Digital Position Control Research Articles

On the Stability of Digital Position Control with Viscous Damping and Coulomb Friction

In this paper, we investigate the combined effect of viscous damping and Coulomb friction on sampled-data mechanical systems. In these systems, instability can occur due the sampling of the applied discrete-time controller which is compensated by the two different physical dissipation effects. In order to investigate the interplay between these, we focus on how the stable domain of operation is extended by the dry friction compared to viscous damping. We also show that dry friction causes concave envelope vibrations in this extended region. The analytical results, presented in the form of stability charts, are verified by a detailed set of simulations at different representative control parameter values.

Delayed digital position control of a single-DoF system and the nonlinear behavior of the act-and-wait controller

The act-and-wait concept is a recently developed type of controller, which is receiving growing interest because of its promising features with respect to the control of systems with feedback delay. Although most of its advantages have been widely discussed and verified experimentally, a detailed analysis of the nonlinear behavior of this type of controller is still missing. In this paper, we apply the act-and-wait controller to the digital position control of a single-degree-of-freedom system. The analysis shows both the linear stability and the post-bifurcation behavior of the system, comparing the system with a regular proportional-differential controller and with the act-and-wait controller. The performed investigation confirms most of the advantages of the act-and-wait controller, already known in the literature, regarding the enlargement of the stable region and the possibility of achieving deadbeat control, also in the presence of delay. On the other hand it shows some drawbacks of this controller, related to the post-bifurcation behavior, which presents unbounded motions, and to the robustness of the stability, which appears to be limited.

Bifurcation analysis of a two-DoF mechanical system subject to digital position control. Part I: theoretical investigation

This paper analyzes the double Neimark–Sacker bifurcation occurring in a two-DoF system, subject to PD digital position control. In the model the control force is considered piecewise constant. Introducing a nonlinearity related to the saturation of the control force, the bifurcations occurring in the system are analyzed. The system is generally losing stability through Neimark–Sacker bifurcations, with relatively simple dynamics. However, the interaction of two different Neimark–Sacker bifurcations steers the system to much more complicated behavior. Our analysis is carried out using the method proposed by Kuznetsov and Meijer. It consists of reducing the dynamics of the nonlinear map to its local center manifold, eliminating the non-internally resonant nonlinear terms and transforming the nonlinear map to an amplitude map, that describes the local dynamics of the system. The analysis of this amplitude map allows us to define regions, in the space of the control gains, with a close interaction of the two bifurcations, which generates unstable quasiperiodic motion on a 3-torus, coexisting with two stable 2-torus quasiperiodic motions. Other regions in the space of the control gains show the coexistence of 2-torus quasiperiodic solutions, one stable and the other unstable. All the results described in this work are analytical and obtained in closed form, numerical simulations illustrate and confirm the analytical results.

Bifurcation analysis of a two-DoF mechanical system subject to digital position control. Part II. Effects of asymmetry and transition to chaos

Considering a two DoF system subject to digital position control, of interest for robotic application, we analyze the dynamics of the system at the intersection of two loci of Neimark–Sacker bifurcations, where a double Neimark–Sacker bifurcation is taking place. In the system, the saturation of the control force is the only nonlinear term considered, other than this, the system is piecewise linear. Starting from the analytical investigation already performed in Part I (Habib et al. in Nonlin. Dyn., under review, 2013), in this paper the effects of an asymmetry of the saturation of the control force are investigated, both analytically and numerically. The results show the increasing complexity of the dynamics for a more and more asymmetric system. First, the asymmetry is making the bifurcation transit from supercritical to subcritical, then it generates a stable torus that breaks down into a strange attractor, associated with a chaotic motion. In the last part of the paper, the torus breakdown and the onset of chaos are investigated, furthermore the evolution of complex dynamics through regions of phase locking and higher-dimensional chaos is outlined.

Stability analysis of a two-degree-of-freedom mechanical system subject to proportional–derivative digital position control

In this paper we present an analysis of the stability of a two-degree-of-freedom system, modeling a robotic arm connected to the actuator through an elastic joint and subject to digital position control. The system consists of two lumped masses connected to each other through a spring and a damper. In the model there is only one actuator, so the system is underactuated in a certain sense; two cases are considered, referring to a collocated and a noncollocated configuration. Stability analysis is presented using both a continuous and a discrete time approach. The discrete time approach is related to the case of a digital controller, typical in real applications. This samples the position and the velocity signals at discrete time intervals and, therefore, it generates a piecewise constant control force, introducing a delay in the control system as well. The stability charts are presented in the parameter space of the sampling time and the control gains. Their differences highlight the role played by the resonances between the finite sampling frequency and the natural frequency of the system in achieving robust stability with respect to parameter variations.

