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Showing papers on "Open-loop controller published in 1999"


Patent
Randall Hayes Ubillos1
07 Apr 1999
TL;DR: In this paper, a scalable scroll controller with a scale controller is used to modify a scale for controlling a magnification for accessing a data field having fine resolution, where the scale is adjusted based on the position of the scale controller.
Abstract: A method for accessing a data field having fine resolution is disclosed. The method includes providing a scalable scroll controller with a scale controller to modify a scale for controlling a magnification for accessing data within the data field. The method also includes receiving a first user event to select the scale controller and receiving a second user event to modify a position of the scale controller. The scale is adjusted based on the position of the scale controller. An apparatus for performing the method is also disclosed.

225 citations


Journal ArticleDOI
TL;DR: The design and evaluation of a fuzzy logic traffic signal controller for an isolated intersection designed to be responsive to real-time traffic demands and compared to that of a traffic-actuated controller for different traffic conditions on a simulated four-approach intersection.
Abstract: This paper presents the design and evaluation of a fuzzy logic traffic signal controller for an isolated intersection. The controller is designed to be responsive to real-time traffic demands. The fuzzy controller uses vehicle loop detectors, placed upstream of the intersection on each approach, to measure approach flows and estimate queues. These data are used to decide, at regular time intervals, whether to extend or terminate the current signal phase. These decisions are made using a two-stage fuzzy logic procedure. In the first stage, observed approach traffic flows are used to estimate relative traffic intensities in the competing approaches. These traffic intensities are then used in the second stage to determine whether the current signal phase should be extended or terminated. The performance of this controller is compared to that of a traffic-actuated controller for different traffic conditions on a simulated four-approach intersection.

192 citations


Journal ArticleDOI
TL;DR: In this article, a simple PI conventional controller for the exciter loop is carried out by using a first-order model and compared four control algorithms based on conventional and intelligent control theories.
Abstract: This paper discusses the control problem for a class of wind energy conversion systems (WECS). It first develops a detailed model and then compares four control algorithms based on conventional and intelligent control theories. A simple PI conventional controller for the exciter loop is carried out by using a first order model. When the system operating points change, the PI controller fails to provide sufficient damping or acceptable performance. Therefore both fuzzy voltage and fuzzy power regulators are introduced. Also a conventional adaptive pitch controller is proposed to adjust the pitch angle of the rotor blades in order to maximize the energy capture and reduce the mechanical loads. As an alternative to this controller, a neural network controller is also designed. Using the existing nonlinear wind model and the different control algorithms, the dynamic behavior of the controlled (WECS) is simulated. By selecting convenient wind data, the system characteristics such as its tracking performance, its robustness and its ability to recover from large disturbances are studied and discussed.

190 citations


Journal ArticleDOI
TL;DR: In this article, a PPF controller may be formulated as an output feedback controller, and both centralized and decentralized controllers are considered, and optimal control methods are used to demonstrate how control design algorithms for output feedback systems may be used to design PPF controllers.
Abstract: The vibration control of structures may be approached in many ways. Often a robust controller is difficult to design as spillover from modes not considered in the controller design can cause the closed loop system to be unstable. One great advantage of positive position feedback (PPF) control is that the frequency response of the controller rolls off quickly, making the closed loop system robust to spillover. Unfortunately methods to design a PPF controller are not as advanced as other approaches in the control literature. This paper shows that a PPF controller may be formulated as an output feedback controller, and both centralized and decentralized controllers are considered. Optimal control methods are used to demonstrate how control design algorithms for output feedback systems may be used to design PPF controllers. The method is demonstrated using a single-degree-of-freedom system.

149 citations


Journal ArticleDOI
TL;DR: A robust sliding-mode controller, suitable for the output voltage control of voltage-sourced unity-power-factor three-phase pulsewidth modulation (PWM) rectifiers, presenting no steady-state errors, is described, which exceeds the performance of existing hysteretic current-mode control systems.
Abstract: A robust sliding-mode controller, suitable for the output voltage control of voltage-sourced unity-power-factor three-phase pulsewidth modulation (PWM) rectifiers, presenting no steady-state errors, is described. This "just-in-time" switching controller controls the output voltage and the line input currents, while providing bidirectional power flow, near-unity-power-factor operation, low harmonic content, fast dynamic response of the output voltage, and minimum switching frequency due to a new /spl alpha/-/spl beta/ space-vector current regulator. The voltage controller performance is compared with the behavior of the conventional proportional integral output voltage control, aided by PWM current-mode modulators, and with the nonrobust fast and slow manifold sliding-mode approach. The comparison shows that the proposed controller confers faster dynamics and does not present steady-state errors. Test results confirm that the performance of the controller is independent of system parameters and load and exceeds the performance of existing hysteretic current-mode control systems.

