Response Of Closed-loop System Research Articles

Time-domain analysis and synthesis of active noise control systems in ducts

This paper presents time-domain analysis and synthesis of active low-frequency noise control systems in rigid-walled ducts. In contrast to frequency-domain analysis, time-domain modeling provides a direct physical insight of the noise cancellation mechanism, where noise signals are assumed to be arbitrary real functions of time instead of harmonics. The time-domain analysis is based on a state-space model which is derived from the governing wave equation using combined numerical (finite difference) and analytical techniques. Optimal feedback control laws are synthesized for a variety of active noise control systems with different sensor and source arrangements. The responses of closed-loop systems are simulated, and the results are compatible with those of transfer function synthesis. In addition, the active control systems so designed have the potential of providing global, broadband, and optimal noise reductions without running into the annoying feedback problems in most feedforward control systems.

Development of a feedback controller tuner using virtual fuzzy sets

This paper presents the development of a fuzzy tuner for tuning PI and PID feedback controllers. The implementation is based on the concept of virtual fuzzy sets and an adaptive fuzzy inference scheme. The tuner uses the standard Ziegler-Nichols tuning rules for initial gain setting according to the open-loop step response of the process. Then the fuzzy system fine tunes the controller iteratively based on the performance of the closed-loop controlled system response. The tuning knowledge is extracted automatically from the tuning of a representative process. Expert rules of thumb can be incorporated into the rule base, and explanatory capability is also available through the use of the IF-THEN rule base. Finally, examples covering a wide range of process dynamics are tested to demonstrate the excellent performance of the tuner.

Modelling and controller design of an isolated diesel engine permanent magnet synchronous generator

A method to analyze the steady-state performance of a stand-alone permanent magnet synchronous generator driven by a diesel engine is presented. The proposed method is based on equivalent d-q circuits and the phasor diagram of such a generator under steady-state conditions. A fixed capacitor-thyristor controlled reactor scheme is used to regulate the generator terminal voltage by controlling the thyristor ignition angle. Furthermore the overall system dynamics are modelled in terms of state variables and control inputs. Based on a reduced order linearized model, digital optimal state and output feedback controllers are designed by minimising a quadratic performance index using the dynamic programming technique. The objective of the controller is to maintain the load voltage and frequency constant under varying load conditions. The controller's effectiveness is assessed by examining the closed-loop system response to sudden load changes.

Identification of Stochastic System and Controller via Projection Filters

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

Auto-Tuning of Low-Order Controllers by Direct Manipulation of Closed-Loop Time Domain Measures

Many controller tuners are based on linear models of both the controller and process. Desired performance is often predetermined or adjusted in a manner that is not directly related to the desired response. All physical processes contain non-linearities, commonly of the actuator saturating type, and many controllers contain heuristics for implementation in real systems, such as anti-integral wind-up in PID (proportional integral differential) controllers. For different processes a range of closed-loop response shapes are desired, often described by features of the response such as rise time, overshoot and settling time. This paper investigates the possibility of basing controller tuning on closed-loop system response data such that desired performance is incorporated directly in terms of familiar time domain features or labels, thus eliminating the need for a mathematical process model and repeated tuning reformulations to achieve the desired performance. A controller tuning method named label-based neuro-tuning (LBNT) is developed and analysed by application to PID controller tuning for process models indicative of real process behaviour. Simulations and numerical investigation indicate that LBNT is a viable technique for the tuning of low-order SISO (single-input-single- output) controllers. Tuning is straightforward, flexible and copes well with process parametric changes and performance specification reformulation. The drawbacks are a complicated pretune phase, a limited selection of suitable labels and a difficulty in defining general classes of tuning problems for its application. The technique is not based on the assumption of process linearity, but due to the inability to characterize classes of input signals and operating points the types of process non-linearity are restricted. The controller may be non-linear, but must be structurally predetermined, and an input/output process model of arbitrary structure is required.