Nonlinear Bifurcation Analysis of a Single-DoF Model of a Robotic Arm Subject to Digital Position Control

Abstract Precision and stability in position control of robots are critical parameters in many industrial applications where high accuracy is needed. It is well known that digital effect is destabilizing and can cause instabilities. In this paper, we analyze a single DoF model of a robotic arm and we present the stability limits in the parameter space of the control gains. Furthermore we introduce a nonlinearity relative to the saturation of the control force in the model, reduce the dynamics of the nonlinear map to its local center manifold, study the bifurcation along the stability border and identify conditions under which a supercritical or subcritical bifurcation occurs. The obtained results explain some of the typical instabilities occurring in industrial applications. We verify the obtained results through numerical simulations.

A Self-Control Assembly Machine Based on Vision System

Based on the special-shaped spring assembly of thermostat, a corresponding pickup fixture can be designed to ensure parts in a unique state in displacement process. The digital position control and machine visual identification technology are adopted for picking up part and then taking it into plastics casing riveting through the way no contact accurate positioning and control. The problem of the location of special-shaped small parts has been Solved in the thermostat assembly process. The process automation in thermostat assembly has been realized and production efficiency has been improved.

Motion analysis of digitally controlled machines

AbstractThe non‐linear dynamics of digital position control is investigated in the presence of Coulomb friction and round‐off errors. Periodic, transient chaotic, chaotic motions are found even in linear stable cases. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical and experimental investigation of a pulse-width modulated digital hydraulic position control system

In this study, the open loop and closed loop behaviours of a pulse-width modulated hydraulic system are investigated both theoretically and experimentally. First a mathematical model is formulated for the system and methods for obtaining system responses to pulse-width modulated inputs are developed. Using these methods, the responses of the servo valve, the open loop as well as closed loop hydraulic systems are calculated for pulse-width modulated step and sinusoidal inputs. Effect of pulse frequency on the sinusoidal response is investigated. An experimental set-up, which consists of a PC as the controller, a pulse-width modulator, a servo valve driven hydraulic system and feedback elements, was constructed. Experiments show that precise position control can be achieved by using pulse-width modulated inputs in electro-hydraulic control systems. The results obtained for sinusoidal reference inputs show that the pulse frequency should be more than 50 times the reference input frequency for a satisfactory performance of the tested system, if the reference frequency is less than 10 Hz.

205 高速光ディスク装置用繰り返し補償器の検討

This paper discussed the design and experimental verification of a new digital position control method for a high-speed optical disc drive. The position control method needs to improve disturbance suppression capability, as the disc rotation speed becomes higher. We apply a repetition compensator in order to reduce repeatable position error. The control system is implemented in an optical disc drive set-up. The optical disc can rotate at speed of 9000rpm and its sampling frequency is 176kHz. The experimental results that the proposed repetition compensator with 5th order compensator can reduce both the focus and the tracking error caused by the disc disturbances.

DC Thruster Controller Implementation with Integral Anti-wind up Compensator for Underwater ROV

This paper presents the implementation and experimental results of different conventional position control schemes for positioning an experimental model, the THETIS Underwater Remotely Operated Vehicle (UROV). To achieve minimum response time and in order to avoid the so-called Integral Wind-up phenomenon, Proportional-Integral (PI) plus integral antiwind-up compensation is used. Hardware implementation of the design is described and experimental results of a digital position control system over one direction using two dc thrusters fed by four quadrant (PWM-Driven) transistor choppers are given. All control algorithms are implemented using a TI‘s Digital Signal Processor (DSP). The actual position and orientation of the vehicle in a 3-D space is derived through a combination of an ultrasonic scanning system, a direction gyrocompass, and a pressure depth sensor. The vehicle‘s use at the present stage of development is to perform water pollution measurements.

