Dead Time Element Research Articles

New Findings in the Stability Analysis of PI-state Controlled Systems with Actuator Saturation

In this paper, a simple, generally valid stability proof for an anti-windup method for PI-state controlled systems is presented, with which it is possible to directly conclude the stability of the PI-state controlled system from a stable P-state controlled system with constraints in the manipulated variables, i.e. without having to perform a separate stability investigation of the anti-windup measures. The technique presented is based on the system description by means of state equations and Lyapunov's Direct Method using quadratic Lyapunov functions. Furthermore, the PI-state controller is designed in such a way that it provides the same command response as the P-state controller, for which a stability statement is already available. Both continuous-time and discrete-time systems are considered, which, apart from the saturation of the manipulated variables, show linear, time-invariant behavior. In addition, a general stability proof is given for discrete-time systems, which makes it possible to establish stable anti-windup methods for P- and PI-state controlled systems, which contain dead time elements in the path of the manipulated variables, without having to carry out separate stability investigations for them. For this purpose, the state controller design for the system with dead time elements in the manipulated variable paths is based on the principle that the same characteristics of the control behavior should be achieved as for the system without such dead time elements, but delayed by the dead time. The effectiveness of the presented methods is illustrated by an example from the field of electrical drives.

An Optimal Dead Time Compensator Design for Nonsquare Process with Disturbance Rejection

This work aims to establish an optimal design of the Smith dead-time compensator for a nonsquare multivariable system with a transfer function matrix containing first-order dead time elements. The scheme has a set point tracking controller along with disturbance rejection using an optimal estimator. An inverse signal from the estimator eliminates the disturbance. The proposed method significantly improves the disturbance rejection and performance index compared to the other established methods. The common evolutionary algorithms such as the grey wolf optimization technique and teaching learning based algorithm have been used to tune the controllers.

Dead-Time Pseudo-Compensation for Improvement of Accurate Characteristics of a Continuous Control System with Correction According CP a Smith Predictor

This paper describes the use of a cascade compensator constructed according to a Smith scheme in the forward loop of a system being designed for the purpose of analyzing the quality of processes in steady states. This can be effectively used to solve the problem of providing the system with a required reserve of stability by placing a dead-time element outside a closed loop. The dead-time effect manifests only when the transient time increases by the value of dead time with no changes in the overshoot value. It is determined that the velocity Q-factor of the system with a cascade compensator constructed according to a Smith scheme theoretically cannot be larger than the reciprocal of the dead time. This paper also demonstrates the possibility of reducing this negative property of the cascade compensator constructed according to a Smith scheme by dead-time pseudo-compensation with the use of differentiating elements.

Sensitivity analysis of systems with a cascade compensator embedded in a Smith predictor to dead-time variation

This paper considers the use of a cascade compensator embedded in a Smith predictor in the forward path of a system being designed, which is an effective way to solve two problems: providing the desired process performance in the system and placing the dead-time element outside the closed loop so that it only increases the transient time by the value of the time delay and does not affect the overshoot value. It is shown that the Smith predictor should be used with caution because, being based on an additive signal compensation scheme, it may be not robust and may require accurate knowledge of the time-delay value for robust implementation. The problem of sensitivity analysis of the system to dead-time variation is stated and solved.

Analysis and Compensation Control of Dead-Time Effect on Space Vector PWM

Dead-time element must be set into space vector pulsed width modulation signals to avoid short circuits of the inverter. However, the dead-time element distorts the output voltage vector, which deteriorates the performance of electrical machine drive system. In this paper, dead-time effect and its compensation control strategy are analyzed. Based on the analysis, the voltage distortion caused by dead-time is regarded as two disturbances imposed on dq axes in the rotor reference frame, which degenerates the current tracking performance. To inhibit the adverse effect caused by the dead-time, a control scheme using two linear extended state observers is proposed. This method provides a strong ability to suppress dead-time effects. Simulations and experiments are conducted on a permanent magnet synchronous motor drive system to demonstrate the effectiveness of the proposed method.

Equilibrium-point control of human elbow-joint movement under isometric environment by using multichannel functional electrical stimulation.

Functional electrical stimulation (FES) is considered an effective technique for aiding quadriplegic persons. However, the human musculoskeletal system has highly non-linearity and redundancy. It is thus difficult to stably and accurately control limbs using FES. In this paper, we propose a simple FES method that is consistent with the motion-control mechanism observed in humans. We focus on joint motion by a pair of agonist-antagonist muscles of the musculoskeletal system, and define the “electrical agonist-antagonist muscle ratio (EAA ratio)” and “electrical agonist-antagonist muscle activity (EAA activity)” in light of the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, respectively, to extract the equilibrium point and joint stiffness from electromyography (EMG) signals. These notions, the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, are based on the hypothesis that the equilibrium point and stiffness of the agonist-antagonist motion system are controlled by the central nervous system. We derived the transfer function between the input EAA ratio and force output of the end-point. We performed some experiments in an isometric environment using six subjects. This transfer-function model is expressed as a cascade-coupled dead time element and a second-order system. High-speed, high-precision, smooth control of the hand force were achieved through the agonist-antagonist muscle stimulation pattern determined by this transfer function model.

