy obtained 2-HOSMC motivates the implementation of the schemes for demanding control applications under heavy uncertainties.

Conventional robot manipulators have singularities in their workspaces and constrained spatial movements. Flexible and soft robots provide a unique solution to overcome this limitation. Flexible robot arms have biologically inspired characteristics as flexible limbs and redundant degrees of freedom. From these special characteristics, flexible manipulators are able to develop abilities such as bend, stretch and adjusting stiffness to traverse a complex maze. Many researchers are working to improve capabilities of flexible arms by improving the number of degrees of freedoms and their methodologies. The proposed flexible robot arm is composed of multiple sections and each section contains three similar segments and a base segment. These segments act as the backbone of the basic structure and each section can be controlled by changing the length of three control wires. These control wires pass through each segment and are held in place by springs. This design provides each segment with 2 DOF. The proposed system single section can be bent 90° with respective to its centre axis. Kinematics of the flexible robot is derived with respect to the base segment.

The purpose of this study is to control simultaneously, motion and vibration of flexible 2-link robot arms. For this purpose, we had used modeling method called an 'extended reduced-order physical model (extended model)' to make a model of one-link flexible robot arm. The model of the flexible 2-link robot arms is made of a combination of the model of each link that is regarded as one link flexible robot arm. To connect each link, the constraint addition method is used. This is creating method of an equation of motion in multi-body systems. It is verified that the results of the simulation are effective for control of flexible 2-link robot arms.

Abstract: This paper studied the problems of trajectory tracking and vibration suppression of the end for single-linked flexible arm. The dynamic model of the flexible manipulator is established by the Lagrange method and assumed mode method, and then, we decomposed the model into a double time scale model, which is fast and slow based on singular perturbation theory. We design the controller for the two models separately. As to the slow time scale model, we created a controller with adaptive robust sliding mode, and for the fast one, we designed a controller based on Linear- Quadratic Form (which is LQR). By improving particle swarm optimization, the weight matrix Q in the LQR was optimized independently. Combining the control rate of the fast and the slow, tracked the flexible arm’s trajectory and suppressed its terminal vibration at the same time. The simulating results show that the proposed method greatly improves the trajectory tracking accuracy of flexible manipulator, and reduces the end vibration effectively. Background: Since flexible robotic arms generate free vibration during operation due to the special characteristics of the material, vibration suppression and control are the primary problems in this field. objective: The research objective of this paper is to design an improved controller for a single link flexible robotic arm system that utilises a new control method to achieve more accurate tracking accuracy and less end vibration during the movement of the robotic arm. Objective: The research objective of this paper is to design an improved controller for a single-link flexible robotic arm system that utilizes a new control method to achieve more accurate tracking accuracy and less end vibration during the movement of the robotic arm. Methods: An adaptive robust sliding mode controller is designed for the slow time scale model, a linear quadratic (LQR) controller is designed for the fast time scale model, and the weight matrix Q in the LQR is autonomously optimised by an improved particle swarm algorithm, which combines the control rates of the two to control the trajectory tracking of the flexible robotic arm while suppressing the end vibration. Results: Experimental and comparative studies show that the method proposed in this paper substantially improves the trajectory tracking accuracy of the flexible robotic arm and reduces the end vibration to a large extent with obvious advantages, which verifies the reasonableness of the improved controller. Conclusion: The method proposed in this paper has more prominent advantages in trajectory tracking of flexible robotic arms, which is reflected in its smaller trajectory tracking error and relatively shorter time to track the target curve. At the same time, the search speed and convergence accuracy of the optimal value are improved to make the end vibration smaller, which largely reduces the end vibration of the flexible robotic arm and reduces the mechanical fatigue damage of the flexible robotic arm, which is of great significance for the research and development in this field.