124 citations


Journal ArticleDOI
TL;DR: In this paper, a simple water level controller for irrigation and drainage canals is proposed; the proposed controller has a master-slave structure where the slaves control the flow rates through the control structures.
Abstract: A simple water level controller for irrigation and drainage canals is proposed; the proposed controller has a master-slave structure where the slaves control the flow rates through the control structures. The master controller consists of PI-based controllers for feedback, and a decoupler and feedforward controller that are based on the inversion of a simple dynamic model of the canal system. The applicability of the controller is demonstrated in field experiments.

114 citations


Proceedings ArticleDOI
01 Jan 1999
TL;DR: In this article, a modified sliding-mode controller is proposed to compensate the effects of the varying time delay which deteriorates the performance of the regular slidingmode controller, in which the nonlinear gain can be set independently of the time delay variation.
Abstract: Bilateral teleoperation systems connected to computer networks, such as Internet, have to deal with varying communication time delay. The entire system is easy to become unstable due to irregular time delay. In this paper, we design a sliding-mode controller for the slave and an impedance controller for the master. We propose a modified sliding-mode controller, in which the nonlinear gain can be set independently of the time delay variation. The proposed controller effectively compensates the effects of the varying time delay which deteriorates the performance of the regular sliding-mode controller. We illustrate the validity of the proposed controller using simulations with 1-DOF master/slave bilateral teleoperation system.

110 citations


Journal ArticleDOI
Tetsuo Semba1, T. Hirano, J. Hong, L.-S. Fan
18 May 1999
TL;DR: The experimental results of the track following control with the dual-stage actuator using a conventional VCM and a MEMS microactuator showed that the fourth-order servo controller can achieve a high bandwidth of more than 2 kHz.
Abstract: A MEMS microactuator provides a low-cost and high-performance solution to realize high track densities of HDD, because of the batch fabrication process and its clean mechanical characteristics. However, the servo system to control such a dual-stage system tends to be more complicated than a conventional HDD system. In this paper, a simple and efficient design method of a dual-stage servo controller for HDD applications is described. The experimental results of the track following control with the dual-stage actuator using a conventional VCM and a MEMS microactuator showed that the fourth-order servo controller can achieve a high bandwidth of more than 2 kHz.

107 citations


ReportDOI
30 Jul 1999
TL;DR: In this paper, a simple, rigid, non-linear turbine model was used to systematically perform trade-off studies between two performance metrics, and the robust nature of the proportional-integral-derivative (PID) controller was illustrated, and optimal operating conditions were determined.
Abstract: Variable-speed, horizontal axis wind turbines use blade-pitch control to meet specified objectives for three regions of operation. This paper focuses on controller design for the constant power production regime. A simple, rigid, non-linear turbine model was used to systematically perform trade-off studies between two performance metrics. Minimization of both the deviation of the rotor speed from the desired speed and the motion of the actuator is desired. The robust nature of the proportional-integral-derivative (PID) controller is illustrated, and optimal operating conditions are determined. Because numerous simulation runs may be completed in a short time, the relationship of the two opposing metrics is easily visualized. Traditional controller design generally consists of linearizing a model about an operating point. This step was taken for two different operating points, and the systematic design approach was used. A comparison of the optimal regions selected using the n on-linear model and the two linear models shows similarities. The linearization point selection does, however, affect the turbine performance slightly. Exploitation of the simplicity of the model allows surfaces consisting of operation under a wide range of gain values to be created. This methodology provides a means of visually observing turbine performance based upon the two metrics chosen for this study. Design of a PID controller is simplified, and it is possible to ascertain the best possible combination of controller parameters. The wide, flat surfaces indicate that a PID controller is very robust in this variable-speed wind turbine application.

99 citations


Journal ArticleDOI
TL;DR: This work develops a fuzzy model reference learning controller, a genetic model reference adaptive controller, and a general genetic adaptive controller and investigates their ability to reduce the effects of variations in the process due to temperature.
Abstract: There exist several problems in the control of brake systems including the development of control logic for antilock braking systems (ABS) and "base-braking." Here, we study the base-braking control problem where we seek to develop a controller that can ensure that the braking torque commanded by the driver will be achieved. In particular, we develop a fuzzy model reference learning controller, a genetic model reference adaptive controller, and a general genetic adaptive controller, and investigate their ability to reduce the effects of variations in the process due to temperature. The results are compared to those found in previous research.

