Dynamic and Process Control, Essays (university) of Chemical Processes

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Basic

DYNAMICS and CONTROL

Finn Haugen

TechTeach

August 2010

ISBN 978-82-91748-13-

• 1 Introduction to control
  • 1.1 The principle of error-driven control, or feedback control
  • 1.2 A case study: Level control of wood-chip tank - and block diagram 1.2.1 Description of the control system with P&I diagram
    • 1.2.2 How the level control system works
  • 1.3 The importance of control
  • 1.4 Some things to think about
  • 1.5 About the contents and organization of this book
• I PROCESS MODELS AND DYNAMICS
  • and state-space models 2 Representation of differential equations with block diagrams
  • 2.1 Introduction
  • 2.2 What is a dynamic system?
  • 2.3 Mathematical block diagrams
    • 2.3.1 Commonly used blocks in block diagrams
    • 2.3.2 How to draw a block diagram
    • 2.3.3 Simulators based on block diagram models
  • 2.4 State-space models
  • 2.5 How to calculate static responses
• 3 Mathematical modeling
  • 3.1 Introduction
  • 3.2 A procedure for mathematical modeling
  • 3.3 Mathematical modeling of material systems
  • 3.4 Mathematical modeling of thermal systems
  • 3.5 Mathematical modeling of motion systems
    • 3.5.1 Systems with linear motion
    • 3.5.2 Systems with rotational motion
  • 3.6 Mathematical modeling of electrical systems
• 4 The Laplace transform
  • 4.1 Introduction
  • 4.2 Definition of the Laplace transform
  • 4.3 Laplace transform pairs
  • 4.4 Laplace transform properties
• 5 Transfer functions
  • 5.1 Introduction
  • 5.2 Definition of the transfer function
  • 5.3 Characteristics of transfer functions
  • 5.4 Combining transfer functions blocks in block diagrams
  • 5.5 How to calculate responses from transfer function models
  • 5.6 Static transfer function and static response
• 6 Dynamic characteristics
  • 6.1 Introduction
  • 6.2 Integrators
  • 6.3 Time-constant systems
  • 6.4 Time-delays
  • 6.5 Higher order systems
• II FEEDBACK AND FEEDFORWARD CONTROL
• 7 Feedback control
  • 7.1 Introduction
  • 7.2 Function blocks in the control loop
    • 7.2.1 Automatic and manual mode
    • 7.2.2 Measurement lowpass (smoothing) filter
    • 7.2.3 Scaling with percentage values
    • 7.2.4 Scaling with physical (engineering) values
  • 7.3 The PID controller
    • 7.3.1 The ideal PID controller function
    • 7.3.2 How the PID controller works
      • direct action? 7.3.3 Positive or negative controller gain? Or: Reverse or
  • 7.4 Practical modifications of the ideal PID controller
    • 7.4.1 Lowpass filter in the D-term
    • 7.4.2 Reducing P-kick and D-kick caused by setpoint changes
    • 7.4.3 Integrator anti wind-up
    • 7.4.4 Bumpless transfer between manual/auto mode
  • 7.5 Control loop stability
• 8 Feedforward control
  • 8.1 Introduction
  • 8.2 Designing feedforward control from differential equation models
  • 8.3 Designing feedforward control from experimental data
• 9 Controller equipment
  • 9.1 Process controllers
  • 9.2 Programmable logical controller (PLC)
  • 9.3 Programmable Automation Controller (PAC)
  • 9.4 SCADA systems
  • 9.5 DCS systems
  • 9.6 Embedded controllers in motors etc.
• 10 Tuning of PID controllers
  • 10.1 Introduction
  • 10.2 The Good Gain method
  • 10.3 Skogestad’s PID tuning method
    • 10.3.1 The background of Skogestad’s method
    • 10.3.2 The tuning formulas in Skogestad’s method
    • 10.3.3 How to find model parameters from experiments
    • 10.3.4 Transformation from serial to parallel PID settings
    • 10.3.5 When the process has no time-delay
  • 10.4 Auto-tuning
  • 10.5 PID tuning when process dynamics varies
    • 10.5.1 Introduction
    • 10.5.2 PID parameter adjustment with Skogestad’s method
    • 10.5.3 Gain scheduling of PID parameters
    • 10.5.4 Adaptive controller
• 11 Various control methods and control structures
  • 11.1 Cascade control
    • 11.1.1 The principle of cascade control
    • 11.1.2 Benefits of cascade control
    • 11.1.3 Controller selection and controller tuning
    • 11.1.4 Cascade control and state feedback
  • 11.2 Ratio control
  • 11.3 Split-range control
  • 11.4 Flow smoothing with sluggish level control
    • 11.4.1 The control task
    • 11.4.2 Controller tuning
  • 11.5 Plantwide control
• 12 Sequential control
  • agrams A Codes and symbols used in Process & Instrumentation Di-
  • A.1 Letter codes
  • A.2 Instrumentation symbols used in P&IDs

The theoretical parts of the book assumes basic knowledge about differential equations. A minimal introduction to the Laplace transform, which is the basis of transfer function models which are used in several sections of the book, is given in a separate chapter of the book.

