Augmented PD Controller Research Articles

Dynamic analysis and robust control of ship-mounted crane with multi-cable anti-swing system

In this study, a novel fuzzy sliding mode anti-sway controller (FSMASC) is proposed by combining the in-plane angle and the out-plane angle with the fuzzy sliding mode technology, with the aim of addressing the existing problems facing simple control algorithms, low control accuracy of ship-mounted crane by the mechanical anti-sway method. Moreover, an improved reaching law adaptive sliding mode cooperative controller (ASMCC-IRL) is developed by integrating the cooperative motion between the anti-sway cables with the adaptive sliding mode technology, with the aim of addressing the ineffective cooperative motion between the anti-sway cable in the multi-cable system. First, a model of the ship-mounted crane and a dynamic model of the multi-cable system are built by employing the design prototype of the 45-ton ship-mounted crane on the 27,000-ton multi-purpose ship of COSCO Shipping Group. Subsequently, the FSMASC is proposed to suppress the swing of the load, and the ASMCC-IRL is developed to control the cooperative motion between anti-sway cables. Lastly, the control effectiveness of the FSMASC and the ASMCC-IRL is verified through simulation experiments. As indicated by the simulation results, compared with the scenario without the anti-sway control, the in-plane angle and out-plane angle of the FSMASC decrease by over 75%. Compared with the augmented PD controller (APDC), the error control performance of the ASMCC-IRL is enhanced by over 77.5%, and the convergence speed increases by over 50%.

Optimal Augmented Linear and Nonlinear PD Control Design for Parallel Robot Based on PSO Tuner

This article presents the optimal control design for trajectory tracking of Delta\Par4-like parallel manipulator controlled by two augmented control schemes: Augmented PD Controller (APD) and Augmented Nonlinear PD (ANPD) Controller. Firstly, the Particle Swarm Optimization (PSO) technique is employed for optimal tuning of design parameters for each control structure in order to reach better dynamic performance. Then, two comparisons are made in order to evaluate the performance of parallel robot based on optimized ANPD and APD controllers. The first comparison is established in terms of tracking error accuracy due to the involved controllers, while the other one is based on the strength of robustness granted by each controller against variation of parallel robot parameters. The verification of performance comparisons is made via simulation within the environment of MATLAB/Simulink programming platform. The circular path is used for performance evaluation of controllers for trajectory tracking control. The simulated results have showed that ANPD controller outperforms the APD controller in terms of tracking accuracy and robustness.

Design of Augmented Nonlinear PD Controller of Delta/Par4-Like Robot

This work presents the design of two control schemes for a Delta/Par4-like parallel robot: augmented PD (APD) controller and augmented nonlinear PD (ANPD) controller. The stability of parallel robot based on nonlinear PD controller has been analyzed and proved based on Lyapunov method. A comparison study between APD and ANPD controllers has been made in terms of performance and accuracy improvement of trajectory tracking. Also, another comparison study has been presented between augmented nonlinear PD (ANPD) controller and nonaugmented nonlinear PD (NANPD) controller in order to show the enhancement of introducing the augmented structure on dynamic performance and trajectory tracking accuracy. The effectiveness of augmented PD controllers (APD and ANPD) and nonaugmented nonlinear PD (NANPD) controller for the considered parallel robot are verified via simulation within the MATLAB environment.

Structural error and friction compensation control of a 2(3PUS + S) parallel manipulator

To reduce the adverse effects of structural error and joint friction on a 2(3PUS + S) parallel manipulator, studies on the compensation method are conducted. The static structural errors such as machining error and assembly error are compensated through the kinematic model which is corrected based on the error modeling. Dynamic structural error, which is caused by the elastic deformation and clearance of the joint, is related to the motion state and external load. Owing to the difficulty of calculating and identifying dynamic structural error directly, it is compensated in the working space based on the predicted posture errors of the moving platform. Regarding the friction in the artificial hip joint, thrust ball bearing and linear module, friction modeling and parameter identification are conducted, and then they are compensated through a feedforward compensation method. With the structural error and friction compensated simultaneously, a compensation control strategy for the 2(3PUS + S) parallel manipulator is designed based on the Augmented PD control method and experiments are performed. The results from the experiment indicate that the motion accuracy of the moving platform is improved through the structural error and friction compensation.