Closed-loop system identification using the dual Youla control parametrization

Identification of an unknown plant operated in a closed-loop environment in the presence of external disturbance is considered. Under closed-loop experiment, the objectives of system identification are not only to obtain a best fit of the unknown plant but also to make close prediction or estimation of closed-loop system responses. By using the a priori information of a known stabilizing controller and the dual Youla control parametrization, identification of an unknown plant in a closed-loop system can be simplified to that of an open-loop reduced system. It is shown that the output prediction errors of the estimates for both the original plant and the reduced system are equal. Furthermore, if the feedback controller is of normalized coprime factorization, then to find a best fit of the reduced system amounts to establishing a nominal closed-loop system with which the signals of the true closed-loop system can be predicted in a least squares sense. In addition, the optimal experimental designs for reducing bias distribution of the estimate of the reduced system, fitting of closed-loop frequency responses, and estimating the unknown plant expressed by coprime factors are coincidental.

Optimal Tracking Control of Multi-Zone Indoor Environmental Spaces

Optimal control of indoor environmental spaces is explored. A physical model of the system consisting of a heating system, a distribution system and an environmental zone is considered and a seventh order bilinear system model is developed. From the physical characteristics and open-loop response of the system, it is shown that the overall system consists of a fast subsystem and a slow subsystem. By including the effects of the slow subsystem in the fast subsystem, a reduced order model is developed. An optimal control law is designed based on the reduced order model and it is implemented on the full order nonlinear system. Both local and global linearization techniques are used to design optimal control laws. Results showing the disturbance rejection characteristics of the resulting closed-loop system are presented. The use of optimal tracking control to implement large changes in setpoints, in a prescribed manner, is also examined. A general model to describe environmental zones is proposed and its application to multi-zone spaces is illustrated. A multiple-input optimal tracking control law with output error integrators is designed. The resulting closed-loop system response to step-like disturbances is shown to be good.

A neural network PI controller tuner

The development of a neural network system for tuning proportional and integral (PI) feedback controllers is presented. The tuning process includes an initial gain setting procedure and a fine tuning procedure. The initial gain settings are obtained by using the standard Ziegler-Nichols tuning rules based on the openloop step response of the process. The fine tuning procedure is performed iteratively by using a neural network. The neural network suggests adjustments to the proportional gain and integrator time based on the closed-loop controlled system response. Four parameters are defined to describe the response characteristics. They are the normalised peak rise time, normalised overshoot, normalised peak to peak height, and normalised final error. These four parameters are used as inputs to the neural network. The tuning knowledge of the neural network is extracted from the tuning of a representative process. Finally, examples covering a wide range of process dynamics are tested to demonstrate the excellent performance of the tuner.

Active Control of Chaotic Vibration in a Constrained Flexible Pipe Conveying Fluid

An active vibration control system is designed, and is numerically verified, to suppress the undesirable chaotic vibration in a constrained flexible pipe conveying fluid, which exhibits regions of flutter and chaotic motions at sufficiently high flow velocity. The four-dimensional analytical model obtained from the continuous system by Galerkin's method, that has been previously verified to represent adequately the dynamics, is utilized for designing the control law. Various control design methodologies are investigated for different situations. Firstly, optimal regulator theory is applied to obtain feedback gains to stabilize the system with full state information. The effects of the location and length of the piezoelectric actuators on the efficiency as a vibration damper are theoretically examined in this case. Secondly, a state observer is added to estimate the required state signals. To cover the situation when the states are not directly measurable, dynamic compensators are obtained to control the system with only the output feedback. Finally, a robust controller for such a system with large flow velocity variations, without sensing the flow velocity or gain-scheduling, is developed. The robust control method is based on a newly developed sensitivity-based Quantitative Feedback Theory (QFT) scheme, which allows the controller to make the closed loop system response meet quantitatively specified performance requirements even though the system has large parameter variations. Numerical simulations are carried out for the different controllers and they validate the effectiveness of the proposed control scheme. The QFT scheme yields a remarkable result in stability robustness with respect to flow velocity variations.

