PMC ProcessControl Lecture1&2

© Dr. Muhammad Zaman, SE, PIEAS

Process Modeling & ControlBooks:

1. Process Control, Modeling, Design and Simulations, by B. Wayne Bequette

2. Process Dynamics, Modeling and Control, by B. A. Ogunnaike, and W. H. Ray

3. Process Control (Designing Processes and Control Systems for Dynamic Performance), T. E. Marlin

4. Principles and Practice of Automatic Process Control, C. A. Smith and A. B. Corripio

Introduction


Introduction

Control ObjectivesInput variables (manipulated or disturbance variables)Output variables (measured or unmeasured)Constraints (hard or soft)Operating characteristics (continuous or batch or semibatch (semicontinuous))Safety, environment and economic considerationsControl structure (feedback or feedforward)


Introduction

Figure 1.1: Tank level problem / Surge tank


Introduction

Feedback Control (Scenario 1)Process 2 regulated F2, depending on steam demandF2 is disturbance stream, as regulation of F2 is by another systemUse F1 as manipulated variableF1 is adjusted to maintain a desired tank height


Introduction

Feedback Control (Scenario 1)


Introduction

Feedback Control (Scenario 2)Process 1 regulates the flow rate F1, disturbanceAdjust F2 to maintain tank height, manipulated variableControl valve, fail-open or air-to-close


Introduction


Introduction

Feedforward Control


Introduction

Feed-forward/ feedback control structure


Introduction

Tune level controller for fast or slow response? Preferable to tune slow return to the set-point Mostly true for scenario 2 Outlet flow is manipulated but affect process 2 Change the outlet flowrate slowly, yet fast enough that the

tank does not overflow or go dry Importance of the dominant timescale of the process e.g.,



Introduction

Taking a ShowerMultivariable controlControl objectivesInput variables Output variablesConstraints Operating characteristics safety, environment and economic considerationControl structure (FB or FF)

Introduction

Instrumentation Sensor Actuator Controller Continuous or discrete signals

Analog Current, voltage and pneumatic

Digital D/I, I/P


Introduction

Instrumentation Control valve placement


Introduction

Process Model and Dynamic BehaviorFirst principle basedImperial modelsInput vs output relations


Introduction to Feedback Control

What is control algorithm? How does the controller change the flow rate to the

process? Number of possible algorithms



On-off controller



Proportional ControlMake the signal to valve proportional to the error

b is the bias term and kc is the proportional gain



Process gain is simply SS change in output for a SS change in process input

Process gain

Valve gain Overall gain (valve and process)



For the second strategy, the process gain is negative (an increase in F2 causes a decrease in h)

Valve gain

The gain between valve-top pressure and tank height is



Valve Gains3 and 15 psig

Fail close

Maximum flow rate through the valve is 120 gpm

Similarly, a fail-open valve of the same size would have a negative gain (-10 gpm/psig)



Development of Control Block DiagramsAll dynamic elements in a control loop are combined, using their Laplace transfer function representationBlock diagrams are based on Laplace domain signals, which are assumed to be in deviation variable (perturbation from steady state) form



The block diagram for previous P&ID has the following componentsLevel controller (relates error to controller output)Valve (relates controller output signal to flow-through valve)Process (relates manipulated input to process output)Disturbance (relates the disturbance input to the process output)Sensor (measures tank level)



Controller Transfer Function Compares the hm to the hsp.From the proportional control law (algorithm) for this system b = Pv1s (SS pressure to valve), we find the controller input-output relationship




Where the controller input signal is the error We write the equation [where, c(s) is the controller

output, the pressure to the valve]

Transfer function form for a proportional-only controller



When analyzing block diagrams, the comparator is shown outside the controller transfer function block.

The block diagram uses r(s) to represent the set-point The orientation for the TF representation of the controller

is slightly different from that of the physical system

Block diagram relationship for controller transfer function.


Valve transfer functionThe input signal is the pressure to the valve top and the output is the flow rate of fluid through the valve


Block diagram of the valve and physical system


Process transfer functionThe input to the block is the flow rate to the tank, and the output is the tank level.Block diagram of the manipulated input effect on the process

© Dr. Muhammad Zaman, SE, PIEASBlock diagram of the manipulated input effect on the process


Disturbance transfer function The disturbance input is the flow rate from the tank and the output is the tank levelBlock diagram of the disturbance input effect on the process

© Dr. Muhammad Zaman, SE, PIEASBlock diagram of the disturbance input effect on the process


Measurement (Sensor) transfer functionThe input to the block is the tank level and the output is the actual measurement of tank level.

© Dr. Muhammad Zaman, SE, PIEASBlock diagram of sensor



Control block diagramCombine the previous five figures to obtain the feedback control system block diagram shown below.Two externally supplied signals, the set-point and the disturbance

Control system block diagram


We often assume that the output variable can be perfectly measured, and that process input (usually a flow rate) is directly manipulated; in this case we do not include the valve and measurement TFs in the closed-loop block diagram

Equivalently, we can “lump” the valve and measurement dynamics into the process TF, again allowing us to neglect the valve and measurement TFs.

Similarly, the measurement device can be lumped into the disturbance transfer function



Response to set-point changesassuming gm(s)=gv(s)=1 This simplification is equivalent to lumping the measurement and valve dynamics into the process TF.Notice that we are focusing on set-point changes only, so we have not included the disturbance block.


Fig. 5.10

Simplified control block diagram, disturbances are neglected, valve & measurement dynamics are lumped into the process TF


To find the output response to a set-point change A critical aspect is to determine the closed-loop stability Use block diagram manipulation to find the relationship

between the set-point and the output Closed-loop diagram of previous figure into a single TF

block, to provide the closed-loop relationship between set-point and process output.



To obtain the output y(s) as a function of set-point, r(s)

Combine the process input-output relationship, y(s) = gp(s) u(s), with controller relationship, u(s) = gc(s) e(s), to find

The error is defined as e(s) = r(s) – y(s), we can write

Relationship between r(s) & y(s) as the closed-loop transfer function, gCL(s),



If all of the poles of gCL(s) are stable, then the closed-loop system is stable

The denominator of gCL(s) is also known as the characteristic equation

Previous equation has been derived for the simple diagram shown in fig. 5.10.

Please realize that more-complex block diagrams will have more-complex closed-loop transfer functions.

The closed-loop TF for figure 5.9 (neglecting disturbance)


PMC ProcessControl Lecture1&2

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