A Study on the Class of Controllers in Model Feedback Control

A method for optimal trajectory control of robotic manipulators is considered in this paper. In particular, a control scheme is proposed such that, while the manipulator passes two or more prescribed points, the resulting trajectory of motion is smooth. Such a problem is formulated by employing a criterion of minimum-mean-square acceleration during the entire period of motion. Although the motion of robot manipulators is governed by a system of second-order differential equations which are highly non-linear, it is shown that the control problem can be solved rigorously under such a criterion. The optimal control consists of non-linear compensation terms and other linear feedback terms. The results of computer simulation studies for a two-link manipulator are also included.

Robust trajectories following control of a 2-link robot manipulator via coordinate transformation for manufacturing applications

A discrete-time learning control for robotic manipulators is studied using its pulse transfer function. Firstly, the discrete-time learning stability condition which is applicable to single-input two-outputs systems is derived. Secondly, the stability of the learning algorithm with a position signal is studied. In this case, when the sampling period is small, the algorithm is not stable because of an unstable zero of the system. Thirdly, the stability of the algorithm with position and velocity signals is studied. In this case, we can stabilize the learning control system which is unstable in the case of learning with only the position signal. Finally, simulation results on the trajectory control of robotic manipulators using the discrete-time learning control are shown. The simulation results agree well with the analytical results.

A discrete-time learning control for robotic manipulators is studied from a viewpoint of zeros of a control system. The signal used for learning is a position signal of each joint detected by a pulse encoder. Firstly, we show that when sampling period is small, the learning is unstable because of an unstable zero of the system. Secondly, we show that we can stabilize the learning control system with small sampling period by using a low pass filter, and also show that a tracking error converges not to zero but to a certain value in that case. Finally, experimental results on the trajectory control of robotic manipulators using the discrete-time learning control are shown. These experimental results agree well with the analytical ones.

In the last few decades, the stabilization in stationary states has emerged as a new auspicious campaigner in chaos theory and found a celebrated place through various control techniques such as predictive control, delayed feedback control, constant proportional feedback control and oscillating feedback control system. Generally, it is accepted that the superiority of control systems is not only to quash the irregular distribution of stationary states, but also to illustrate its basin of attractions as large as possible depending on the numerical as well as analytical observance. In this article, the universal stabilization in unstable stationary states is studied through superior fixed point feedback control system for a family of one-dimensional maps. Further, it is interesting to know that the novel system provides freedom in the control parameter γ due to which the stabilization increases more rapidly for the lager range of parameter γ in [0,1]. The analytical as well as numerical simulations are demonstrated to examine the behavior of parameter γ for which the unstable stationary state admits universal stability.

This work is concerned with the existence of asymptotically stable 2-D (2-dimensional) systems by means of a feedback control model represented by the system of partial difference equations and their Lagrange solutions. Thus, the goal is to establish a controller that provides a feedback control system with state variables depending solely on its Lagrange solution in the sense that the solution to the variable state is not a linear combination of other Lagrange solutions. Roughly speaking, the results showed that, to achieve such a control system, the controller has to diagonalize the block matrices of the matrices composing the system description model. Finally, a numerical example is presented to show how the controller is designed in order to generate a stable feedback control with given Lagrange solutions.

PurposeTo assess whether the use of a patented, novel feedback device intended to accurately control phacoemulsification tip elongation is effective under varying machine settings and material resistance.MethodsSculpt mode phaco (550-mm Hg Venturi pump; elongations, 35 and 70 µm) and quadrant settings (550-mm Hg Venturi pump; elongations, 15, 30, and 60 µm) were used in agar gel of incremental density (1%, 2%, 3%, and 6% in demineralized water). Dispersed lens fragments were also simulated with 6% agar gel spherules (2–5 mm in diameter; 550-mm Hg vacuum, and 60-µm elongation). Actual phaco tip elongation was measured on voltage readings from the piezoelectric crystals and compared to nominal elongation with feedback control off and on.ResultsMismatch between nominal and actual elongation when feedback control was off in sculpt mode varied between –13.51 µm and –23.07 µm of nominal elongation; in quadrant mode, mismatch varied between –2.79 µm and –20.41 µm. When the feedback control system was switched on, mismatch varied between –0.02 µm and +0.43 µm (P < 0.001 for all matchings). When the feedback system was off, the elongation mismatch among the 1%, 3%, and 6% agar was also statistically significant (P < 0.001). Elongation was 44.72 ± 4.16 µm with feedback control off and 60.02 ± 1.63 µm with it on (nominal elongation 60 µm; P < 0.001) when emulsifying agar 6% gel fragments. Dispersion of elongation data was also significantly wider when feedback control was turned off.ConclusionsA novel feedback control system effectively controls elongation accuracy regardless of the resistance offered by incremental agar gel concentrations.Translational RelevanceImplementing feedback control in phaco handpieces dramatically improves surgical accuracy. The translational value of this research relies on its immediate applicability to routine cataract surgery, resulting in a more appropriate use of ultrasound energy.

