Abstract
In order to predict the performance of an automatic regulator, it is necessary to know the characteristic of the plant to which the regulator will be applied. A plant may consist of one or more capacities separated by resistances, and is characterized by its plant constants.
The behaviour of an uncontrolled plant can be described by a non-homogeneous differential equation of the same order as the number of capacities forming the plant. The independent variable in this equation is the time; the dependent variable is the deviation of the plant from equilibrium; and the disturbance function is a function of the disturbance applied to the plant. This disturbance function and the resulting deviation will, in general, be different for disturbances created at the supply and discharge side of the plant.
The use of hydraulic plants as models demonstrates clearly the physical meaning of the terms involved which can easily be translated into terms of thermal, flow, electrical, or other problems. Assuming a viscous medium with linear resistance to flow, linear differential equations are obtained and the deviations from equilibrium due to different forms of disturbances are examined for single- and multiple-capacity plants. Inversely, it is demonstrated how the plant constants can be determined from observed deviations when definite disturbances are applied to the plant.
It is also shown why, for the control of multiple-capacity plants, it may be of advantage to use regulators that respond not only to the deviation from equilibrium but also to the speed and the higher derivatives of the deviation. The relative merits of placing the regulator at the discharge or supply end of the plant are also discussed.
Finally, it is indicated how the equations of a regulator and of the plant can be combined to describe the behaviour of the regulating system and the interaction of regulator and plant, and how its stability criteria can be established.
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