A Theoretical Model of Feedback in Pharmacology Using Signal Flow Diagrams

Feedback as defined by the engineering concepts of control systems started in the 1920's and 1930's and was first given voice in Minorsky's paper on the steering of ships in 1922 and followed by Nyquists' paper on Regeneration Theory, 1932, and Hazen's paper on the Theory of Servomechanisms in 1934 (Chang, 1961: 1). Brown and Whiteley's work on servomechanism theory and Tustin's work on non-linear elements in servo-design are also worth mentioning (Porter, 1950: 2). The first practical application of feedback control was James Watt's flyball governor to the steam engine in 1775 (Murrill, 1967: 4). A system is defined as an orderly combination or arrangement of parts into a whole and that these combination of parts represent a methodological arrangement that represent a system (Koenig and Blackwell, 1961: 1). A feedback control system is a combination of elements which cooperate to maintain a physical quantity, the output, equal to the desired output that is related to other physical quantities known as inputs (Newton and Gould, 1957: 1-2). A feedback system is distinguished from a network by the presence of at least one unilateral element that represents power, information, or a commodity that can flow in only one direction (Smith, 1958: 1).

All automatic regulating systems can be divided into two groups, the direct-acting and the indirect-acting systems. The direct-acting systems is were the action of the sensitive element on the regulatory organ is operated with the introduction of additional source of energy and the indirect system is when the sensitive element acts on the regulatory organ directly through a special amplifier as an auxillary source of energy (Popov, 1962: 17-19).

Feedback can be considered a form of communication in which an input is responded to by an output (James, Nichols and Phillips, 1964: 1). The loss of time between actions and reactions is the major point of control systems problems and represents the measure of a disturbance (Holzbock, 1958: 3).

A closed-cycle control system is any signal that is supplied to the controller as a function of the object or device being controlled (Zeines, 1959: 22), (Horowitz, 1963: 58) and (Ku, 1962:10). A physical system is stable if, when disturbed from its equilibrium state, it can ultimately return to that original condition, it is unstable if it increases in indefinitely with time (Hardie, 1964: 188). The parameters of such a system must be 'optimally adjusted' to insure optimum control action and is the heart of the feedback system (Oldenbourg and Sartorius, 1953) and (Kipiniak, 1961: 1).

The selection of these primary measuring elements are important in that they must conform to the control requirements of the process in controlling the variables (Hadley and Longobardo, 1963: 4). Most control feedback systems are defined as servomechanisms and represent a closed-loop system (Chubb, 1967: 3) and (Gille, Pelegrin and Decauline, 1959: 15). The elements which constitute the essentials of a servomechanism are also the inherent properties of a vibrating system and can be detrimental to a servomechanism (Bulliet, 1967: 92). A power control system is considered to be an object of automation and servo-systems the tools to automation (Bulgakov, 1965: vii).

The sole purpose of a control system is to minimize the 'process-upset when such a disturbance arises (Tucker and Willis, 1958: 3). The use of 'set points' as an ideal or specified process are the guidelines used to keep the control in a system and are used to measure all deviant actions to maintain control (Rusinoff, 1957: 19). Modelling of such a system allows for the evaluation of systems that would otherwise be beyond the direct observation of a feedback system but special care must be taken to insure that the model accurately describes the function it is modelling (Seifert and Steeg, 1960: 15) and (Derusso, Roy and Close, 1965:1).

Feedback systems are all dynamic systems and fundamentally similar and operate on the difference between the actual state of the system and the arbitrarily varied ideal state (Ahrendt, 1954: 1) and (Bowen and Schultheises, 1961: 4). Feedback is also a form of self-regulation and and are an inherent process in both living and non-living processes of nature (Nagel, 1948: 2). In defining sub-units of a feedback system, elementary components should be defined by there functions rather than by appearance and that before a physical quantity can be controlled, it is essential that it be measurable (Warren, 1967: 9), (West, 1953: 12) and (Qvarnstrom, Schurt, and Runnstrom-Reio, 1965: 41).