Supplementary material is available from http://techteach.no:

• Tutorials for LabVIEW, MATLAB/SIMULINK, Octave, and Scilab/Scicos.
• SimView which is a collection of ready-to-run simulators.
• TechVids which is a collection of instructional streaming videos, together with the simulators that are played and explained in the videos.
• An English-Norwegian glossary of a number of terms used in the book is available at the home page of the book at http://techteach.no.

This book is available for sale only via http://techteach.no.

It is not allowed to make copies of the book.

About my background: I graduated from the Norwegian Institute of Technology in 1986. Since then I have been teaching control courses in the bachelor and the master studies and for industry in Norway. I have developed simulators for educational purposes, and video lectures, and I have been writing text-books for a couple of decades. I have been engaged in industrial projects about modeling, simulation and control. (More information is on http://techteach.no/adm/fh.)

What motivates me mostly is a fascination about using computers to model, simulate and control physical systems, and to bring theoretical solutions into actions using numerical algorithms programmed in a computer. National Instruments LabVIEW has become my favourite software tool for implementing this

Finn Haugen, MSc

TechTeach

Skien, Norway, August 2010

Chapter 1

Introduction to control

Automatic control is a fascinating and practically important field. In short, it is about the methods and techniques used in technical systems which have the ability to automatically correcting their own behaviour so that specifications for this behaviour are satisfied.

In this chapter the basic principles of automatic control and its importance are explained, to give you a good taste of the core of this book! Chapter 7 (and the chapters following that chapter) continues the description of control topics.

1.1 The principle of error-driven control, or

feedback control

The basic principle of automatic control is actually something you (probably) are familiar with! Think about the following:

• How do you control the water temperature of your shower? I guess that you adjust the water taps with you hand until the difference between the desired temperature — called the reference or setpoint — and the temperature measured by your body is sufficiently small, and you readjust the taps if the difference for some reason becomes too large (water is too hot or too cold). This difference between setpoint and measurement is denoted the control error. Thus, the temperature control is error-driven.
• How is the speed of a car controlled? The gas pedal position is

1

Process

Sensor

ySP e u Controller

y

Control d error

Process measure- ment

ym

n Measurement noise

Reference or Setpoint

Control variable

Process output variable

Feedback

Filter

ym,f Filtered measure- ment

Disturbance (environmental variable)

Control loop

Figure 1.1: Block diagram of an error-driven control system

variable (control signal) via the controller. Hence, error-driven control implies feedback control.

Feedback control is not the only solution to the control problem! Although it is the most important and the most frequently used control principle, control can be improved by also including feedforward control in the control system. Feedforward control is based on measuring process disturbances, and adjusting the control signal as a function of the disturbance to obtain a direct direct and momentary compensation of the disturbance, keeping the process variable closer to the setpoint that with only feedback control. (Feedforward control can also include a direct coupling from the setpoint or reference to the control signal to improve reference tracking.) For example, in a position control system for keeping a ship (e.g. an oil tanker) at a specified position at the sea, more accurate position control can be obtained by measuring the wind speed and direction and using this measurement to directly adjust the thruster force to compensate for the wind force. We will not study feedforward control in this introductory chapter, but you can look forward to Chapter 8 which is all about feedforward control.

1.2 A case study: Level control of wood-chip

tank

1.2.1 Description of the control system with P&I diagram

and block diagram

We will study an example of a real industrial control system. Figure 1. shows a level control system for a wood-chip tank with feed screw and conveyor belt which runs with constant speed. Wood-chip is consumed via an outlet screw in the bottom of the tank.^1 2 3 The purpose of the control system is to keep the measured chip level ym equal to a level setpoint ySP , despite variations of the outflow, which is a process disturbance d.

The level control system works as follows (a more detailed description of how the control system works is given in Section 1.2.2): The controller tries to keep the measured level equal to the level setpoint by adjusting the rotational speed — and thereby the chip flow — of the feed screw as a function of the control error (which is the difference between the level setpoint and the measured level).

A few words about the need for a level control system for this chip tank: Hydrogene sulphate gas from the pulping process later in the production line is used to preheat the wood chip. If the chip level in the tank is too low, too much (stinking) gas is emitted to the athmosphere, causing pollution. With level control the level is kept close to a desired value (set-point) at which only a small amount of gas is expired. The level must not be too high, either, to avoid overflow and reduced preheating.

In Figure 1.2 the control system is documented in two ways:

• Process and instrumentation diagram or P&I diagram which is a common way to document control systems in the industry. This diagram contains easily recognizable drawings and symbols of the process to be controlled, together with symbols for the controllers and the sensors and the signals in the control system. Appendix A (^1) This example is based on an existing system in the paper pulp factory Södra Cell Tofte in Norway. The tank with conveyor belt is in the beginning of the paper pulp production line. (^2) The tank height is 15 m. The diameter is 4.13 m, and the cross-sectional area is 13.4 m^2. The nominal wood-chip outflow (and inflow at steady state) is 1500 kg/min. The conveyor belt is 200 m long, and runs with fixed speed. The transportation time (time-delay) of the belt is 250 sec = 4.17 min. (^3) A simulator of the system is available at http://techteach.no/simview.

noisy measurement. It is not common to show the filter explicitely in P&I diagrams.