This article presents an original motion control strategy for robot manipulators based on the coupling of the inverse dynamics method with the so-called second-order sliding mode control approach. Using this method, in principle, all the coupling non-linearities in the dynamical model of the manipulator are compensated, transforming the multi-input non-linear system into a linear and decoupled one. Actually, since the inverse dynamics relies on an identified model, some residual uncertain terms remain and perturb the linear and decoupled system. This motivates the use of a robust control design approach to complete the control scheme. In this article the sliding mode control methodology is adopted. Sliding mode control has many appreciable features, such as design simplicity and robustness versus a wide class of uncertainties and disturbances. Yet conventional sliding mode control seems inappropriate to be applied in robotics since it can generate the so-called chattering effect, which can be destructive for the controlled robot. In this article, this problem is suitably circumvented by designing a second-order sliding mode controller capable of generating a continuous control law making the proposed sliding mode controller actually applicable to industrial robots. To build the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified relying on a practical MIMO identification procedure recently devised. The proposed inverse dynamics-based second-order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.

This paper presents design and practical implementation of robust super twisting type Second Order Sliding Mode (SOSM) controller for an under actuated 2-DOF flexible link manipulator system. The flexible link system resembles to a robotic arm having two flexible links governed by two DC motors. The mathematical model of the system is derived using Euler-Lagrange formula. A goal of Super Twisting (ST) controller is to regulate the position of both arms simultaneously having coupling effect. The STA of SOSMC attenuate the chattering effect that predominates in the classical sliding mode controller. The efficacy of the controller is checked in both simulation as well experimentally. The simulation is carried out using MATLAB R2016. The experiment is carried out on a laboratory setup using QUARC software (for hardware interfacing) and MATLAB R2016. The simulation as well experimental results are compared with conventional LQR controller and classical f-order sliding mode controller. The results endows that the 2-order SMC controller outperforms the other controllers.

The integration of renewable energy sources (RESs) at the edge of the grid plays a contributory role in advancing the transition to a sustainable energy future. However, this transition introduces significant variability, which challenges the maintenance of frequency stability in power systems. To address the impacts of RES variability, various robust control strategies have been developed. This paper compares the performance of different advanced sliding mode control (SMC) approaches, i.e., super twisting (ST) algorithm‐based second order sliding mode control (STSOSMC), second order sliding mode control (SOSMC), double integral sliding mode control (DISMC) and integral sliding mode control (ISMC) with conventional sliding mode control (SMC) for load frequency control with stochastic RESs such as biogas generators (BG) and wind‐based doubly fed induction generators (DFIG). The impact of the advanced sliding mode controllers on the voltage and rotor angle stability of the system is also explored. The efficacy of the controllers is tested under different load disturbances, considering nonlinearities such as communication delay (CD), sensor inaccuracy (SI), governor dead band (GDB), and generation rate constraint (GRC). The results demonstrate that STSOSMC achieves superior frequency regulation with minimal chattering and outperforms other controllers in terms of settling time, overshooting, and undershooting in frequency deviation. The result also demonstrates the effectiveness of STSOSMC in managing the variability and disturbances of RESs. Therefore, it could be considered the most robust control mechanism from the edge of the grid system with high penetration of RESs.

Structural flexibility in robotic systems has been emerging as an issue of increasing concern, for it is only realistic to include the vibration of such a system in the design of control to secure a certain degree of accuracy. The demands for high speed and low cost are driving the research for control of lightweight flexible robots. In this paper, we first formulate a mathematical model for flexible robot arms. This model describes a one-dimensional vibrating robot arm with a moving base. In general, a Cartesian robot consists of components which are flexible robot arms. There have been many investigations of the subject. Amongst them we list a few, such as works of Cannon and Schmitz [1] in 1984 and more recent work of Z.H. Luo, etc. [6,7,8]. Many of these works approach the subject from the design points of view. They have specific “goal items” to be controlled and designed controls accordingly. Our approach is more theoretical and general. First, we take a fourth order partial differential equation, the beam equation, to model the dynamics of the Cartesian flexible robot arm with several boundary conditions. Then, we consider a corresponding state-space control system in which the parameter matrix has its entries differential operators. In this setting we are able to determine the spectrum of the parameter matrix (see Section 2), and subsequently show that the system is both controllable and observable (see Section 3). In this infinite dimensional control analysis, one needs a heavy dose of functional analysis and operator theory in order to investigate the controllability and observability. This work has laid down a foundation for the design of a real-time closed loop feedback control for a flexible Cartesian robot. It is becoming more urgent that the traditional design of robot arms dependent on only the kinematics needs a makeover to include the dynamics of the system into the control. Our work fits nicely in this thrust of research which is becoming the focus of the research of dynamical robotics. The results of this article are taken from [4]. Further work is presently being pursued.