Frequency response model of skeletal muscle and its association with contractile properties of skeletal muscle

The aims of the present study were to develop a mathematical model of the skeletal muscle based on the frequency transfer function, referred to as frequency response model, and to presume the relationship between the model elements and skeletal muscle contractile properties. Twitch force in elbow flexion was elicited by applying a single electrical stimulation to the motor point of biceps brachii muscles, and then analyzed visually by the Bode gain and phase diagram of the force signal. The frequency response model was represented by a frequency transfer function consisting of five basic control elements (proportional element, dead time element, and three first-order lag elements). The model element constants were estimated by best-fitting to the Bode gain and phase diagram of the twitch force signal. The proportional constant and the dead time in the frequency response model correlated significantly with the peak torque and the latency in the actual twitch force, respectively. In addition, the time constants of the three first-order lag elements in the model correlated strongly with the contraction time and the half relaxation time in the actual twitch force. The results suggested a possibility that the individual elements in the frequency response model would reflect the biochemical and biomechanical properties in the excitation–contraction coupling process of skeletal muscle.

Tuning Method of PI Controller with Desired Damping Coefficient for a First-order Lag Plus Deadtime System

This paper presents an entirely new tuning method of PI controller with a desired damping coefficient. We consider a plant model described by a first-order lag plus deadtime system in the process control. The ultimate sensitivity method presented by Ziegler and Nichols has been still widely used, but it has a disadvantage that gives an oscillatory response. In recent years a less oscillatory response has been judged to be more appropriate for process controls. In tuning PI controller it is often convenient to determine the damping coefficient to obtain the desired control performance. The deadtime element can be approximated by the Padé equation to determine the damping coefficient for the equivalent second-order lag system. In this paper the integral time is normally chosen equal to the time constant of a plant to degenerate the order of the closed-loop transfer function so that pole-zero is cancelled. As a result, the relations among the gain constant, the time constant, the deadtime of the plant and the proportional gain of the controller are clarified when the desired damping coefficient is provided.

Development of a Handshake Robot System Based on a Handshake Approaching Motion Model

Humans shake hands as greetings of a first meeting to show a feeling of closeness. A handshake is an embodied interaction involving a physical contact to make communication smooth. A natural handshake between a robot and a human would presumably have the same effect. In this paper, we analyzed mutual handshaking between humans with and without voice greetings and propose a handshake approaching motion model based on the analysis. In this model, a robot can generate handshake approaching motion that is acceptable to a human using second-order lag and dead time elements from the trajectory of a human hand. Furthermore, we developed a handshake robot system by applying the proposed handshake approaching motion model and demonstrated the effectiveness of the approaching handshaking motion model and the handshake robot system through sensory evaluation.

Steam Temperature Prediction Control Method Using Prediction Model of Multi Heat Exchangers for Thermal Power Plants

This paper proposes a new prediction control method for thermal power plants. In the method, steam temperatures are predicted using prediction model of multi heat exchangers. Each model of a heat exchanger consists of a lumped parameter physical model and a dead time element. State variables of the heat exchanger are estimated using a Kalman Filter, and near future changes of steam temperatures are predicted by integrating multi heat exchanger models, and fuel flow and water spray flows are compensated accordingly.The results of simulation using a practical scale simulator of the thermal power plant show that the proposed method is so practical that changes of main steam temperature are reduced by half comparing with those of PID control method.

Adaptive Self-Tuning Speed Control for Permanent-Magnet Synchronous Motor Drive With Dead Time

In this paper, an adaptive self-tuning speed control for a permanent-magnet synchronous motor (PMSM) drive with dead time is proposed. Firstly, to equivalently place the dead time element outside the closed-loop speed control, a dead time compensator (DTC), based on the Smith predictor and a self-tuning proportional-integral model-following controller (ST-PI-MFC) is proposed. The model-following error is used to adaptively update the gains of the ST-PI-MFC via the affine projection algorithm (APA). Secondly, a disturbance observer, based on the time delay control (TDC) approach is used for torque feed forward control. The system's model is greatly simplified when the disturbance observer is combined with the motor. Relying on the simplified model, a natural adaptive observer is used to estimate the motor speed. Unknown motor parameters are estimated by minimizing the state estimation error using an iterative gradient algorithm offered by the affine projection. The estimated parameters are used to update the gains of the integral-proportional (IP) servo loop controller, the disturbance observer and the Smith model. The validity and usefulness of the proposed control scheme are verified through simulation and experimental results

On the extraction of dead-time controllers and estimators from delay-free parametrizations

An approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. In the paper, the extraction procedures are developed in both H/sup 2/ and H/sup /spl infin// settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators.

