Symbolic Array Programming for Control System Analysis by Digital Computer

Design and analysis of high-order control systems requires a great deal of laborious calculations. Stability analyses are usually conducted with standard techniques such as root locus or frequency response. The calculations involved in these analyses are generally too complex to do by hand. Graphical techniques and approximations may be used, but often introduce unacceptably large errors.

The computer program LCAP2 (Linear Controls Analysis Program) provides the analyst with the capability to numerically perform classical linear control analysis techniques such as transfer function manipulation, transfer function evaluation, frequency response, root locus, time response and sampled-data transforms. It is able to deal with continuous and sampled-data systems, including multiloop multirate digital systems, using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s, z</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</tex> transforms. This program has been used extensively for years at the Aerospace Corporation in the analysis and design of satellite and launch vehicle control systems.

Stability and steady state analysis of control and safety systems of Nuclear Power Plants

Distributed control systems are crucial for regulating manufacturing processes by controlling field devices. Delays in device operation can significantly impact the time response of the process control system, affecting overall stability. To enhance network performance and process time response, it is essential to study the inherent delays of field and network devices. This paper examines process control loops involving a 3-layered network based on the OSI model’s physical, network, and application layers. The proposed networked control system assesses time delays within and between field devices configured through these layers, which are essential for control loops, including open, closed, and cascade loops. Analyzing these time delays enables effective control loop configuration, improving the process control time response and overall stability.

This paper describes a package of digital computer subprograms which provides control systems engineers at Autonetics with an easy-to-use, comprehensive, and flexible design-aid tool The subprograms are written in FORTRAN IV for the IBM 7094. Most of the subprograms are similar to ones found in almost every company's program files. They provide such standard capabilities as the generation of Bode plots, Root Locus plots, Nyquist plots, Nichols charts, and time and frequency response. The package contains three subprograms, however, which are not standard. These employ dichotomous techniques to generate transfer functions for active networks and continuous control systems. Since these techniques are currently attracting widespread interest, the three subprograms which implement them will be discussed in some detail.

The description presents a general programming technique in ALGOL using a KDF9 computer for time-response computation for linear control systems. It is a continuation of the method used for frequency-response computation and plotting. 1-5 The control system is introduced to the computer in symbolic-array form through the input data. To compute the responses of different control systems or to improve the system by compensation or optimisation, all that is necessary is to change the input data for every transfer function, leaving the main program unaltered. The program can be used to analyse control systems containing one real pole or a pair of complex poles, of nth-order multiplicity with any number of simple poles and zeros.

Stability is one of the most important concepts of analysis and design of control systems. Stability analysis of fuzzy control systems has been difficult since fuzzy systems are essentially nonlinear systems. Recently, stability analysis techniques [l]-[6] [13]-[16] based on nonlinear stability theory have been reported. Langari and Tomizuka [2, 6] analyzed stability of fuzzy linguistic control systems. Kitamura [3] realized stability analysis of fuzzy control systems by using extended circle criterion. Farinwata [5] and Kato [14] utilized phase plane analysis type of techniques, tanaka and co-authors [1,3,4] applied Lyapunov approach to fuzzy control systems and recently developed LMI-based designs [10, 17, 28-37], where LMI stands for nonlinear matrix inequality.

One of the primary concerns in industrial motor drive systems is the suppression of the vibration caused by the elasticity of mechanical load. This paper is intended to clarify the conditions required to obtain the desirable damping by a simple control system through the analysis of the frequency response of a two-mass control system, considering the plant of left-coprime factorized form. The paper also presents some useful findings for practical design of the vibration suppression control, showing that if the above-mentioned conditions are satisfied, sufficient control performance can be obtained by a two degrees of freedom controller of the same structure as that for rigid load, and that we are compelled to reduce the stability margin in the vibration suppression control where the anti-resonant frequency and resonant frequency are near to each other.

The paper presents a method of engineering analysis and design for complex control systems, the time-domain infinite-matrix method. The formulation of the infinite matrix follows from the convolution summation of sampled-data systems. The mathematical basis of the time-domain matrix formulation is related to the applicable concepts of infinite matrices and sequence spaces. The method is applicable to both continuous-data and sampled-data systems. For continuous systems it is necessary to introduce a fictitious sampler and `hold? of sufficient sampling rate to effect an accurate approximation. The time-domain-matrix method is presented and illustrated as a method of analysis and design of linear, non-linear, and time-varying systems of the continuous-data or sampled-data class. The investigation of non-linear systems is greatly simplified by the time-domain approach. Multi-loop systems may be investigated, and the signals at intermediate points throughout the loops are readily available. Also, systems with multiple non-linearities may be investigated. Two methods of design of a discrete compensator for a sampled-data system are presented. These methods are accomplished directly in the time domain and allow for a compromise of specifications in the time domain. In one design procedure the response between sampling instants is also accounted for. The time-domain-matrix method may be readily programmed on a digital computer, and therefore provides a rapid analysis and design technique.