Robust Control of Flexible Structures Using Multiple Shape Memory Alloy Actuators

The design and implementation of control strategies for large, flexible smart struc tures presents challenging problems. To demonstrate the capabilities of shape-memory-alloy (SMA) actuators, we have designed and fabricated a three-mass test article with multiple shape-memory- alloy, NiTiNOL, actuators. Both force and moment actuators were implemented on the structure to examine the effects of control structure interaction and to increase actuation force. These SMA actu ators exhibit nonlinear effects due to dead band and saturation. The first step in the modeling process was the experimental determination of the transfer function matrix derived from frequency response data. A minimal state space representation was determined based on this transfer function matrix. Finally, a reduced order state space model was derived from the minimal state space representation. The simplified analytical models were compared with models developed by structural identification techniques based on vibration test data. From the reduced order model, a controller was designed to dampen vibrations in the test bed. To minimize the effects of uncertainties on the closed-loop system performance of smart structures, a linear quadratic Gaussian loop transfer recovery, LQG / LTR, control methodology was utilized. A standard LQG/LTR controller was designed; however, this controller could not achieve the desired performance robustness due to saturation effects. Therefore, a modified LQG / LTR design methodology was implemented to accommodate for the limited control force provided by the actua tors. The closed-loop system response of the multiple input multiple output (MIMO) test article with robustness verification was experimentally obtained and is presented in this paper. The modified LQG / LTR controller demonstrated performance and stability robustness to both sensor noise and parameter variations.

Dynamic Modeling and Control of Packing Pressure in Injection Molding

A dynamic model of injection molding developed from physical considerations is used to select PID gains for pressure control during the packing phase of thermo-plastic injection molding. The relative importance of various aspects of the model and values for particular physical parameters were identified experimentally. The controller gains were chosen by pole-zero cancellation and root-locus methods, resulting in good control performance. Both open and closed-loop system responses were predicted and verified, with good overall agreement.

Identification of system, observer, and controller from closed-loop experimental data

This paper considers the identification problem of a system operating in a closed loop with an existing feedback controller. The closed-loop system is excited by a known excitation signal, and the resulting time histories of the closed-loop system response and the feedback signal are measured. From the time history data, the algorithm computes the Markov parameters of a closed-loop observer, from which the Markov parameters of the individual open-loop plant, observer, and controller are recovered. A state-space model of the open-loop plant and the gain matrices for the controller and the observer are then realized. The results of the paper are demonstrated by an example using wind tunnel aircraft flutter test data.

ROBUST CONTROL OF A CHAOTIC VIBRATORY SYSTEM

An active robust control system is designed, and is numerically verified, to suppress the undesirable chaotic vibration in a constrained flexible pipe conveying fluid, which exhibits regions of flutter and chaotic motions at sufficiently high flow velocity. The four-dimensional analytical model obtained from the continuous system by Galerkin's method is utilized for designing the control law. Some interesting nonlinear behaviors with the four-dimensional analytical model are discussed as well. Without sensing the flow velocity or gain-scheduling, a robust controller is developed for the system under large flow rate variations by using a newly developed Quantitative Feedback Design (QFD) method. This technique allows the controller to make the closed loop system response meet quantitatively specified performance requirements even though the system has large parameter variations. Numerical simulations validate the effectiveness of the QFD method which yields a remarkable result in stability and performance robustness with respect to flow velocity variations.

Energy start-stop and fluid flow regulated control of multizone HVAC systems

Temperature control of multizone indoor environmental spaces heated by a water-loop heat-pump system is studied. The system consists of a boiler, an evaporative cooler, heat pumps, a storage tank and environmental zones. An analytical model for the system is developed and a multivariable control strategy, which consists of both start-stop and integral mode controllers, is designed. Results showing the closed-loop system response subject to changes in heating and cooling loads are given.