On the extraction of dead-time controllers from delay-free parametrizations

A novel approach to the analysis and design of dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller. This enables one to use well-understood parametrizations of all delay-free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. It is shown in the paper that the proposed approach yields simple solution procedures and transparent and intuitively appealing structures of the resulting controllers and filters in both the H2 and H∞ cases.

Temperature Control of a Highly Active Catalyst Polyolefin Polymerization Reactor at an Unstable Operating Point

The invention of a new catalyst, Metallocenes, which is highly active, selective and able to control polymer structure more precisely than the ordinary catalyst, leads the polyolefin polymer production to a new catalyst revolution. However, because the catalyst is sensitive to temperature, it pushes the plant to operate at an open-loop unstable point. This paper deals with a design problem of temperature controller for an industrial polypropylene polymerization reactor, which is open-loop unstable when the new catalyst is used. The dynamics of the open-loop unstable process is identified by a first order system with integral and dead time element. Then, the controller is realized in an I-PD structure. The application result illustrates that the developed controller can successfully stabilize the plant.

実数型位相進み遅れ補償器を用いた制御系設計法

The new type of the design method proposed in this paper is similar to the one using phase lead-lag compensator and has two particular characteristics. First, the approximate system described real order lag element with a dead time element is specially adopted to identify the controlled object. The principle of the identification derived from the frequency characteristics is presented. Secondly, the compensator is composed by an integral element and phase lead-lag elements having multiple zeros and multiple poles. The order of phase lead-lag elements is, in general, an integer but in this design it will be treated as a real number. In order to use practically the compensator, the impulse response function of the compensator is obtained in the form of a series expansion of a gamma function and it can be performed by the convolution method between the impulse response function of the compensator and a deviation error signal.The compensator parameters are determined by a rule of trial and error in order to obtain a quick response using manipulating variable under the maximum value assigned in advance. Since the order of the compensator can be adjusted finely through numerical treatment as to a real, the quick response by a relatively small manipulating variable has been performed. Then, the selection of the sampling time in the case of practical digital control is considered in detail. The effectiveness of this control design method is shown by examples.

An Application of Time-Optimal Control by Using Switching Surface

The authors have previously proposed a design method of time-optimal feedback control system by using switching hypersurface. In the present paper, the proposed method is applied to construct the control system of the training ship Ohshimamaru 330 GT, and then the practical applicability is shown in the sea trial.The dynamics of a ship is presented by a complicated mathematical model with some nonlinear elements and dead time elements. To make the design of the dual mode controller tractable, the model of ship dynamics is simplified from the practical point of view. And dead time problem is evaded by making use of predictive control. In the simulated course changing control using the nonlinear mathematical model as a controlled object, it is confirmed that the time-optimal control is approximately realized, It is demonstrated that the proposed method is efective showing the resemblance of the results in the sea trial, with those in the simulation.

Voltage Feedback Control of PWM Inverter.

A feedback control seems to be useful to improve regulation and accuracy of an inverter. However, it has been pointed out that a feedback around a triangular wave carrier PWM inverter may cause a switching of output signal independent of the carrier frequency.An analysis of a voltage-output PWM inverter with an integral feedback loop suggests that, if a dead time element is incorporated in the pulse transfer path of the inverter and if the dead time is adjusted depending on the reference input value, then the output pulse can be synchronized to the carrier even at a higher loop gain.This was verified in a series of experiments conducted with a three-phase transistor inverter. As the dead time was adjusted properly, the three output pulse sequences were synchronized to the carrier signal when the reference input value was within 78% of full range. Outside this range, the output pulse frequency lowered. Sinusoidal disturbances up to half the carrier frequency were reduced by the increased-gain feedback control.

Reduced order process modelling in self-tuning control

One major objection to the model-based auto-tuning and self-tuning control is based on the observation by Bristol that a reduced order model being identified would not yield good control of the actual high order process. In this paper we have re-examined the work of Bristol and argued that this observations could not be generalized. We then consider reduced order modelling which incorporates a deadtime element. It is shown that the deadtime could help to provide a close match of the freqency response near the critical frequencies. Extensive simulation studies have also confirmed that reduced order modelling with deadtime included could be an adequate model for practical self-tuning control.

Design of a state-feedback controller with a maximum forcing-function specification

An iterative design technique is described for determining suitable closed-loop pole positions in the z domain to meet compatible indicial response specifications and forcing-function limitations in a state-variable-feedback system. An example is given of the application of the method to a linear system containing a dead-time element.

Stabilization of a relay system containing three-position element and dead time†

An exact method of analysis of non-linear systems containing a three-position relay element and a dead-time element is given. Such a system shows two limit cycles, an unstable limit cycle and a stable limit cycle. Expressions are derived to evaluate the period and amplitude of the oscillations. Using the phase-plane concept it is shown that the given system can be stabilized by adding a zero to the second-order transfer function of the rational part.