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Sliding Mode Controller Design for Flexible Joint Robot
... The method was evaluated on a flexible joint manipulator, demonstrating effectiveness under uncertainty. Gorial [2] employed sliding mode control (SMC) on a flexible joint robot actuated by a direct current (DC) motor model. Wajdi et al. [3] proposed SMC for handling matched and mismatched uncertainties along with external disturbances in suspension dynamics. ...
This study introduces a novel robust optimal control design for a flexible joint robot manipulator. The proposed control design combines robust optimal control (ROC) and robust optimal integral sliding mode control (ROISMC), transforming the robust control problem into an optimal control problem for both matched and mismatched unknown functions, as demonstrated through the Lyapunov function. The validity of both schemes is established through comparison with the desired results of flexible joint angle and rotor joint angle and velocity. It is found that their results are accurately alignment with the desired trajectory, even in the presence of mismatched functions.
... At present, scholars from various countries have accumulated a great deal of research experience in dealing with the flexibility of space robot arms [11]; they have also achieved certain results in the control and vibration suppression problems of flexible jointed robots [12]; they have also obtained stage results in dealing with the influence of the flexibility of a certain two types of components in the existence of bases, arms and joints of space robots [13]. Li et al. [14] discussed collision motion control of a flexible two-armed space robot capturing a rotating object. ...
The dynamic modeling, motion control and flexible vibration active suppression of space robot under the influence of flexible base, flexible link and flexible joint are explored, and motion and vibration integrated fixed-time sliding mode control of fully flexible system is designed. The flexibility of the base and joints are equivalent to the vibration effect of linear springs and torsion springs. The flexible links are regarded as Euler–Bernoulli simply supported beams, which are analyzed by the hypothetical mode method, and the dynamic model of the fully flexible space robot is established by using the Lagrange equation. Then, the singular perturbation theory is used to decompose the model into slow subsystem including rigid motion and the link flexible vibrations, and fast subsystems including the base and the joint flexible vibrations. A fixed time sliding mode control based on hybrid trajectory is designed for the slow subsystem to ensure that the base and joints track the desired trajectory in a limited time while achieving vibration suppression on the flexible links. For the fast subsystem, linear quadratic optimal control is used to suppress the flexible vibration of the base and joints. The simulation results show that the controller proposed in the paper can make the system state converge within a fixed time, is robust to model uncertainty and external interference, and can effectively suppress the flexible vibration of the base, links, and joints.
... The slender link easily causes vibrations at the end effector [8]. The flexible driver causes asynchrony between the rotation angle of the motor rotor and the actual rotation angle of the joint, resulting in joint vibration [9]. Therefore, it is of practical significance to consider the flexibility of the base, joints and links of the space robot. ...
During the process of satellite capture by a flexible base–link–joint space robot, the base, joints, and links vibrate easily and also rotate in a disorderly manner owing to the impact torque. To address this problem, a repetitive learning sliding mode stabilization control is proposed to stabilize the system. First, the dynamic models of the fully flexible space robot and the captured satellite are established, respectively, and the impact effect is calculated according to the motion and force transfer relationships. Based on this, a dynamic model of the system after capturing is established. Subsequently, the system is decomposed into slow and fast subsystems using the singular perturbation theory. To ensure that the base attitude and the joints of the slow subsystem reach the desired trajectories, link vibrations are suppressed simultaneously, and a repetitive learning sliding mode controller based on the concept of the virtual force is designed. Moreover, a multilinear optimal controller is proposed for the fast subsystem to suppress the vibration of the base and joints. Two sub-controllers constitute the repetitive learning sliding mode stabilization control for the system. This ensures that the base attitude and joints of the system reach the desired trajectories in a limited time after capturing, obtain better control quality, and suppress the multiple flexible vibrations of the base, links and joints. Finally, the simulation results verify the effectiveness of the designed control strategy.
Appl ying automatic control on gantry cranes to move loads with minimal sway angle is considered as a challenge due to the crane system uncertain parameters and a robust automatic control is needed. In this paper a sliding mode controller is applied to overcome the crane system uncertainties and achieve the desired performance. Some labor is spent to transform the system to the regular form and an error function is written depending on the transformed variables then a switching function in terms of the error function is constructed and a sliding mode controller is designed to make the error function reach zero so the crane moves to the specified displacement with minimum sway angle. Stability analyses are provided to show that the system is stable under the control we proposed. Simulations are held by software to validate the effectiveness of our work and prove that the proposed control is successful in giving our system the preferred behavior then Results are discussed and some point view is to be put.