Temperature and humidity control of indoor environmental spaces

The temperature and humidity control of indoor environmental spaces is studied. A constant volume heating and humidification system consisting of a boiler, a heating coil, ductwork and a fan, and a two-zone building is considered. The temperature and humidity control models are developed and multivariable controllers are designed. The closed loop system responses subject to step disturbances in outdoor temperatures and relative humidity are given. Also, results showing a typical-day operating performance of the closed loop system are given.

A Discrete Version of Zakian's Method of Inequalities

Abstract The method developed in this correspondence, is aimed for finding a series or adjustable parameters or a digital controller followed by observation the closed-loop system response to step input until a satisfactory performance specifications are obtained. The method is based on three main algorithms; the stabilization algorithm, The search technique and a method for the computation or time response

Optimization method for PID controller design

An optimization method for PID controller design is delt with in this paper. In handling the design problem, the simplex method and Powell's method in nonlinear programming are used under a flexible objective function that provides design options of closed-loop system response curves to meet various practical requirements. Numerical examples are given to demonstrate the design procedures.

Microcomputer-Based Digital Control Laboratory Exercises

This paper describes a set of laboratory exercises, concerning computer-controlled systems. A personal computer and a real plant are used to present chosen aspects of digital control systems, like obtaining a discrete-time model of a plant, design, and behavior of some representative, digital control algorithms, synthesized in the domain of polynomials. The exercises are performed with an extensive computer help, in order to allow a student to concentrate on a specific control problem. The control laws, presented in the exercises, are: PED controller, pole-placement controller and self-tuner. The paper presents in a detailed way an experiment in pole-placement design. A real plant is used for the experiments, namely a heated-air column apparatus. This plant is connected to an IBM PC, which is used as a computational tool. A unified software, based on the Matlab CAD package and on the Modula2 programming language, is developed for the exercises. Using this software, the student can design a controller, simulate a closed-loop system response, activate a realtime control program and, finally, after performing an experiment, post-process the results. The software is menu driven and easy to use.

A New Approach to the Direct Synthesis of a Digital Controller

A procedure for the design of digital controllers, without referring to the analytical model of the closed loop system, is presented. The pocedure can be applied when the model of the plant is available and the sampling time is fixed. The main requirements of a closed-loop system are defined by referring to the step and the frequency responses.By applying a spline function approximation, the sampled values of the impulsive response of closed-loop system are directly worked out. From these latter the controller is synthetized as a non recursive filter by applying a deconvolution approach. Since the implementation of a non recursive filter could require a computing time not compatible with the sampling time, a recursive filter can be deduced from the sampled values of the impulsive response of the controller. Identification procedures, based on the least square approximation, can be suitably used to this aim. An appropriate choice of the structure of the recursive filter allows to improve the accuracy without increasing its order.A CAD program, based on the proposed procedure, has been assembled by using only few commads of the MATLAB package. The program has been organized so as it can be by people not acquainted with the control of digital systems but intesested to improve the performance of the closed-loop system by using a signal processor for implementing the controller.

Brief communication, Digital control loop based on a microprocessor for optimal gain tuning

This paper investigates the hardware implementation of a digital control loop based on a microprocessor for optimal gain tuning. It consists of a digital controller implemented on an 8085 microprocessor and an analogue plant simulation (implemented on an analogue computer). Automatic adjustment of a time-variant gain controller is carried out to improve the dynamic performance of the closed-loop system response. The optimum tuning for the gain contoller is solved analytically using the Phillips integral algorithm in the sense of minimizing the integral-squared error (ISE) criterion formulated in the time domain. An example of a third-order servomechanism control system is considered to show the usefulness and efficiency of this technique in improving the transient response of the closed-loop control system. A comparison is made between the theoretical system response (obtained using an off-line computation procedure) and the real-time implementation of the control problem.