Study and implementation of a simplified and robust position digital controller for a PM synchronous actuator

This paper presents a fully digital position control system for small power surface mounted PM synchronous actuators. The control algorithm relies on a simplified decoupling state feedback in order to obtain field orientation. There is no current measurement, and the current values needed to compute the control algorithm are predicted from a model. This makes it possible to use a fully digital position controller by using low cost 8 bit microprocessors with only a position sensor. Moreover, it is shown in this paper that it is preferable to use, in the decoupling state feedback, an estimated, instead of a measured, value of the current to ensure stability and to improve the robustness of the system regarding parameter uncertainties. Furthermore, as the actuator model is linearized by a decoupling state feedback, the robustness of the system has been further improved by using appropriate techniques evolved for linear systems to synthesize the position controller. The performance of the proposed control system is analyzed by a theoretical study and digital simulations. It has been implemented around two 8 bit MCS 8051 microcontrollers and tested on a 2 kW machine.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust digital position control of brushless DC motor with adaptive load torque observer

A new control method for the robust position control of a brushless DC (BLDC) motor using the adaptive load torque observer is presented. It is shown that the augmented state variable feedback can be applied to the BLDC motor system approximately linearised using the field-orientation method. To overcome the problem of an unknown parameter or a parameter variation such as a flux linkage, an adaptive mechanism is employed. As a result, the robustness can be obtained without affecting the overall system response. The load disturbance is detected by the adaptive 0-observer of an unknown and inaccessible input, and is compensated by feedforwarding the equivalent current having the fast response.

A microcontroller for closed-loop motion control

The Spherosyn displacement transducer's robustness offers many advantages in closed-loop digital motion or position control systems. The microprocessor interface is fundamental to the operation and performance under the arduous conditions typical of automated industrial machinery. Through comparisons of a number of differing circuit techniques, a reliable minimal microcontroller design is presented. Optimization through modelling and the results of experimentation are supported by a novel interface arrangement. The final configuration provides a basis for a number of performance enhanced systems.

Design and analysis of a modular CNC system

Recent focus of manufacturing research has been in the development of unmanned machining systems. Modular Computer Numerical Control (CNC) units, which control and monitor many tightly coupled machining tasks, are required. This paper describes the detailed design and analysis of a modular, research CNC system for a milling machine. The feed drive servo of the milling machine consists of continuous and digital position control blocks. Continuous and discrete transfer functions of the complete system are derived and experimentally verified. A state space model of a feed drive servo is developed for a time domain analysis of actual position, velocity and armature current for given position input and machining force disturbances. A complete experimental verification of the system's model is presented.

Hybrid Control System for D-C Servomotors

A control system for positioning d-c servomotors is described and its performances are analyzed by means of a theoretical analysis and some experimental tests. This control system includes a high gain internal velocity control loop inside a digital position control loop. The latter consists of a proportional controller and a disturbance observer based on a model of the velocity control system. It is shown that this control system gives better results than conventional controllers and may be very well applied to low cost improvements of existing positional control systems.

Digital Position Servo System: A State Variable Feedback System

A digital position control system using a dc motor fed by a four-quadrant transistor chopper is presented. All control functions are handled by a microcomputer requiring only an incremental encoder for position and speed sensing. Two control approaches are considered: the classical control approach and the state feedback approach. For each approach, static and dynamic control performance is studied in terms of system parameters. Experimental-results are given and discussed.

The Argonne plasma engineering experiment (APEX) tokamak

The Argonne plasma engineering experiment (APEX) tokamak was designed to provide hot plasmas for reactor-relevant experiments with rf heating (current drive) and plasma wall experiments, principally in situ low- Z wall coating and maintenance. The device, sized to produce energetic plasmas at minimum cost, is small ( R=51 cm, r=15 cm) but capable of high currents (100 kA) and long pulse durations (100 ms). A design using an iron central core with no return legs, pure tension tapewound toroidal field coils, digital radial position control, and UHV vacuum was used. Diagnostics include monochrometers, X-ray detectors, and a microwave interferometer and radiometer for density and temperature measurements. Stable 100 ms shots were produced with electron temperatures in the range 500–1000 eV. Initial results included studies of thermal desorption and recoating of wall materials.

Teaching of digital control with microprocessors

This paper describes the control of several motors by microprocessors: the motors, their power supplies and their shaft encoders are simulated by analogic chips. The digital position and velocity control algorithms are implemented on a development tool of 8080 microprocessor.

A System for Retrieving and Processing Data from Balloons at High Altitudes

A system was developed to transfer digital nuclear data and position control data from a high altitude balloon to earth for experiment control and monitoring purposes. The system was designed to be operated and maintained by personnel without access to, or familiarity with more complex military-aerospace telemetry data systems. Low cost, accessibility to the equipment and versatility are emphasized. Simple interfaces connect varied data sources and monitoring instruments to standard transfer units on the balloon and on the ground. A multiplexer-interface was designed to transfer data, recorded during a balloon flight, from a magnetic tape to a small computer which produces an IBM-compatible tape suitable for analysis by a large computer.