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

Abstract

This work describes the application of digital control systems analysis and design techniques to improve performance of an instrument. The basic approaches are the mathematical modelling of the instrument, stability analysis, controller design to achieve satisfactory performance, and computer simulations of the system. The combination of theoretical analysis and computer simulation provides an effective and economical solution. Nomenclature ca distance (m) Aj, effective area at nozzle side of booster enclosure (nr) A, effective area of feedback bellows (my) 4~ effective area of sensing diaphragm (m'-) A&dquo; effective area at output side of booster enclosure {m'b distance (m) Co capacitance of output enclosure of booster ~~~;-m' ~/~ C h capacitance of nozzle side of booster ((kg-m2)/N) C, capacitance of feedback bellows ~(kg-M2'/N) c,~ distance cm) e clearance at nozzle (m) F,, sensing diaphragm force (N) Fji, feedback bellows force (N) F~j fulcrum force fizz F'~i, spring force (N) g distance (m) K,, spring constant of feedback bellows (l~1/rcỹ sensing diaphragm spring constant (~t/mj Kjj spring constant at the output of booster (N/m) K, spring constant of range spring (N/m) Ki) valve constant for supply air (~~.~/~s-m)ĩ , distance (nix) I distance (m) P,, pressure at nozzle side of booster enclosure (N/M2) P, pressure of feedback bellows (N/M2) &dquo; pressure of nozzle tip (N/M2) Qj pressure at output side of booster enclosure (N/m2) PS supply pressure (N/m2) R~ tubing resistance between output and feedback ((N-S)/(kg-m2)) RJ~ tubing resistance between nozzle and booster ((N-S)/(kg-m2)) T, booster relay time-constant (s) T, feedback bellows time-constant (s) 1~ b nozzle feedback time-constant (s) x booster diaphragm displacement (m) Xd motion of sensing diaphragm (m) xf,, motion of feedback bellows (m) x~, motion of fulcrum (rn) x~, motion of adjustment screw (m) Xs displacement at range spring (m) y distance (in) z distance (m)