Appendix 1: Glossary of Symbols Used in the Book

a _f1, a _f2, b _f1=Parameters of a filter in series with some PID controllers

a ₁, a ₂, a ₃, b ₁, b ₂, b ₃=Parameters of a third order process model

a ₁, a ₂, a ₃, a ₄, a ₅, b ₁, b ₂, b ₃, b ₄, b ₅=Parameters of a fifth order process model

A ₁=y ₁( ?), A ₂=y ₂( ?), A ₃=y ₃( ?), A ₄=y ₄( ??), A ₅=y ₅( ?)

A _m=Gain margin

A _p=Peak output amplitude of limit cycle determined from relay autotuning

b, c=Weighting factors in some PID controller structures

D _R=Desired closed loop damping ratio

d(t)=Disturbance variable (time domain)

du/dt=Time derivative of the manipulated variable (time domain)

e(t)=Desired variable, r(t), minus controlled variable, y(t) (time domain)

E(s)=Desired variable, R(s), minus controlled variable, Y(s)

FOLPD model=First Order Lag Plus time Delay model

FOLIPD model=First Order Lag plus Integral Plus time Delay model

F _p, F _i, F _d=Weights on the desired variable for one PID controller structure

G _c(s)=PID controller transfer function

G _CL(s)=Closed loop transfer function

G _CL(j ?)=Desired closed loop frequency response

G _cp(s)=Ideal PID controller transfer function

G _cs(s)=Series PID controller transfer function

G _m(s)=Process model transfer function

G