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 addresses the design of a robust Lyapunov-based controller for flexible-joint electrically driven robots considering to voltage as control input. The proposed approach is related to the key role of electrical subsystem of the motors, thus is free from mechanical subsystem of the actuator dynamics, considered here as unmodeled dynamics. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear actuated robot dynamics and the proposed controller is BIBO stable, while actuator/link position errors are uniformly ultimately bounded stable in agreement with Lyapunov’s direct method in any finite region of the state space. It also forms a constructive and conservative algorithm for suitable choice of gains in PID controller. The analytical studies as well as experimental results produced using MATLAB/SIMULINK external mode control on a flexible-joint electrically driven robot demonstrate high performance of the proposed control schemes.
Electromechanical systems (EMS) may be considered as devices transforming electrical into mechanical energy. Every system that belongs to the electromechanical class can be decomposed in an electrical (ES) and a mechanical subsystem (MS). The motion control systems can be quite complicated because many different factors have to be considered in the design of electromechanical systems. These factors can be summarized as the nonlinearity, non-smoothness in its model, the uncertainty in system model parameters and non-satisfying matching condition.
In this paper a new sliding mode control design approach for the EMS is proposed without neglecting the inductance in the electrical part or approximating the non-smooth perturbation. The first step in the proposed controller design consists of transforming the ES to a low pass filter (LPF) and then (the second step) designing a sliding mode controller (SMC) to the MS that will reject system model uncertainty and the effect of non-smooth disturbances. With a suitable selected LPF time constant, the SMC which controls the MS is nearly the equivalent control and as a result the chattering is attenuated greater than that in the case of classical SMC which designed by ignoring the electrical subsystem and also with a smaller control effort. The simulation results, of applying the proposed sliding mode control to an electromechanical system, show its superiority compared with classical SMC designed in two effective SMC features beside forcing the state to follow the desired position where chattering amplitude is greatly reduced with a significant reduction in control action value (approximately equal to third the required input voltage with the classical SMC).
This paper concerns the dynamic modeling and vibration control of a space two-link flexible manipulator. Two types of PZT actuators, PZT shear actuator and torsional actuator, are used to suppress the bending-torsional-coupled vibration of the space manipulator. Using extended Hamilton’s principle and the finite element method, equations of motion of the space flexible manipulator with PZT actuators and tip mass are obtained. Based on modal analyze theory, the state space model of the system is then used to design the control system. A linear quadratic regulator (LQR) controller is designed to achieve vibration suppression of the space manipulator system. From the numerical results, we can get that the proposed controller has a suitable and efficient performance suppressing the bending-torsional-coupled vibration of the space two-link flexible manipulator.
Lowering the emission, fuel economy and torque management are the essential
requirements in the recent development in the automobile industry. The main engine control
input that satisfies the above requirements is the throttling angle which adjusts the air mass
flow rate to the engine port. Due to the uncertainty and the presence of the nonlinear
components in its dynamical model, the sliding mode control theory is utilized in this work
for the throttle valve angle control system to design a robust controller for this system in the
presence of a nonlinear spring and Coulomb friction. A continuous sliding mode control law
which consists of a saturation function, instead of a signum function, and the integral of
another saturation function is used in this work. This choice for the control structure will
prevent the chattering to occurs but with a certain steady state error. On the other hand, the
addition of the integral term will effectively reduce the steady state error according to the
choice of its parameters. The simulations result for typical references of the opining throttle
angle demonstrate the effectiveness of the proposed controller, especially after the addition of
a nonlinear integral term.
This article proposes a sliding mode control for electromechanical systems, for instance a DC motor with an inverted pendulum as load is considered. In contrast to conventional cascade control structures not only the variables of the mechanical system but also the electrical variables are part of the control law and voltage is used as discontinuous control input. The new control approach offers better performance, minimial implementation complexity, provides robustness, and a decrease of power consumption. The performance of the presented approach is demonstrated via numerical simulations and a real experiment.
We consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state-dependent drift and input matrix. The general case of both, matched and unmatched disturbances affecting the system is addressed. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms, which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified. A simulation of the proposed technique, applied to a dynamically feedback linearized unicycle, illustrates its effectiveness, even in presence of nonholonomic constraints.
The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H∞ is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination.
This paper reports preliminary experiments with a new robot system designed to cooperatively extend a human's ability to perform fine manipulation tasks requiring human judgement, sensory integration and hand-eye coordination. A recently completed steady-hand robot is reported. A stable force control law is reviewed. Preliminary experiments validate theoretical predictions of stable one-dimensional control of tool-tip forces in contact with both linearly and nonlinearly compliant objects. Preliminary feasibility experiments demonstrate stable one-dimensional robotic augmentation and "force scaling" of a human operator's tactile input.
Apply Sliding Mode Theory to Solve Control Problems
Interest in SMC has grown rapidly since the first edition of this book was published. This second edition includes new results that have been achieved in SMC throughout the past decade relating to both control design methodology and applications.
