PD-like Controller Research Articles

EKF-Based PI-/PD-Like Fuzzy-Neural-Network Controller for Brushless Drives

This paper presents the development of a fuzzy-neural-network (FNN) proportional-integral (PI)-/proportional-derivative (PD)-like controller with online learning for speed trajectory tracking of a brushless drive system. The design implements the novel use of the extended Kalman filter (EKF) to train FNN structures as part of the PI-/PD-like fuzzy design. The FNN structure has two parallel FNN PI-/PD-like controllers, each with four internal layers. EKF trains each FNN by modifying the weights and the membership function parameters. Thus, the proposed EKF-based architecture presents an alternative to control schemes employed so far. The objective is to replace the conventional PI-derivative (PID) controller with the proposed FNN PI-/PD-like controller with EKF learning mechanism. Comparisons of the algorithm performances provide evidence of improvement of the FNN PI-/PD-like controller over PID control. A test bench enables design implementation in the laboratory on hardware using a dSPACE DS1104 DSP and MATLAB/Simulink environment. Experimental testing results show that the proposed controller learns and robustly responds to a wide range of operating conditions in real time.

Exhaustive stability analysis in a consensus system with time delay and irregular topologies

A consensus problem and its stability are studied for a group of agents with second-order dynamics and communication delays. The communication topologies are taken as irregular but always connected and undirected. The delays are assumed to be quasi-static and the same for all the interagent channels. A decentralised, PD-like control structure is proposed to create a consensus in the position and velocity of the agents. We present an interesting factorisation feature for the characteristic equation of the system which simplifies the stability analysis considerably from a prohibitively large dimensional problem to a manageable small scale. It facilitates a rare stability picture in the space of the control parameters and the delay, utilising a paradigm named cluster treatment of characteristic roots (CTCR). The influence of the individual factors on the absolute and relative stability of the system is studied. This leads to the introduction of two novel concepts: the most exigent eigenvalue, which refers to the one that defines the delay stability margin of the system, and the most critical eigenvalue, which is the one that dictates the consensus speed of the system. It is observed that the most exigent eigenvalue is not always the most critical, and this feature may be used as a design tool for the control logic. Case studies and simulations results are presented to verify these concepts.

Position Tracking for Non-linear Teleoperators with Variable Time Delay

In this paper the problem of position tracking in the presence of variable time delay is studied. It is proved that simple P-like and PD-like controllers can stabilize the teleoperator under variable time delays and, moreover, they provide position tracking. Then, a controller based on the scattering transformation that also provides position tracking is proposed. In this paper we present the conditions under which the velocities and position error of the non-linear teleoperator, for the three controllers, are bounded, and if the human does not move the local manipulator and the remote manipulator does not interact with the environment, then it is proved that velocities and position error converge to zero. Simulations and real experiments, using the Internet from Urbana-Champaign (USA) to Barcelona (Spain), validate the proposed schemes.

Switched PD-like Controllers for First Order Unstable Systems with Time Delay

A new method is proposed for the design of PD-like (first order stable) controllers for switched first order unstable systems with time delays. For this purpose, a dwell-time based stability condition of Yan and Özbay (2008) is used for the class of switched time delay systems studied here. The proposed method finds the values of PD-like controller parameters which minimize an upper bound of the dwell time, minimum time needed between the switching instants to preserve stability. The conservatism analysis of this method is done by time domain simulations. The results show that the calculated upper bound for the dwell time is close to the lower bound of the dwell time observed by simulations.

Implementation of a Physiologically Identified PD Feedback Controller for Regulating the Active Ankle Torque During Quiet Stance

Our studies have recently demonstrated that a proportional and derivative (PD) feedback controller, which takes advantage of the body's position and velocity information to regulate balance during quiet standing, can compensate for long neurological time delays and generate a control command that precedes body sway by 100-200 ms. Furthermore, PD gain pairs were identified that ensure a robust system behavior and at the same time generate dynamic responses as observed in quiet standing experiments with able-bodied subjects. The purpose of the present study was to experimentally verify that the PD controller identified in our previous study can: 1) regulate the active ankle torque to stabilize the body during quiet standing in spite of long neurological time delays and 2) generate system dynamics, i.e., a motor command and body sway fluctuation, that successfully mimic those of the physiologic system of quiet standing. Our real-time closed-loop feedback circuit consisted of a center of mass position sensor and a functional electrical stimulator that elicited contractions of the plantar flexors as determined by the aforementioned PD controller. The control system regulated upright stance of a subject who was partially de-afferented and de-efferented due to a neurological disorder called von Hippel-Lindau Syndrome (McCormick Grade III). While the subject was able to generate a motor command for the ankle joints, he could not regulate the resulting torque sufficiently due to a lack of sensory feedback and motor control. It is important to mention that a time delay was included in the closed-loop circuit of the PD controller to mimic the actual neurological time delay observed in able-bodied individuals. The experimental results of this case study suggest that the proposed PD controller in combination with a functional electrical stimulation system can regulate the active ankle torque during quiet stance and generate the same system dynamics as observed in healthy individuals. While these findings do not imply that the CNS actually applies a PD-like control strategy to regulate balance, they suggest that it is at least theoretically possible.

Lorentz Force-Type Integrated Motor-Bearing System in Dual Rotor Disk Configuration

An integrated motor-bearing system combines the functions of an active magnetic bearing and an electric motor into a single unit. This paper proposes a generalized principle for the generation of torque and radial force in integrated motor-bearing systems using Lorentz force. The derived constraints lead to various feasible combinations of design parameters. Dual rotor disk configuration with a coreless stator is also proposed. It induces no negative stiffness, which is useful for the system stability and robustness to the tilting motion of the rotor. The test rigs are developed for five and six windings with an eight-pole rotor and operated successfully employing a simple PD-like controller.

H/sub /spl infin// control for suppressing stick-slip in oil well drillstrings

We show, applying the linear H/sub /spl infin// control design technique, that the suppression of stick-slip oscillations and transient behavior can be largely improved over a PD-like control system currently applied in oil well drilling. Using rough knowledge (e.g. size and induced oscillation frequency) of the friction disturbance, the appropriate choice of dynamic weighting functions can make the closed loop system robust toward the substantial uncertainty in the knowledge of the nonlinear friction. After an introduction to drilling engineering and a description of the drilling system, a condensed analysis of the stick-slip phenomenon in drillstrings and a brief history of control solutions for the drillstring problem are given, and H/sub /spl infin// control solutions for allied systems are described. Then, the general principles of linear H/sub /spl infin// control design are sketched. Subsequently, the H/sub /spl infin// control design technique is applied to design a controller for the system under study. Next, the improved closed-loop behavior toward stick-slip oscillations is shown in simulations and experiments. Conclusions with respect to the results are drawn.

Global Tracking Control of One Degree of Freedom Euler-Lagrange Systems without Velocity Measurements

The problem of global outputfeedback tracking control of robot manipulators has been open for several years. In this short note we propose a computed torque plus (nonlinear) PD-like controller to solve the output feedback tracking control problem ofone degree of freedom (dof) Euler-Lagrange (EL) systems. We prove in this case global asymptotic stability. Our approach is the extension ofour previous semi-global result (Loria and Ortega, Appl Math Comp Sci 1995; 5:2, 101–113 [1]). Even though we can not claim the same result for systems of more than one dol, as far as we know, none of the semi-global solutions present in the literature has been proved to be global even for one dof systems.