Siemens PCS 7 2.3 Examples of Unstable Control Loops

Introduction

MPC Level

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2.3 Examples of Unstable Control Loops

If the level of a tank with continuous feed is to be controlled via an adjustable drain

as actuator (e.g. pump or valve with or without flow control), the control loop shows

integrating behaviour.

An equilibrium condition of the level only exists if the drain is exactly equal to the

feed. The level permanently decreases until the tank is empty, if the drain is in-

creased stepwise starting at this equilibrium condition. In contrast the level perma-

nently increases until the tank overflows, if the drain is decreased stepwise starting

at the equilibrium condition.

Figure 2-2 Types of level control, taken from Related Literature /1./.

Exception natural drain: If only a valve with constant pressure behind exists in the

drain of the tank, the drain flow depends according to the drain formula of Toricelli

not only on the valve position (manipulated variable of the controller) but also

nonlinearly on the level h itself (proportional to gh2 with acceleration of gravity

g). Compensation can be reached after small steps in the valve position in such

control loops. The level is decreasing if the valve at the drain is opened a little bit

starting at the equilibrium condition. Thus the hydrostatic pressure at the bottom of

the tank is decreasing, and accordingly the drain flow is decreasing until a new

equilibrium condition is reached. Anyway, the application of the techniques de-

scribed in the following is helpful for stabilization of a natural drain too, as the

mechanism of compensation only works for small steps and cannot be modelled

linearly.

In process plants there are many tanks where level control is necessary, e.g. surge

drums, separation tanks, stirred tank reactors, column sumps, feed water tanks,