In that time, Sliding Mode Control (SMC) has continued to gain increasing importance as a universal design tool for the robust control of linear and nonlinear electro-mechanical systems. Its strengths result from its simple, flexible, and highly cost-effective approach to design and implementation. Most importantly, SMC promotes inherent order reduction and allows for the direct incorporation of robustness against system uncertainties and disturbances. These qualities lead to dramatic improvements in stability and help enable the design of high-performance control systems at low cost.
Written by three of the most respected experts in the field, including one of its originators, this updated edition of Sliding Mode Control in Electro-Mechanical Systems reflects developments in the field over the past decade. It builds on the solid fundamentals presented in the first edition to promote a deeper understanding of the conventional SMC methodology, and it examines new design principles in order to broaden the application potential of SMC.
SMC is particularly useful for the design of electromechanical systems because of its discontinuous structure. In fact, where the hardware of many electromechanical systems (such as electric motors) prescribes discontinuous inputs, SMC becomes the natural choice for direct implementation. This book provides a unique combination of theory, implementation issues, and examples of real-life applications reflective of the authors’ own industry-leading work in the development of robotics, automobiles, and other technological breakthroughs.
Among numerous torque-based control strategies proposed for flexible joint robot manipulators in the literature, a basic incorrect assumption is that torque can be exerted to manipulator link directly; so the actuator dynamics is not taken into account. In this paper a voltage-based technique for control of flexible joint robot manipulator actuated by brushed DC motor is proposed. The backstepping method is applied to cope with the difficulty introduced by the cascade structure and to find the control law to accomplish stabilization and tracking a desired trajectory. The suggested controller does not need the measurements of acceleration and jerk for feedback which are difficult to be measured. Simulation results are presented for a single link flexible-joint robot actuated by brushed DC motor to show the effectiveness of the designed controller in stabilization and trajectory tracking in presence of external disturbances.
Nonlinear equations of motion are developed for flexible manipulator arms consisting of rotary joints that connect pairs of flexible links. Kinematics of both the rotary-joint mo tion and the link deformation are described by 4 X 4 trans formation matrices. The link deflection is assumed small so that the link transformation can be composed of summations of assumed link shapes. The resulting equations are pre sented as scalar and 4 X 4 matrix operations ready for pro gramming. The efficiency of this formulation is compared to rigid-link cases reported in the literature.
This paper is concerned with mathematical modeling and optimal motion designing of flexible mobile manipulators. The system is composed of a multiple flexible links and flexible revolute joints manipulator mounted on a mobile platform. First, analyzing on kinematics and dynamics of the model is carried out then; open-loop optimal control approach is presented for optimal motion designing of the system. The problem is known to be complex since combined motion of the base and manipulator, non-holonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of the flexible nature of both links and joints are taken into account. In the proposed method, the generalized coordinates and additional kinematic constraints are selected in such a way that the base motion coordination along the predefined path is guaranteed while the optimal motion trajectory of the end-effector is generated. This method by using Pontryagin’s minimum principle and deriving the optimality conditions converts the optimal control problem into a two point boundary value problem. A comparative assessment of the dynamic model is validated through computer simulations, and then additional simulations are done for trajectory planning of a two-link flexible mobile manipulator to demonstrate effectiveness and capability of the proposed approach.
This article addresses the motion tracking control for a class of flexible-joint robotic manipulators actuated by brushed direct current motors. This class of electrically driven flexible-joint robots is perturbed by time-varying parametric uncertainties and external disturbances. A novel observer-based robust dynamic feedback tracking controller without velocity measurements will be developed such that the resulting closed-loop system is locally stable, all the states and signals are bounded and the trajectory tracking errors can be made as small as possible. Only the measurements of link position and armature current are required for feedback and so the number of sensors in the practical implementation of the developed control scheme can be greatly reduced. The observer structure is of reduced order in the sense that the observer is constructed only to estimate the velocity signals and whose dimension is half of the dimension of flexible-joint robots. Especially, for the set-point regulation problem, the developed controller is simplified to a linear time-invariant controller. Consequently, the robust tracking control scheme developed in this study can be extended to handle a broader class of uncertain electrically driven flexible-joint robots and the developed robust control schemes possess the properties of computational simplicity and easy implementation. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control algorithms.