Model-free approach based on intelligent PD controller for vertical motion reduction in fast ferries

A new model-free approach was investigated to control two moving aps and a T-foil of a fast ferry traveling in the head sea. Considered as a highly perturbed system, fast ferries in sea waves suffer from the undesirable effects of pitch and heave motions causing severe vertical accelerations that lead to the discomfort of passengers who then experience seasickness. To appropriately control this multivariable system, a model-free control strategy was adopted. An augmented PD controller with compensating terms resulting from an online identification of an ultralocal model of the system was designed. Relying only on input{output data and using online numerical differentiation based on a fast estimation technique, a nonphysical model was designed and continuously updated to capture all the unknown system dynamics, uncertainties, and perturbations. The resulting controller, known as an intelligent PD (iPD) controller, has been proven to be of a reduced design complexity but able to cope with the system's changing characteristics under high perturbations. The robustness to parameter variations was analyzed and compared to a classic PD controller's performance. The results showed that good reductions in the system's vertical motions and seasickness were obtained with a low computational cost. Moreover, the iPD successfully exhibited very robust behavior based on its model-free property when changing the system parameters and the operating velocity.

Model-based control of redundantly actuated parallel manipulators in redundant coordinates

Model-based control of parallel kinematics machines (PKM) relies on computationally efficient formulations in terms of a set of independent joint coordinates. Since PKM models are commonly expressed in terms of actuator or end-effector coordinates the models are not valid at input- or output-singularities, respectively. Moreover input-singularities limit the motion range of PKM. Actuation redundancy is a means to increase the singularity-free range of motion. However, due to the redundancy only a subset of the actuator coordinates constitute independent coordinates. This subset corresponds to the actuator coordinates of the non-redundant PKM, which does generally not constitute proper minimal coordinates for the entire workspace. Hence a redundantly actuated PKM (RA-PKM) controlled by a model-based controller in terms of minimal coordinates would exhibit the same limitations as the non-redundant PKM. One approach to tackle this problem is to switch between different minimal coordinates, i.e., different motion equations are used within the controller.In this contribution a computed torque and augmented PD control scheme in redundant coordinates is proposed, as an alternative to coordinate switching, and applied to the control of redundantly actuated PKM. That is, no minimal coordinates are selected. This novel formulation is numerically robust and does not suffer from input- or output-singularities. Even more the formulation is always valid except at configuration space singularities. For the redundancy resolution within the inverse dynamics the pseudoinverse of a rank deficient matrix is required, for which an explicit formulation is presented. For both controllers exponential trajectory tracking is shown. Experimental results are reported for a planar 2 DOF RA-PKM.

On Passivity‐Based Control of Non‐Classical Electromechanical Systems

AbstractPassivity‐based control has exclusively been pursued for dynamical systems possessing energetic state functions that are quadratic in the generalized velocities. This assumption does not apply to many dynamical systems, for instance in electromechanics, thus passivity‐based control has not been established for these classes of systems. This contribution presents an augmented PD control scheme for such systems. To this end the system dynamics is represented in the event space considered as a Finsler space. It is shown that in this setting the skew symmetry property is retained. A passivity‐based augmented PD controller is designed in the event space, and restricted to the configuration space giving rise to a passivity‐base control law. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Augmented Nonlinear PD Controller for a Redundantly Actuated Parallel Manipulator

In order to improve trajectory tracking accuracy for a redundantly actuated parallel manipulator, a so-called augmented nonlinear PD (ANPD) controller based on the conventional dynamic controller is proposed in this paper. The ANPD controller is designed by replacing the linear PD in the augmented PD controller with a nonlinear PD algorithm. The stability of the parallel manipulator system with the proposed ANPD controller is proven using the Lyapunov stability theorem, and the ANPD controller is further proven to guarantee asymptotic convergence to zero of both the tracking error and error rate. The superiority of the ANPD controller is verified through trajectory tracking experiments of an actual 2-d.o.f. redundantly actuated parallel manipulator.

A passivity‐based control of Euler‐Lagrange systems with a non‐quadratic Lagrangian

AbstractIn this paper, the classical augmented PD control method is extended to a passivity‐based control of Euler‐Lagrange systems with a non‐quadratic Lagrangian. It is assumed that the systems are fully actuated. The problem is treated with two geometrically different approaches. The first approach is dealing with state space control in the configuration space by introducing the kinetic energy via the Legendre transformation of the kinetic co‐energy. The second approach considers the system's dynamics in the event space endowed with a Finsler metric based on the kinetic co‐energy. It is shown that the control laws of both approaches achieve uniformly asymptotically stable trajectory tracking.

Non-linear control of electrically driven micromirrors by means of inverse dynamics

Based on a unified mathematical approach for modelling electromechanical systems (EMS), this paper shows a method to control dynamically the motion of an electrically driven micromirror on a nominal trajectory. For every time interval, this is done in three steps: Inverse dynamics of the mechanical subsystem, calculation of appropriate charges to produce the control forces electrically, and inverse dynamics of the electrical subsystem. The usage of an augmented PD-control law in the first step guarantees global exponential stability of the mirror on the nominal trajectory. The second step is carried out by an optimization method of linear programming. In the third step, the voltages are computed neglecting the dynamics of the electrical subsystem. Finally, these voltages are applied at the simulation model of the micromirror.