99 citations


Journal ArticleDOI
01 Sep 1999
TL;DR: In this article, a conceptual and practical difficulty with the continuous-time generalised predictive controller is solved by replacing the continuously moving horizon by an intermittently moving horizon, which allows slow optimisation to occur concurrently with a fast control action.
Abstract: A conceptual, and practical difficulty with the continuous-time generalised predictive controller is solved by replacing the continuously moving horizon by an intermittently moving horizon. This allows slow optimisation to occur concurrently with a fast control action. Some nonlinear simulations illustrate the potential of this approach.

Journal ArticleDOI
01 May 1999
TL;DR: In this article, a fuzzy neural network (FNN) sliding-mode controller is investigated, in which the FNN is utilised to estimate the bound of uncertainties in real-time.
Abstract: A sliding-mode controller with an integral-operation switching surface is adopted to control the position of an induction servomotor drive. Moreover, to relax the requirement for the bound of uncertainties, a fuzzy neural network (FNN) sliding-mode controller is investigated, in which the FNN is utilised to estimate the bound of uncertainties in real-time. The theoretical analyses for the proposed FNN sliding-mode controller are described in detail. In addition, to guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the FNN. Simulation and experimental results show that the proposed FNN sliding-mode controller provides high-performance dynamic characteristics and is robust with regard to plant parameter variations and external load disturbance. Furthermore, compared with the sliding-mode controller, smaller control effort results, and the chattering phenomenon is much reduced by the proposed FNN sliding-mode controller.

Patent
19 Aug 1999
TL;DR: In this article, a method and apparatus for tuning control loop parameters in a motion control system is presented, which can automatically predict, or simulate, the effects of the proposed parameters on bandwidth, gain margin and phase margin, based upon the composite data.
Abstract: A method and apparatus for tuning control loop parameters in a motion control system, is provided. In one embodiment, tuning of the proportional and integral gains of a servocontroller's velocity loop compensator is provided, as well as tuning of the cutoff frequencies of the servocontroller's low pass filters. In this embodiment, random noise excitation is added to the velocity command during a plurality of movement types for a machine tool axis. During each movement type, frequency response measurements are taken. Then, a composite frequency response can be selected by concatenating portions of the various frequency response measurements, so as to simulate a worst case scenario for the machine tool axis. From this composite response, an open loop response can be calculated and displayed, as well as bandwidth, phase margin, and gain margin values. The user can then enter the compensator parameters which were used when this data was taken, as well as proposed parameters. The system can automatically predict, or simulate, the effects of the proposed parameters on bandwidth, gain margin, and phase margin, based upon the composite data. Accordingly, the user need not actually try out the proposed parameters on the machine. Moreover, the simulated responses for the proposed parameters are based upon actual frequency response data taken during actual operating conditions of the system, and, accordingly, the inaccuracies of using mathematical assumptions are avoided.

Journal ArticleDOI
TL;DR: It is shown that a special type of DC-DC switched mode power supply can be handled by the theory of affine-input systems and the stability of the closed loop can be guaranteed in the sense of Lyapunov.
Abstract: We present a state feedback controller for the Cuk converter. It is shown that a special type of DC-DC switched mode power supply can be handled by the theory of affine-input systems. The controller design is based on the H/sub /spl infin//-theory of nonlinear systems. Using an appropriate exogenous system, the stationary control error can be made arbitrarily small. Furthermore, this design method leads to a simple controller and the stability of the closed loop can be guaranteed in the sense of Lyapunov. The implementation for a laboratory model shows a good tracking and disturbance behavior, which proves the feasibility of the proposed procedure.

Patent
13 Aug 1999
TL;DR: In this article, a sequencing control strategy for environmental system controllers that takes better advantage of the capabilities of the system elements to enhance performance and reduce operating costs is presented. But it is not suitable for the use of a single controller.
Abstract: The present invention provides a sequencing control strategy for environmental system controllers that takes better advantage of the capabilities of the system elements to enhance performance and reduce operating costs. Digital controller technology is included and operates in accordance with a state transition diagram clarifying conditions that must exist for the environmental controller to switch from one mode of operation to another (e.g., from a cooling mode with dampers set at the minimum position to a cooling mode with the dampers modulating to reduce the energy used for mechanical cooling). Several a controllers, or a single controller operating on several sets of control parameters, sequentially operate in accordance with transition data and system performance characteristics for controlling system operation.