This project takes place in the EFDA Remote Handling (RH) activities for the fusion reactor International Thermonuclear Experimental Reactor (ITER). The aim of the R&D program is to demonstrate the feasibility of in-vessel RH intervention by a long reach, limited payload manipulator which penetrates the first wall using the six IVVS penetrations. Potential activities for this device include close inspection of the plasma facing surfaces and leak detection. The work includes the design, manufacture and testing of a demonstrator articulated manipulator called the In-Vessel Penetrator (IVP). The first part of this work concerned the analysis of the requirements and resulted in the development of the conceptual design of the overall manipulator, comprising a 5 module, 11 d.o.f robot based on a parallelogram structure. A scale one mock up of a representative segment was manufactured and tested. In parallel, a feasibility study of the IVP operation was made and provided recommendations to modify the design for intervention under vacuum and temperature. Some technologies were selected and analysed to determine their suitability to the IVP application and items identified for further validation. This paper presents the whole robot concept, the results of the test campaign on the prototype demonstrator and the vacuum and temperature technologies study.
An improved method for deriving elastic generalized coordinatesis considered. Then Kane''s equations of motion for multibody systemsconsisting of an arbitrary number of rigid and elastic bodies ispresented. The equations are in general form and are applicable for anydesired holonomic system. Flexibility in choosing generalized speeds interms of generalized coordinate derivatives in Kane''s method is used. Itis shown that proper choice of a congruency transformation betweengeneralized coordinate derivatives and generalized speeds leads toequations of motion for holonomic multibody systems consisting of anarbitrary number of rigid and elastic bodies. These equations aredecoupled in first-order terms. In order to show the use of this method,a simple system consisting of a lumped mass, a spring and a clamped-freeelastic beam is modeled. Finally, the numerical implementation ofdecoupling using congruency transformation is discussed and shown viasimulation of a two-degrees-of-freedom flexible robot.
The aim of the paper is to analyze the nonlinear dynamics of robotic arms with elastic links and joints. The main contribution
of the paper is the comparative assessment of assumed modes and finite element methods as more convenient approaches for computing
the nonlinear dynamic of robotic systems. Numerical simulations comprising both methods are carried out and results are discussed.
Hence, advantages and disadvantages of each method are illustrated. Then, adding the joint flexibility to the system is dealt
with and the obtained model is demonstrated. Finally, a brief description of the optimal motion generation is presented and
the simulation is carried out to investigate the role of robot dynamic modeling in the control of robots.
Keywordsrobotic arms–elastic link–elastic joint–nonlinear dynamics–optimal control
This paper proposes adaptive control methods based on reaction dynamics for different types of space robotic systems. Reaction dynamics feature the dynamic coupling between an actively operated part and a passively moving part in a multibody robotic system. The reaction dynamics have been used to develop trajectory tracking control of a free-floating space robot or vibration suppression control of a flexible-structure-based manipulator system. However, the presence of dynamic parameter uncertainties degrades the control performance of the above-mentioned methods, since the methods require accurate values of both kinematic and dynamic parameters. To resolve such parameter uncertainties, practical adaptive control methods are proposed in this study. The proposed methods overcome two inherent difficulties in the adaptive control design of space robotic systems, such as nonlinear parameterization of the dynamic equation and uncertainties in coordinate mapping from Cartesian space to joint space. To confirm the validity of the proposed methods, numerical simulations are carried out using three-dimensional realistic models of two types of space robotic systems.
Minimally invasive endoscopic fetal surgery enables intrauterine intervention with reduced risk to the mother and fetus. A novel surgical manipulator is described for stabilizing the fetus and restraining it from floating free during endoscopic intrauterine surgery.
We designed and fabricated a prototype fetus-supporting manipulator equipped with flexible joint and bending mechanisms and a soft balloon stabilizer. The flexible joint and bending mechanisms enable the stabilizer to reach the target sites within the confined space of the uterus under the guidance of an ultrasound device. The balloon stabilizer could be inserted into the uterus through a small incision.
The accuracy evaluation showed that the maximum error of the bending mechanism was as small as 7 mm and the standard deviation of the joint mechanism was just 1.6 degrees. In the experiments using a fetus model, the manipulator could be well controlled with guidance from ultrasound images and its bending mechanism with the balloon stabilizer could be clearly visualized while stabilizing the fetus model.
The manipulator has the potential to be used in minimally invasive intrauterine surgery, although further improvements and experiments remain to be carried out.
The dynamics modelling of a single-link flexible robot with a rigid mass attached to the tip is addressed. The flexibility is represented by lateral bending motion of the robot link. The model is obtained using a Newton-Euler formulation and the natural frequencies and mode shapes are obtained using a constrained mode approach. The paper models the flexibility effects as an internal disturbance torque generated by lateral bending which affects the rigid body motion. The model is suitable for control system analysis and synthesis. A numerical example is presented for the purpose of illustrating the calculation of natural frequencies, mode shapes, and other modal parameters based on the model developed.
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Nonlinear Stabilizing Controller for a Special Class of Single Link Flexible Joint Robots
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