The objective of this paper is to verify the effectiveness of the control method and sensitivity analysis by experiments which were described in the previous paper. Here, a two-link flexible robotic arm with three degrees of freedom is employed in experimental equipment, and force sensors and encoders are employed as sensors. In particular the force sensor is used to suppress the vibrations of the flexible arm. First, it is shown that the residual vibrations in positioning control can be suppressed by the state feedback control method with optimal gains. Second, it is shown that the closed-loop system by using the optimal control theory becomes unstable when parameter's uncertainties such as the second arm's length or payload weight are included. Thus the allowance of parameter variations given by this paper is verified by both simulated and experimental studies.

Practical second order sliding modes in single-loop networked control of nonlinear systems

Modelling errors and robust stabilization/tracking problems under parameter and model uncertainties complicate the control of the flexible underactuated systems. Chattering-free sliding-mode-based input-output control law realizes robustness against the structured and unstructured uncertainties in the system dynamics and avoids the excitation of unmodeled dynamics. The main purpose of this paper was to propose a robust adaptive solution for stabilizing and tracking direct-drive (DD) flexible robot arms under parameter and model uncertainties, as well as external disturbances. A lightweight robot arm subject to external and internal dynamic effects was taken into consideration. The challenges were compensating actuator dynamics with the inverter switching effects and torque ripples, stabilizing the zero dynamics under parameter/model uncertainties and disturbances while precisely tracking the predefined reference position. The precise control of this kind of system demands an accurate system model and knowledge of all sources that excite unmodeled dynamics. For this purpose, equations of motion for a flexible robot arm were derived and formulated for the large motion via Lagrange’s method. The goals were determined to achieve high-speed, precise position control, and satisfied accuracy by compensating the unwanted torque ripple and friction that degrades performance through an adaptive robust control approach. The actuator dynamics and their effect on the torque output were investigated due to the transmitted torque to the load side. The high-performance goals, precision and robustness issues, and stability concerns were satisfied by using robust-adaptive input-output linearization-based control law combining chattering-free sliding mode control (SMC) while avoiding the excitation of unmodeled dynamics. The following highlights are covered: A 2-DOF flexible robot arm considering actuator dynamics was modelled; the theoretical implication of the chattering-free sliding mode-adaptive linearizing algorithm, which ensures robust stabilization and precise tracking control, was designed based on the full system model including actuator dynamics with computer simulations. Stability analysis of the zero dynamics originated from the Lyapunov theorem was performed. The conceptual design necessity of nonlinear observers for the estimation of immeasurable variables and parameters required for the control algorithms was emphasized.

The Doubly Fed Induction Generator (DFIG) in wind system is linked to the power-grid, which is vulnerable to significant grid failures. Because of the DFIG’s sensitivity to disturbances in the grid, designing of the controller is considered. In this article, the Feed-Forward Neuro-Second Order Sliding Mode (FFN-SOSM) controller and the Second Order Sliding Mode (SOSM) controller are compared for the Low Voltage Ride Through (LVRT) enhancement under voltage sag situation. Convergence in the sliding surface control is assisted by the use of higher-order switching functions in the FFN-SOSM. Importantly, controller benefits are such that reduction in chattering effect and minimized settling time for the system’s parameters as a result in the implementation of the FFN-SOSM method. With the assistance of MATLAB/SIMULINK, a comparison is made between the performances of the FFN-SOSM controller and those of SOSM controller, which is described in the existed research. The results of the simulation indicate that the "FFN-SOSM controller improved the LVRT capability of the DFIG-Wind Turbine (WT) system" when it is functioning under dynamic conditions.

This paper discusses the open loop control problem of a flexible joint robot that is oriented in the vertical plane. This orientation of the robot arm introduces gravity constraints and imposes undesirable nonlinear behavior. Friction is also added at the joints to increase the accuracy of the model. Including these dynamics to the robot arm amplifies the open loop control problem. Differential flatness is used to propose a feed-forward control that compensates for these nonlinearities and is able to smoothly steer the robot from rest to rest positions. The proposed control is achieved without solving any differential equations which makes the approach computationally attractive. Simulations show the effectiveness of the open loop control design on a single link flexible joint robot arm.