Journal ArticleDOI
TL;DR: In this article, an anti-windup design for feedback linearizable nonlinear systems with input constraints, subject to dynamic controllers with linear dynamics and non-linear gains is proposed, which allows reducing the behavior of the closed-loop system under the dynamic feedback controller to that under a given static feedback linearizing controller, arbitrarily fast.
Abstract: This article addresses the problem of anti-windup design for feedback linearizable non-linear systems with input constraints, subject to dynamic controllers with linear dynamics and non-linear gains. A method for designing the controller gains and a non-linear 'observer-based' anti-windup modification is proposed, which allows reducing the behaviour of the closed-loop system under the dynamic feedback controller to that under a given static feedback linearizing controller, arbitrarily fast. The proposed anti-windup method allows, thus, to attenuate the effect of windup arbitrarily fast and guarantee that the region of closed-loop asymptotic stability under the dynamic controller is limited only by the corresponding region under the static feedback linearizing controller. The application and advantages of the method are illustrated through a simulation study on a methyl-methacrylate polymerization reactor.

Proceedings ArticleDOI
29 Nov 1999
TL;DR: The design, implementation and experimental results on load and no-load conditions are presented and the controller can be implemented by using only a small amount of components and easily improved to be an adaptive fuzzy controller.
Abstract: This paper describes an alternative method to implement a fuzzy logic speed controller for a DC motor using a fuzzy logic microcontroller. The design, implementation and experimental results on load and no-load conditions are presented. The controller can be implemented by using only a small amount of components and easily improved to be an adaptive fuzzy controller. The controller also provides high performance with compact size and low cost.

Proceedings ArticleDOI
02 Jun 1999
TL;DR: In this article, a combined steering and speed controller for the automated highway system (AHS) program of the California Partners for Advanced Transportation and Highways (PATH) is presented.
Abstract: This paper covers developments in the control integration part of the automated highway system (AHS) program of the California Partners for Advanced Transportation and Highways (PATH). The control integration project investigates the potential for improving controller performance through an integrated design of a combined steering and speed controller specifically designed to address the coupling between the steering and speed controls. The following results are presented: (1) the identification and characterization of the various coupling effects through an analysis of vehicle dynamics; (2) the design of a combined controller which compensates for the coupling effects; and, (3) the evaluation of the improvements contributed by the coupling compensation through simulations and through experiments on full-scale test vehicles. Sliding control and dynamic surface control (DSC) methods are used to facilitate the inclusion of the complex, nonlinear coupling effects in the controller derivation. A multiple-rate observer is designed to obtain a lateral velocity estimate which is essential to the implementation of the controller on the test vehicle. Simulations and experiments show that the coupling compensation does improve controller performance and that the combined controller is robust to modeling imperfections and vehicle parameter variations. The combined controller described in this paper may be the ideal basis for future implementation of the automated highway system.

Journal ArticleDOI
TL;DR: Experimental results are given to demonstrate the input-output controller's effectiveness in providing the tracking of a given position and speed trajectory while simultaneously tracking the optimal flux reference.
Abstract: Generalizes the authors' work on high-performance control of induction motors to machines that exhibit significant magnetic saturation. The controller design is based on the standard d-q model of the induction motor which has been modified to account for the saturation of the iron in the main (magnetic) path of the machine. An input-output linearization controller is used to provide independent (decoupled) control of the speed and flux. With this controller, the flux reference becomes an extra degree of freedom for the designer to help achieve performance objectives. Taking into account saturation along with the voltage and current constraints, the flux reference is chosen to achieve the optimal torque (maximum for acceleration and minimum for deceleration) at any given speed. Experimental results are given to demonstrate the input-output controller's effectiveness in providing the tracking of a given position and speed trajectory while simultaneously tracking the optimal flux reference. The set of experiments are fast point-to-point motion control moves with an inertial load comparing the input-output controller based on the saturated magnetics model with that based on the linear magnetics model.

