Valves

Equations

GenerallyProcess engineer:Bigger valve less pressure drop smaller resistance lower voltage & energy. Pump less less cost BUT harder to controlControl engineer:Smaller valve greater pressure drop larger changes can be made in flow greater cost BUT more control action

Thermocouples

Gain

Variable notation

Electric potentialAssume

Transfer function(Heat balance equations)

Transfer function with correctly installed thermocoupleFinal temp stays the same Steady state temperature

Processes

ARX Model

Zero Order Hold for ARX

Process Gain

Process Time Constant

Process Matrix

Matrix Transformation

Chapter 8

PID Control(Parallel)

PID Control(Series)

Expanded PID

Eliminating Deriv. & Prop. Kick

controller

will never be in the characteristic equation! does affect gain disturbance rejection could cause instability

Reverse or Direct Action

Position

Position

Velocity

Chapter 11

Closed loop trans. function

Routh Stability

Root Locus

Set point offset

Disturbance offset

PI Control & Disturbance Changes

Chapter 12

Direct Synthesis

Unknown t.d. approximate

FOPTD

SOPTD

IMC(use the mofo table 12.1 yo)

Selection of Larger means more conservative controller as while .

Lag Dominant Model

Integral Error Criteria

Suppression of large errors: ISE > IAESuppression of small errors: IAE > ISESuppression of persistent errors: ITAE > ISE, IAE

Tuning Variables

Ziegler NicolsPID

Cohen-CoonPID

Ultimate Model Parameters

Chapter 13

Sinusoidal Forcing of a Process

Integrating Process

2nd Order Process

Process ZeroA denominator of the form is a process lag.

Time Delay

Closed Loop B/W

Chapter 14

Gain & Phase Margins

A well-tuned controller: and .

Sensitivity Functions

Comparing 2 Controllers

Chapter 20: MPC

Control moves:

Gain:

Step response coefficients

Economic Performance Assessment

Average economic performance

Future Value of a single cash flow

Future value of C per period for t periods at r per period