Process Control System Analysis

INTRODUCTION

This section begins with some control-related definitions of some basic terms and concepts. This is followed by some introductory discussion of process dynamics and closed loop feedback control. For an in-depth discussion of analog and digital PID (proportional-integral-derivative) variations, closed loop responses, and the various model-based expert and opti-mizing control systems, the reader should turn to the later sections of this chapter.

During the first industrial revolution, the work done by human muscles was gradually replaced by the power of machines. Process control opened the door to the second indus-trial revolution, where the routine functions of the human mind and the need for the continuous presence of human observers

G. Shinskey’s classic Process Control Sys-tems started to give recognition to process control analysis in the time domain. This is no surprise as progress was always made by the practical users and not by the mathematically oriented theoreticians. One should also understand that before one can control a process one must fully understand the process, and for this reason this section will start with the description of the “personalities” of different processes.

HISTORY OF PROCESS CONTROL

The fly-ball governor was the first known automatic control system. It was installed on Watts’ steam engine over 200 years ago in 1775. As shown in Figure 2.1a, the fly-balls detected the speed of shaft rotation and automatically opened up the steam supply when a drop was registered in that speed. The users of the fly-ball used it without understanding why it works. Another century went by before James Clark Maxwell in 1868 prepared the first mathematical analysis of the fly-ball

These capacitance elements can provide storage for materials (gas, liquid, or solids) or storage for energy (thermal, chemical, etc.). Thermal capacitance is directly analogous to electric capacitance and can be calculated by multiplying the mass of the object (W) with the specific heat of the material it is made of (Cp). The units of thermal capacitance are BTU/F in the English or Cal/C in the metric system.

The capacitance of a liquid or a gas storage tank can both be expressed in area units (ft2 or m2). Figure 2.1e illustrates these processes and gives the corresponding equa-tions for calculating their capacitances. The gas capacitance of a tank is constant and is analogous to electric capacitance. The liquid capacitance equals the cross-sectional area of the tank at the liquid surface, and if the cross-sectional area is constant, the capacitance of the process is also constant at any head.

A tank having only an inflow connection (Figure 2.1f) is a purely capacitive process element. In such a process the level (c) will rise at a rate that is inversely proportional to the capaci-tance (cross-sectional area of the tank) and after some time will flood the tank. The level (c) in an initially empty tank with a constant inflow can be determined by multiplying the inflow rate (m) with the time period of charging (t) and dividing that product with the capacitance of the tank (c 