Control analysis and desig n to improve instrument performance

Abstract

This work describes how the methods of control system analysis and design can be applied to meet performance requirements of an instrument. The basic methods and steps are: mathematical modelling of the instrument, analysis of performance and stability, design modifications to provide satisfactory performance, simulation by computer to verify the design, implementing the modification into the instrument, and verification of the proposed design by tests. Nomenclature (see Fig 2) cm distance (Fig 2) (in) 4 ~ b effective area at nozzle side of booster enclosure (in2) Ac effective area of feedback bellow (in2) And effective area of sensing diaphragm (in2) A~ effective area at output side of booster enclosure (in~) h distance (Fig 2) (in) C,, capacitance of compensation ((Ibm -in2)/Ibf); see Fig 6 Cb capacitance of nozzle side of booster ((Ibm -in2)/ lbf) C~ capacitance of feedback bellow «(lbm-in2)/lbf) '~, capacitance of output enclosure of booster «(lbm-in2)/lbf) d distance (Fig 2) (in) e clearance at nozzle (in) Fd sensing diaphragm force (Ibf) F~d feedback bellow force (Ibf) Ff7 fulcrum force (1bf) F,~ spring force (lbfg distance (Fig 2) (in) k~ spring constant of feedback bellow (Ibf/in) kd sensing diaphragm spring constant (Ibf/in) ko spring constant at the output of booster (Ibf/in) ks spring constant of range spring (Ibf/in) k, valve constant for supply air (lbm/(s-in)) L distance (Fig 2) (in) I distance (Fig 2) (in) Pa a pressure of compensation (lbf/in'); see Fig 6 Pb pressure at nozzle side of booster enclosure (lbf/in2) Pc pressure of feedback bellow (Ibf/in~ 2) p, pressure of nozzle tip (Ibf/in-) po pressure at output side of booster enclosure (Ibf/ur) p, supply pressure (lbf/in') £p p i -pz pressure difference at measuring diaphragms (Ibf/in'2) R resistance of compensation (s/in'); see Fig 6 Ri resistance of compensation (s/in2); see Fig 6 R~ tubing resistance between output and feedback s/in~~R a resistance of compensation (s/in2); see Fig 6 R~, b tubing resistance between nozzle and booster (s/in2) T'1 booster relay time-constant (s); see Eqn (12) T2 feedback bellow time constant (s); see Eqn (12) 7g time constant of compensation (s); see Eqn (13) T4 time constant of compensation (s); see Eqn (13) T,, time constant of compensation (s); see Eqn (13) T~ nozzle feedback time-constant (s); see Eqn (12) x booster diaphragm displacement (in) xd motion of sensing diaphragm (in) xfd motion of feedback bellow (in) x~~, motion of fulcrum (in) xp motion of adjustment screw (in) xs displacement at range spring (in) y distance (Fig 2) (in) z distance (Fig 2) (in) Note: 51 units for corresponding imperial units Ibm, lbf, in, are kg, N, m, respectively.

Application of digital control systems analysis and design techniques to improve instrument performance

“…The physical model of the pneumatic differentialpressure transmitter with the booster relay is taken from Kaya and Verdouw (1983) as an example for the numerical investigation in this paper. The schematic of the transmitter and the booster is shown in Fig 1. in the study of Kaya and Verdouw ~~ I~L 983), a compensating network was introduced into the system between the output p,, and the feedback bellows to stabilise the systems.…”

“…By the application of a digital controller performed by a digital computer, which is connected to the instrument, a satisfactory dynamic response of the instrument is obtained. The references to the above development are Anderson (1967), Ogata (1970 and1978), Kaya and Verdouw (1983), and Doebelin (1980). Stability analysis of the system Dynamic system analysis based on the mathematical model given in Fig 2 is performed.…”