Proceedings ArticleDOI
22 Aug 1999
TL;DR: In this paper, a differentiable, robust tracking controller for a mobile robot system is presented, which provides robustness with regard to parametric uncertainty and additive bounded disturbances in the dynamic model.
Abstract: Presents the design of a differentiable, robust tracking controller for a mobile robot system. The controller provides robustness with regard to parametric uncertainty and additive bounded disturbances in the dynamic model. Through the use of a dynamic oscillator and a Lyapunov-based stability analysis, we demonstrate that the position/orientation tracking errors exponentially converge to a neighborhood about zero that can be made arbitrarily small, i.e. the controller ensures that the tracking error is globally uniformly ultimately bounded (GUUB). In addition, we illustrate how the robust tracking controller can be reconfigured as a variable structure controller that ensures global exponential regulation to an arbitrary desired setpoint.

Proceedings ArticleDOI
02 Jun 1999
TL;DR: In this article, the output feedback controllers for disturbance attenuation of linear systems with constraints on input amplitudes and rates are studied, and the main features include guaranteed performance levels that depend on both actuator magnitude and rate limits, and controllers that operate at, or close to, maximum actuator capacity.
Abstract: Output feedback controllers for disturbance attenuation of linear systems with constraints on input amplitudes and rates are studied. The main features include guaranteed performance levels that depend on both actuator magnitude and rate limits, and controllers that operate at, or close to, maximum actuator capacity. The controllers have a structure similar to those used in the LPV approach.

Journal ArticleDOI
TL;DR: In this paper, a detailed optimal control design based on the general finite element approach for the integrated design of a structure and its control system is presented, where the output feedback controller is then employed to emulate the optimal controller by solving the Riccati equations from the modal space model.
Abstract: This numerical study presents a detailed optimal control design based on the general finite element approach for the integrated design of a structure and its control system. Linear quadratic (LQ) theory with output feedback is considered on the basis of the state space model of the system. Three-dimensional finite elements are used to model the smart structure containing discrete piezoelectric sensors and actuators by the use of combination of solid, transition and shell elements. Since several discrete piezoelectric patches are spatially distributed in the structure to effectively observe and control the vibration of a structure, the system model is thus utilized to design a multi-input-multi-output (MIMO) controller. A modal analysis is performed to transform the coupled finite element equations of motion into the state space model of the system in the modal coordinates. The output feedback controller is then employed to emulate the optimal controller by solving the Riccati equations from the modal space model. An optimal controller design for the vibration suppression of a clamped plate is presented for both the steady state and the transient case. Numerical simulation is also used to predict the reduction in the sound pressure level inside an enclosure radiated from this optimally controlled plate.

Journal ArticleDOI
TL;DR: The unity power-factor controller for a sinusoidal input current is derived using the feedback linearization concept and two active switches and two diodes are utilized for AC-to-DC power conversion.
Abstract: A novel power-factor controller for single-phase pulsewidth modulated rectifiers is proposed. The unity power-factor controller for a sinusoidal input current is derived using the feedback linearization concept. Two active switches and two diodes are utilized for AC-to-DC power conversion. Experimental results obtained on a 4 kW prototype are discussed.

Proceedings ArticleDOI
02 Jun 1999
TL;DR: In this paper, a nonlinear active suspension controller is proposed to compensate for the hydraulic actuator dynamics by using adaptive robust control technique, which is used to design a force controller such that it is robust against actuator uncertainties.
Abstract: Presents a nonlinear active suspension controller, which achieves high performance by compensating for the hydraulic actuator dynamics. The control design problem is decomposed into two loops. At the top is the main loop, which calculates the desired force signal by using a standard LQ design process. An adaptive robust control technique is used to design a force controller such that it is robust against actuator uncertainties. Both state feedback and output feedback algorithms are presented. Simulation results show that the proposed controller works well compared with conventional controllers.

Journal ArticleDOI
T. Hara1, Masayoshi Tomizuka
TL;DR: A new multi-rate controller for hard disk drives is described, which has a modified state estimator to correct the estimated states not only at measurement instances of the position error signal but also at every control instance when updating the control input.
Abstract: This paper describes a new multi-rate controller for hard disk drives, which has a modified state estimator to correct the estimated states not only at measurement instances of the position error signal but also at every control instance when updating the control input. This modification makes the control input smoother compared to the conventional multi-rate scheme. This estimator is obtained as a stochastic optimal estimator for a linear dynamic system with a 'random walk' input noise process. The effectiveness of the modified scheme is demonstrated by experiments.