The introduction of the root-locus method in the z-plane simplifies the investigation of sampled-data control systems, by demonstrating the correlation between transient response and the location of the roots. It is shown that by establishing the correlation between frequency locus and the root locus, the correlation between frequency and transient response of sampled-data systems can be demonstrated.

Design, Analysis and Real-time Implementation of Networked Predictive Control Systems

Frequency responses are frequently referred to in the stability analysis of fractional order control systems. Frequency response-based methods have been introduced in the literature to reduce complex fractional order systems. However, the magnitude and phase response improvement is not handled by these techniques. The optimization methods are utilized to improve the approximation of fractional order filters in the desired frequency range. The article discusses the ideal Fractional-Order Butterworth Filter (FOBF) configuration by utilizing integer-order rational approximations to achieve a precise magnitude and phase response. Additionally, this study utilizes optimal FOBF magnitude and phase characteristics to minimize errors and expands the approximation bandwidth to cover multiple decades in both pass and stop bands. Optimized fractional order Butterworth filter designs have been implemented in biomedical signal processing, audio engineering, telecommunications, and control systems, enhancing performance in noise reduction and signal fidelity across these applications. It is essential to precisely determine these transfer functions regarding frequency and time responses. Therefore, there is room for further enhancements in these approximation methods to reduce errors and enhance the accuracy of real-world implementations. In pursuit of this goal, the study introduced a powerful metaheuristic optimization technique called Enhanced Colliding Bodies Optimization (ECBO), which not only showcases better precision in modelling but also exhibits a higher level of stability when compared to existing methods. This process guides all entities towards an optimal solution in each successive round, boosting the likelihood of finding a superior solution and thoroughly examining the full range of potential solutions. This technique better fits the BF filter function to a fractional-order continuous filter. The digital integrator is optimized in the frequency domain using the Coyote Optimization Algorithm (COA) because of its effectiveness, ease of use, and strength in tackling various complex optimization challenges. This optimizes the magnitude and phase reaction of the low-pass BF filter depending on the Minimum Square Error (MSE). Expanding the scope of the ECBO’s search range allows the enhanced filter to closely replicate the frequency behaviour of fractional order continuous filter functions.

ABSTRACTIn this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.

The determination of the mathematical expectation and correlation function of the output signal of discrete automatic control systems with varying parameters is considered. The statistical characteristics of the output signal are determined by means of an expansion in a certain specially formulated orthonormalized system of functions. The computing algorithm may be realized on a digital computer.

Context. The question of increasing the productivity of technological processes of extraction, processing and preparation of raw materials, improving product quality, reducing energy consumption, as well as creating safe working conditions during technological processes and preventing accidents is always quite relevant and requires the implementation of modern control and management systems. For the effective operation of such systems, it is important to pre-process and filter the data received from the sensors for monitoring the grinding processes and the explosive status of objects. One of the possible ways to increase the informativeness of data is the use of singular spectral analysis.Objective. Increasing the efficiency of technological process control systems and the reliability of explosive control systems of coal mines and oil and fuel complex facilities by processing and pre-filtering data received from sensors for monitoring grinding processes and the state of facilities.Method. To analyze the output signals of sensors used in control and management systems, the method of singular spectral analysis is used, which allows revealing hidden structures and regularities in time series by pre-filtering and data processing of acoustic, thermocatalytic, and semiconductor sensors.Results. A new approach to the management of technological processes of grinding raw materials in jet mills and control of the explosiveness of coal mines and objects of the oil and fuel complex is proposed, based on methods that allow to speed up the processing speed of sensor output data and improve the quality of information. It is shown that one of the promising methods that can be used for the pre-processing of time series of output data of sensors in control and control systems is the method of singular spectral analysis, the use of which allows filtering data, revealing hidden structures and regularities, and forecasting changes based on the analysis of previous information , identify anomalies and unusual situations, make more informed decisions and improve the processes of managing technological processes.Conclusions. The conducted experiments have confirmed the proposed software operability and allow recommending it for use in advancing both theoretical and practical aspects of process control systems through an enhanced singular spectral analysis (SSA) method for time series processing. This improved approach has been successfully demonstrated in real-world applications, including grinding processes in jet mills and explosion monitoring in coal mines and oil and fuel facilities. The implementation demonstrates a significant increase in data processing speed and information quality, which makes it particularly valuable for use in safety-critical industrial facilities.