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Virtual analogue simulation of control systems

International Journal of Electrical Engineering Education, Jul 1997 by Cheung, W N

Abstract This article describes the method of virtual analogue simulation (VAS) using PSpice for learning control systems. Examples are included to demonstrate the application of VAS in studying system transient responses. The effects of controller compensation, component nonlinearity, and transport delays on system performance can be observed readily with VAS.

1 INTRODUCTION

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Historically, computer simulation employs analogue, digital or hybrid computers to provide solutions to a physical system which can be described by mathematical models. Simulation often allows us to focus on the response of the physical system rather than the arduous process of mathematical formulations. It has become a standard approach for designers of new engineering projects. Simulation is also a powerful learning tool. It removes the worry from students of the abstract mathematics involved in system analysis on the one hand, and, on the other, it bypasses any practical problems associated with making equipment work properly in the laboratory. Traditionally, simulation has been used extensively in teaching control systems to engineering students. This is mostly due to the fact that real-life control systems are of numerous varieties and sizes, and are often too expensive to install in the teaching laboratory.

Of the many sound educational arguments for employing simulation in teaching electrical engineering"-3, the following are particularly applicable to teaching control systems:

* to enhance the understanding of theories taught in the class,

* to overcome some analytical difficulty for beginning students, and to facilitate the study of realistic systems that may include nonlinearity, delay, etc., which are not in general easily analysed mathematically. Software packages such as MATLAB^sup 4^ and TUTSIM^sup 5^ have been used at tertiary institutions as teaching aids in control systems. Because PSpice6 has already been extensively used in learning electronic circuits by many students, it is our objective to broaden its application to the study of control systems. The concept of a PC-based analogue computer has been reported in Ref. [7]. The method is further developed and more applications are discussed in this paper.

2.2 Computer simulations

In digital simulation, the system will be represented by a set of canonical state variables which will be solved by standard matrix manipulation and numerical integration. This approach is powerful for advanced studies in control systems, but is rather too theoretical for beginning students.

Analogue simulation, on the other hand, is attractive in that there is a close analogy between the original system and its electronic circuit model. Different parts of the system may be treated as modules and simulated separately. These modules may then be connected together to form a whole system just as in its physical counterpart. It provides a clear insight into the function of each part of the system. However, the conventional analogue computer has the following limitations:

the number of available integrators, summing devices and amplifiers are relatively small - this imposes restrictions on the size of the system to be studied;

speed limitation on operational amplifiers - this requires time scaling;

the voltage range of amplifiers is limited - this imposes saturation levels and therefore requires amplitude scaling.

2.3 Virtual analogue simulation

Because of its inflexibility and high cost, the analogue computer has been largely superseded by digital tools. With the availability of PC's, a 'virtual' analogue machine can be implemented using software such as PSpice. The advantages of virtual analogue simulation (VAS) are:

* it is possible to have almost ideal integrators and amplifiers, which are not subject to amplitude or frequency constraints, hence no need for amplitude or frequency scaling;

* programming may take the form of drawing an analogue simulation schematic diagram or a text file description of the same diagram;

* it does not require the amount of unwieldy wiring needed on the real machine;

* change of parameters or interconnections can be made easily;

* both transient and frequency response of the simulated system can be obtained;

* system imperfections such as feedback delay and nonlinearity can be implemented without additional difficulty.

The state diagram of Fig. 1 can be realised using software implemented electronic circuits, which are similar to the physical circuits used on a conventional analogue computer. Such an implementation is illustrated as shown in Fig. 2, which involves integrators, summing amplifiers or circuits, controlled voltage or current sources, and appropriate control inputs.

The integrator has unity time constant, and it is constructed as a sub-circuit which may be called as many times as needed in the VAS system. The amplifier used in the integrator is modelled by an input resistance equal to 10 MQ and an open-circuit voltage gain of -105. Since the integrator is inverting, we use an inverting voltage-controlled voltage source (VCVS) at the input of each integrator to compensate for the negative sign, hence resulting in non-inverting integration.

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Virtual analogue simulation of control systems

International Journal of Electrical Engineering Education, Jul 1997 by Cheung, W N

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