Journal ArticleDOI
TL;DR: In this article, an accurate dynamic modeling and quantitative controller design for an isolated converter with optocoupler isolation in its feedback loop are considered, since the transfer characteristics of some blocks are highly nonlinear and difficult to be modeled analytically.
Abstract: The accurate dynamic modeling and quantitative controller design for an isolated converter with optocoupler isolation in its feedback loop are considered to be difficult issues, since the transfer characteristics of some blocks are highly nonlinear and difficult to be modeled analytically. First a current-mode controlled flyback converter with an optically isolated feedback path is designed. Then the equivalent control system block diagram is constructed, and its block transfer functions are found. To increase the accuracy, the dynamic models of some critical blocks are estimated from measurements. In order to facilitate the controller design, the model simplification is further made. Finally, based on the reduced dynamic model, a quantitative design procedure is derived to find the parameters of the voltage controller to meet the prescribed regulating specifications. Validity of the estimated dynamic model and the proposed controller design approach is demonstrated by some simulation and experimental results.

Proceedings ArticleDOI
TL;DR: It is proved that if the output and its derivatives up to a given order are driven to zero, and if the system owns a certain Lipschitz property in a suitable neighborhood of the origin, then the system state asymptotically goes to zero.
Abstract: In previous papers the authors presented an elementary theory for feedback control of nonlinear delay systems, in which methods of standard nonlinear analysis were used to solve control problems such as output regulation and tracking, disturbance decoupling and model matching for a class of nonlinear delay systems. Output control was obtained by means of state feedback control laws, but nothing was said about the behavior of the system state. In this paper some results have been obtained about this problem. It is proved that if the output and its derivatives up to a given order are driven to zero, and if the system owns a certain Lipschitz property in a suitable neighborhood of the origin, and the initial state is inside such neighborhood, then the system state asymptotically goes to zero. Simulations on nonlinear delay systems unstable in open loop match the theoretical results.

Proceedings ArticleDOI
02 Jun 1999
TL;DR: Lifting techniques provide a suitable framework for posing a multirate univariate/multivariate problem as a multivariable single-rate problem as well as providing benchmarks for comparing the closed-loop performance of multi-rate and single rate systems in the LQR framework.
Abstract: Multirate systems are encountered when some signals of interest are sampled at a different rate than others. For example, in the process industry, composition measurements in distillation columns are typically sampled at a slower rate than temperatures and flow rates. In the context of closed-loop control, such multirate systems pose a challenging problem due to several reasons such as increased complexity in the design with tighter performance specifications. Lifting techniques provide a suitable framework for posing a multirate univariate/multivariate problem as a multivariable single-rate problem. We discuss the application of lifting techniques with respect to asymptotic setpoint tracking. Theoretical results are provided to show that there are constraints on the controller gains for step-type reference signals to ensure there are no intersample oscillations in the closed-loop system. Discrete lifting usually introduces non-uniform steady-state gains for the open-loop lifted model which could result in oscillatory continuous output signals for the closed-loop system. These results are supported by simulation results of a slow sampled and fast control system. Further, we provide a continuous-time interpretation to the design of multirate controllers while providing benchmarks for comparing the closed-loop performance of multi-rate and single rate systems in the LQR framework.

Proceedings ArticleDOI
01 Jan 1999
TL;DR: The analysis of multi-rate controllers, which update the controller output faster than the measurement sampling frequency by a factor of N, is concerned, and the discrete time controller is obtained as its zero order hold equivalent.
Abstract: The paper is concerned with the analysis of multi-rate controllers, which update the controller output faster than the measurement sampling frequency by a factor of N. The controlled system is continuous, and the discrete time controller is obtained as its zero order hold equivalent. After deriving a set of equations necessary for analysis and design of multi-rate systems, the open loop characteristics of the multi-rate controller and the closed loop characteristics are examined. Several physical meanings can be derived from the formulation of the multi-rate controller.

Patent
26 Feb 1999
TL;DR: In this article, a gas supply system for supplying a gas into a reaction chamber is provided with a pulse valve, a mass flow controller and a back pressure controller, which are connected to a controller so that operations thereof are controlled by this controller.
Abstract: A gas supply system for supplying a gas into a reaction chamber is provided with a pulse valve, a mass flow controller and a back pressure controller. The mass flow controller includes a flow meter and a variable flow control valve, and the back pressure controller includes a pressure gauge and a pressure control valve. The pulse valve, the mass flow controller and the back pressure controller are connected to a controller so that operations thereof are controlled by this controller.