A regressor-based variable-structure control scheme has been developed for the trajectory control of robot manipulators in the presence of disturbances, parameter variations, and unmodeled dynamics. The method is based on the regressor structure given by J.J.E. Slotine and W. Li, without parameter adaptation. This avoids the requirement of persistency of excitation, and the convergence of the overall transient exponential. The method is robust against a class of state-dependent uncertainties, which may result, for example, from unmodeled dynamics. The problem of chattering is solved by the smoothing control law. It is with respect to a set around the origin, which can be made arbitrarily small. To illustrate the feasibility of this controller, it was implemented using a Motorola M68000 microprocessor on a two-link revolute joint manipulator subjected to a variable payload. Experimental results confirm the validity of accurate tracking capability and the robust performance. >

A Novel Variable Structure Control Scheme for Robot Trajectory Control

In tlus work a nonlinear control method is used for the trajectory control of robotic manipulators. In this method, the correct gain values are obtained using an off-line based numerical optimization method. The results obtained are tested on a two link manipulator whose end effector moves along a circular trajectory. The results show that one can obtain very accurate results using this method

BackgroundPatients with neurological disorders including stroke use rehabilitation to improve cognitive abilities, to regain motor function and to reduce the risk of further complications. Robotics-assisted tilt table technology has been developed to provide early mobilisation and to automate therapy involving the lower limbs. The aim of this study was to evaluate the feasibility of employing a feedback control system for heart rate (HR) during robotics-assisted tilt table exercise in patients after a stroke.MethodsThis feasibility study was designed as a case series with 12 patients (n=12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n = 12$$\\end{document}) with no restriction on the time post-stroke or on the degree of post-stroke impairment severity. A robotics-assisted tilt table was augmented with force sensors, a work rate estimation algorithm, and a biofeedback screen that facilitated volitional control of a target work rate. Dynamic models of HR response to changes in target work rate were estimated in system identification tests; nominal models were used to calculate the parameters of feedback controllers designed to give a specified closed-loop bandwidth; and the accuracy of HR control was assessed quantitatively in feedback control tests.ResultsFeedback control tests were successfully conducted in all 12 patients. Dynamic models of heart rate response to imposed work rate were estimated with a mean root-mean-square (RMS) model error of 2.16 beats per minute (bpm), while highly accurate feedback control of heart rate was achieved with a mean RMS tracking error (RMSE) of 2.00 bpm. Control accuracy, i.e. RMSE, was found to be strongly correlated with the magnitude of heart rate variability (HRV): patients with a low magnitude of HRV had low RMSE, i.e. more accurate HR control performance, and vice versa.ConclusionsFeedback control of heart rate during robotics-assisted tilt table exercise was found to be feasible. Future work should investigate robustness aspects of the feedback control system. Modifications to the exercise modality, or alternative modalities, should be explored that allow higher levels of work rate and heart rate intensity to be achieved.

Service process control: conceptualising a service as a feedback control system

In the past, there have been many inconsistent attempts to describe the bandwidth of dynamic systems. Similar definitions of bandwidth have been extended to describe not only the closed-loop bandwidth of feedback control systems but also the frequency at which usefulness of feedback is lost. In this work, we propose and explain the need for a new precise measure for bandwidth that could be used to describe the cut-off frequency at which the feedback control system’s usefulness is no longer advantageous. The tools of neoclassical control are used to define this new measure of bandwidth as the frequency at which the feedback controller ceases to affect the response. This measure is then applied to two example cases to demonstrate its use.

Design of power and phase feedback control system for ion cyclotron resonance heating in the Experimental Advanced Superconducting Tokamak

16 - Design of feedback controls