• Block diagram which is useful in principal and conceptual description of a control system.

Below are comments about the systems and variables (signals) in the block diagram shown in Figure 1.2.

Systems in Figure 1.2:

• The process is the physical system which is to be controlled. Included in the process is the actuator, which is the equipment with which (the rest of) the process is controlled. In the example the process consists of the tank with the feed screw and the conveyor belt.
• The controller is typically in the form of a computer program implemented in the control equipment. The controller adjusts the control signal used to control or manipulate the process. The controller calculates the control signal according some mathematical formula defining the controller function. The controller function defines how to adjust the control signal as a function of the control error (which is the difference between the setpoint and the process measurement).
• The sensor measures the process variable to be controlled. The physical signal from the sensor is an electrical signal, voltage or current. In industry 4—20 mA is the most common signal range of sensor signals. (In the example the sensor is an ultrasound level sensor, as mentioned earlier.)
• The measurement filter is a function block which is available in most computer-based automation systems. The filter attenuates or smooths out the inevitable random noise which exists in the measurement signal. The measurement filter is described in detail in Section 7.2.2.
• The control loop or feedback loop is the closed loop consisting of the process, the sensor, the measurement filter, and the controller connected in a series connection.

Variables (signals) in Figure 1.2:

• The control variable or the manipulating variable is the variable which the controller uses to control or manipulate the process. In this book u is used as a general symbol of the control variable. In commercial equipment you may see the symbol MV (manipulating variable). In the example the control variable (or control signal) adjust the flow through the feed screw.
• The process output variable is the variable to be controlled so that it becomes equal to or sufficiently close to the setpoint. In this book y is used as a general symbol of the process output variable. In commercial control equipment PV (process variable or process value) may be used as a symbol. In the example the wood chip level in the tank is the process output variable. Note: The process output variable is not necessarily a physical output from the process! In our example the chip outflow is not the process output variable. The chip outflow is actually a process disturbance, see below.
• The disturbance is a non—controlled input variable to the process which affects the process output variable. From the control system’s perspective, this influence on the process output variable is undesirable, and the controller will adjust the control variable to compensate for the influence. In this book, d is used as a general symbol for the disturbance. Typically, there are more than one disturbances acting on a process. In the example the chip outflow from the bottom of the tank is the (main) disturbance as it tends to bring the process variable (level) away from the level setpoint. Other disturbances are variations in the inlet flow due to e.g. chip density variations.
• The setpoint or the reference is the desired or specified value of the process output variable. The general symbol ySP will be used in this book. In the example the desired level is the setpoint. A typical value for this tank is 10 meters.
• The measurement signal is the output signal from the sensor which measures the process variable. In the example the measurement signal is a current signal in the range 4 — 20 mA corresponding to level 0 — 15 m.

Process (tank with belt and screw)

Sensor (Level Transmitter

• LT)

ySP (^) e (^) PID u controller

y

d Control error

Process measure- ment

ym

n Measurement noise

Setpoint Control variable

Process output variable

Level controller (LC)

Control Measure- loop ment filter

ym,f Filtered measure- ment

Environmental variable (process disturbance)

Figure 1.3: Simulated responses in various variables of the level control system of the wood chip tank

The control system works as follows:

• At time 300 min the setpoint is changed as a step from 10 to 11 m (see the upper right plot in Figure 1.3), and hence, the control error is suddenly increased from 0 to 1 m. As a consequence of this non-zero error, the controller starts increasing the control signal to the inlet scew (upper left plot), causing an increased chip inflow, thereby increasing the level, thereby reducing the control error. This continues until the level reaches the new setpoint of 11 m, so that control error becomes zero (upper right plot).
• At time 600 min the disturbance (outflow) is changed as a step from 1500 to 1800 kg/min (upper middle plot), causing the level to

decrease, and hence the control error becomes different from zero. The operation of the control system is as after the setpoint change: Because of the non-zero error, the controller starts increasing the control signal to the inlet scew, causing an increased chip inflow, thereby increasing the level, thereby reducing the control error. This continues until the level is at the setpoint of 11 m again.

• The measurement noise is smoothed by the measurement filter, but the noise is not completely removed (lower plots).
• The remaining measurement noise (what remains despite the filtering) is propagated through the controller, causing the control signal to be somewhat noisy (upper left plot).

1.3 The importance of control

In the previous sections we studied a level control system of a wood-chip tank. In general, the following process variables are controlled in industrial and other kinds of technical applications:

• Level or mass (of e.g. a storage tank)
• Pressure (in a chemical reactor)
• Temperature (in a room; in the fluid passing a heat exchanger; in a reactor; in a greenhouse)
• Flow (of feeds into a reactor)
• pH (of a reactor)
• Chemical composition (of nitric acid; fertilizers, polypropylene)
• Speed (of a motor; a car)
• Position (of a ship; a painting robot arm; the tool of a cutting machine; a rocket)

Application of control may be of crucial importance to obtain the following aims: