Module 15: Process Control and Process Integration – Tier I Program for North American Mobility in Higher Education (NAMP) Introducing Process Integration for Environmental Control in Engineering Curricula (PIECE) Module 15: Process Control and Process Integration – Tier I Created at Universidad de Guanajuato & École Polytechnique de Montréal

This module is divided in three essential complements, it will demonstrate the relationship between the use of PI tools to design a process and the control strategies.

Structure Tier one: Tier Two: Tier Three: Basic Concepts About Process Control Tier Two: Use of PI tools and especially dynamic simulation to address control strategies Tier Three: Analysis of a real process.

Index: Tier one: Comparison between Steady State and Dynamic State. Important Definitions about dynamic state. Dynamic Models.

Index: Tier two: Relationship between Process Design and Process Control Dynamic Effect on recycle Structures

Tier 1

Tier 1 Objective: Understand the difference between steady state and dynamic state. Understand basic concepts about control process. Understand the advantages of Dynamic Simulation.

Initial conditions = Final conditions Steady State Initial conditions = Final conditions Process T2 T1 Flow 1 Flow 2 INPUT OUTPUT

When a system is at steady state, there is no change in the process, input and output remains constant in the time. INPUT Process OUTPUT Constant TIME Constant

Initial conditions Final conditions Dynamic State: Initial conditions Final conditions In steady state every variable in the process remain constant while dynamic state one or some variables could change thereby affecting the process CHANGE WITH TIME KEY PHRASE

And now…… What does control mean? Why is it necessary?

Before the next part it is necessary to understand the next concepts: Manipulated Variable A variable that can be changed to maintain constant the controlled variable. Controlled Variable A variable which is desirable to control.

Next there is a typical example of control, everyone has needed to control the temperature when you wish to take a shower………… How ?? An adequate temperature of water is desirable Changing flows of hot and cold water.

Let’s identify new concepts about control…. Disturbance Process Sensor Final Control Element

Variables which help to control temperature Controlled Variable Temperature Variables which help to control temperature Flows of cold and hot water

It is a feedback control loop. It is possible to observe some elements: Sensor Input Output Disturbances Final Control Element Process Desired Temperature Controller Cause Effect It is a feedback control loop.

Either flow of cold or flow of hot water In addition if it is used Either flow of cold or flow of hot water Temperature SISO Single Single Input Output But if…

MIMO Flow of cold and flow of hot water Temperature and Total flow Multiple Multiple Input Output

To Control To take necessary actions to maintain a system in desired conditions.

Why is important to control processes ?

High Quality Manufactured Products Control System High Quality Manufactured Products Raw Materials What would happen if there was lower quality raw materials , what should be considered ?

Some aspects that should be considered: Raw materials quality and availability Services quality and availability Product Quality and throughput Plant equipment availability Environmental conditions Process materials behavior Plant equipment malfunction Control system malfunction Link to other plants Drifting and decaying factors

How is a Control System designed?

Information from existing plants Steps to design a Control System Information from existing plants Formulate Control Objectives Management Objectives Physical and chemical principles Develop process model Computer Simulation Process Control theory Devise Control Strategy Computer Simulation Experience with existing plants Select Control Hardware Vendor Hardware selection Install control system Adjust controller settings Final Control system

Objectives of a control process system Safety Environmental Protection Monitoring and diagnosis Control System Equipment Protection Profit Smooth Operation Product Quality

Environmental Protection Safety Safety of people in the plant and in the surrounding community is of paramount importance. Working at an industrial plant should involve less risk than any other activity in persons life. Environmental Protection Federal, state or local laws regulations require that the effluents of a plant satisfy certain specifications. Equipment protection Operating conditions must be maintained within bounds to prevent damage to expensive equipment Smooth Operation It is desirable because it results in attenuated disturbances to all the integrated units.

Monitoring and Diagnosis Product Quality Process Control contributes maintaining the operation required for excellent product quality set by the purchasers. Optimization It is concerned with operating the process so that the operation results in producing the highest rate of profit. Monitoring and Diagnosis Both the controlled and manipulated variables must be monitored in order to evaluate the performance of a control system.

Control System Less Output Variation Higher Quality When a process control is implemented, the variability of the key parameters is reduced. xA Time 0.97 0.99 0.98 Without control With control Time xA 0.975 0.985 0.98 Control System Less Output Variation Higher Quality

MATHEMATICAL MODELS Are the models necessary? A mathematical model is a representation of a process, using mathematical relationships, an equation or a set of equations. These equations are obtained from basic conservation balances as material, energy and momentum. Basic Balance Equations Mathematical Model Process Constitutive Relationships Are the models necessary?

When should the reaction be stopped to have a maximum B concentration? Models allow to analyze behavior system when any change is made. It is a safe, fast and easy way. What would happen if inlet flow stop, how fast will the tank be empty? Flow Liquid Level

Distributed parameters Classification of Fundamental Models Dependent variables are not function of spatial location Uses macroscopic balances Ordinary Differential equations Lumped Parameters Dependent variables are function of spatial location Uses microscopic balances Partial differential equations Distributed parameters

Dynamic state vs. Steady-State. Model Basic Equations No Accumulation Term Accumulation Term Algebraic Equations Differential Equations Steady State Dynamic State

Steady State Conservation Law . Steady State Conservation Law Mass in Mass produced Mass consumed Mass out - = - + Dynamic State Conservation Law Rate of mass produced Rate of change Rate of mass in Rate of mass out Rate of mass consumed - = - +

The dynamic model gives a relation for determining the output variable as function of time for arbitrary variations in the input. T (Energy) L (Inventory) Accumulation Term Variation with time !! CA (Species)

Dynamic models of chemical processes invariably consist of one or more partial or ordinary differential equations. To solve them it is possible to use the Laplace transform. It means that transient responses of the dependent variables can be found. BUT Just for linear equations !! Laplace Domain Inverse Laplace Laplace Differential equations Model Solution Time Domain

When a system is under control, it is located in a small region. Linearization Very often, it is possible to find non-linear models, and linearized methods provide useful result for many process. The application is justified by the small region of a process when under control. When a system is under control, it is located in a small region.

For this non linear function The linear approximation about (xs,ys) can be obtained by applying a Taylor series expansion to this function truncating the second order and higher order terms. These terms are known because they are evaluated at xs and ys

Transfer Functions

Changes in variable from initial values or conditions. Having the model, now it desirable to make the model as GENERAL as possible in order to analyze the dynamic behavior of different processes. Subtracting the steady state equation and defining deviation variables. How? Deviation variables Changes in variable from initial values or conditions. New conditions Initial conditions

Model Deviation variables Laplace Transform Transfer Function G (s) Y (s) X (s) Transfer Function G (s)

Dynamic relation Input-Output Physical Realizability Condition (Laplace Domain) Input Physical Realizability Condition Transfer function is the Laplace Transform of the output variable Y(s) divided by the Laplace Transform of the input variable X(s) with all the initial conditions equal to zero.

Steps to obtain a transfer function Laplace Transfor m Linear Model Deviation variables Transfer Function Linearization Non Linear

Gain represents the difference between two steady state of the system. Time constant is indicative of the speed of response of the process. It has time units Large Value Slow process response Small Value Fast process response

Transfer function of different systems. Efecto con diferente ganancia, incluir las graficas de entrada, usar las misma variables, in cluir deltaK Transfer function of different systems. Differential Equation Transfer Function Steady-State 63%

Testing another transfer function Steady-State Time

Degree of oscillation in a process response after a perturbation. ADD Graphics Differential Equation Transfer Function Degree of oscillation in a process response after a perturbation. Overdamped Critically Damped Underdamped

Every process can be characterized in term for its values of time constant and gain.

Key characteristics of an underdamped second order response. Rise Time (trise) Time required to first cross the new steady state value and is given by b) Percentage overshoot (B/D*100)

c) Decay Ratio (C/B) d) Period of oscillation (T ) e) Response time Time required for the response to remain within a ± 5% band, based upon the steady state change in y.

C B D Period of oscillation t rise Time

Time Delay Change Response Time θ Impulse

And what is stability……? How is it possible to know if a system is stable? When is a system stable? It is necessary to analyze the poles in the general form of a transfer function

Poles of transfer function General Form Numerator Polynomial in s of order m Denominator polynomial of s of order n Poles of transfer function Poles are the roots of P(s), it means the values that render P(s) zero.

a) Assume that P(s) can be factorized into a series of real poles Pi Inverse Laplace transform Re Im x p>0 p=0 p<0 Time It grows to infinity.

Sinusoidal behavior with amplitude of c/p b) Assume that one of the factors o P(s) is The roots are Sinusoidal behavior with amplitude of c/p Inverse transform Laplace Re Im x Time

c) Assume that one of the factors of P(s) is (s2+as+b) Inverse transform Laplace Factoring If a2- 4b>0 apply a) If a2- 4b=0 Critically damped behavior. If a2- 4b<0 apply the next result:

Inverse transform Laplace Re ● Im P<0 P>0 Time It grows periodically.

For complex conjugated poles, the larger the magnitude of the imaginary component (further the pole is from x axis ) the more oscillatory the response.

Negative real roots is stable Plane Imaginary - Real Re Im Negative real roots is stable Unstable Region If there are positive real roots, even if it is a complex number, it will be unstable

Stability A system is stable when bounded input changes result in bounded output, otherwise it is unstable. A variable is bounded when it does not increase in magnitude to infinity as time increases. The poles of a transfer function indicate very specifically the type of dynamic behavior that the transfer functions represent for a wide variety of inputs .

This is the block diagram for the system Block Diagrams. Individual elements Physical Model Sensor Disturbance Every element has a transfer function !! Process Representation GD Final Control Element Gv GP GS This is the block diagram for the system

Block Diagram Algebra It provides the method for combining individual transfer functions into an overall transfer function behavior. G1(s) Y (s) X (s) Cause Effect Gn(s) G3(s) G2(s) G1(s) X0 X2 X3 Xn

Parallel Structures Recycling Structures G1(s) G2(s) X0 X2 G1(s) G1(s) + X2 X3

Feedback Control

Comparison open-loop and closed-loop u (s) Y (s) G (s) Stimulus Response Control action depends the output Closed Loop. u (s) Y (s) G (s) Stimulus Response Action

Feedback makes use of a output of a system to influence an input to the same system Sensor Input Output Disturbances Final Control Element Process Desired Temperature Controller Negative Action tends to reduce the error from desired Positive Action tends to increase the error from desired

Objectives of a feedback control Maintain safe operation. Maintain quality product.

Structure Measurement Element Measurement Error Detection Element Comparison and Calculation Control Element Correction Basic Elements Basic Actions

Input Output Comparison Desired Output Correction Measurement D(s) Disturbances Comparison D(s) Gd Ysp(s) ≠ Y(s) Desired Output Correction Ysp(s) E(s) C(s) U(s) Y(s) Gc Gv Gp + - Input Output Controller Final element Process Gs Sensor Measurement

Performance Measurement Element (Sensor) Span Zero Accuracy Repeatability Process measurement dynamics Calibration

Closed Loop Transfer Function

Defining Process Gp U(s) Gd D(s) Y(s)

Actuator Gv U(s) C(s) Controller Gc E(s) C(s)

Error E(s) Ysp(s) Ys(s) Sensor Gs Ys(s) Y(s)

Characteristic Equation Closed Loop Transfer Function Characteristic Equation Servo Control

Regulatory control Analyzing the roots of the characteristic equation is possible to know the dynamic behavior, therefore, to know if the system is stable or unstable.

PID Controller Tuning

The controller does this task In a real process what is desired is to maintain the controlled variables in a given value despite the presence of disturbances. The control system does this task. Set Point The controller does this task

Standard form for the PID (Proportional-Integral-Derivative) algorithm Tuning parameters of controller

a) Proportional Control action is proportional to error.

Characteristics of Proportional Action. Proportional action does not change the order of the process. Closed Loop time constant is smaller then the open loop time constant. Proportional action makes faster the response of the process. There is an offset. (The manipulated variable will change until the error is constant)

b) Integral Integral Control action is proportional to the integral of the error. It allows to reduce the error to zero

Characteristics of Integral Action. All steady state corrections for disturbances or set point changes must come from integral actions. There is no offset at steady state. (The manipulated variable will change until error equal to zero) Integral action increase the order of the process dynamics by 1. Increasing the amount of integral action ( decreasing ) results in a faster responding feedback process, but increases the degree of oscillatory behavior.

c) Derivative Derivative Control action that is proportional to the derivative of rate of change or error

Characteristics of Derivative Action. It does not change the order of the process It does not eliminate offset Derivative action tends to reduce the oscillatory nature of feedback, however it amplifies process noise.

Comparison between P, PI and PID action Offset PID

Tuning Criteria Eliminate deviations from set point. Good set point tracking should be minimized. Excessive variations of the manipulated variable should be avoided The controlled process should remain stable for major disturbances upsets.

Deviations from set point Performance Deviations from set point PID controller Reliability Controller’s ability to remain in service while handling major disturbances Tuning consists to find the best parameters for the controller to achieve the control objective.

Performance Assessment IAE (Integral Absolute Error) ITAE (Integral Time Absolute Error) ISE (Integral Square Error) ITSE (Integral Time Square Error)

ISE and ITSE penalize larger deviations more severely than IAE and ITAE ITAE and ITSE penalize deviations at long time more severely than IAE and ISE

Classical Tuning Methods

Cohen and Coon It assumes that a FOPDT model of the process is available. FOPDT (First Order plus Delay Time)

Ziegler-Nichols Tuning The ultimate parameters are obtained by operating a P only controller under sustained oscillations and then measuring the period of the oscillations and noting the gain of the P only controller.   P PI PID Kc 0.5Kcu 0.45Kcu 0.6 Kcu tI - Pu /1.2 Pu /2 tD Pu /8 Ku Ultimate Gain Pu Ultimate Period

Direct Method Synthesis This method is based upon prescribing a desired form for the system’s response and then finding a controller strategy and parameters to give that response. This block diagram Input Output Gv Gp Gc Ysp(s) Y(s) + - has the next closed loop equation for changes in set point:

This is called Synthesis Equation If the system’s response for the relation Y/Ysp, is specified. Then the controller that will give this closed loop response characteristic is that which satisfies the following equation: This is called Synthesis Equation Thus, the required controller can be designed if we have a model of the process, it may have a PID form.

If the desired response form is Then The process model is required

If the process model is a first order process The controller strategy is: This is simply a PI controller with settings Depending the process model, is possible to have a PID controller.

ADVANTAGES FEEDBACK Achieves zero steady state offset for all step-like input. Uses only one measurement Algorithm and tunes rules available

DISADVANTAGES Process output must be upset before feedback action begin Feedback control performance can be poor for some combinations of disturbance frequencies and feedback dynamics Poor feedback can cause instability, PID does not provide the best possible control for all process.

MIMO SYSTEMS

There are many industrial systems which have multiple inputs and multiples outputs …..

Distillation Columns Steam and reflux affect both top and bottom product compositions Gas-liquid separator Gas and liquid product flows affect both tank level and pressure.

Characteristics Multi-input Multi-output (MIMO) processes Several CV’s and several MV’s The numbers of CV’s and MV’s are not necessary same. One MV affects all or some of CV’s. ( Process interaction ) Characteristics Which MV will control which CV? ( Pairing ) One control loop affects the other control loops (Control loop interaction) Decentralized control: Multiple SISO controllers are applied. Centralized control: All MV’s will be manipulated to all or some CV’s.

In contrast Single-input single-output (SISO) processes One CV and one MV: No need of pairing

In a general form

INICIO SISO Affects One Input One Output U(s) Y(s)

It means that there is interaction !! MIMO Affects One Input Two* Outputs U1(s) Y1(s) Y2(s) U2(s) It means that there is interaction !! A multivariable process is said to have interaction when process input (manipulated) variables affect more than one process output (controlled) variable.

Controllability The ease with a continuous plant can be held at a specific steady state. Resiliency Measures the degree to which a processing system can meet its design despite external disturbances and uncertainties in its design parameters.

Controllability is defined for a selected set of manipulated and controlled variables, and a system may be controlled for one selection and uncontrolled for another selection. In order to control the process is necessary to know the interaction among the variables and how the variables will be pairing.

Commonly used controllability measures RGA (Relative Gain Array) (Bristol, 1966) Niderlinski Index Condition Number Model of the process necessary Resiliency measures Relative Disturbance Gain Disturbance Cost (Lewin, 1996) Disturbance Condition Number (Skogestad & Morari, 1987) Model of the process and disturbances necessary

11 : measure of the interaction using u1 to control y1 Relative Array Gain Open Loop Closed Loop Effect y1(s) u1 – y1 G11 u1(s) + K11CL= K11OL K11 + Δyi G21 Interaction G12 u2(s) y2(s) Steady state Controller G22 + 11 : measure of the interaction using u1 to control y1 Gain Open Loop Gain Closed Loop

Recommendation to pairing With the other loops open Recommendation to pairing Pair Do not pair Avoid Avoid Do not pair

Control integral Niderlinski Index Tool for input-output pairing multi-loop SISO controllers with integral action. Sufficient condition for instability if independently tuned controllers with integral action are used. NI<0 Necessary condition for stability of the closed loop system in the case of independent controller tuning. NI>0

Singular Value Decomposition Any matrix can be decomposed as: U is matrix of output singular vectors (output directions) V is matrix of input singular vectors (input directions) Output and input signals are vectors

First Column Represents the input direction with the largest amplification. Matrix V Last Column Represents the input direction with the smallest amplification. First Column Output direction where inputs are least effective Matrix U Last Column Output direction where inputs are more effective

Σ is a diagonal matrix containing the singular values of G The maximum singular value represents the largest gain for any input direction, while the minimum singular value represents the smallest gain for any input direction.

Esquema explicativo, razon. Condition Number It is an indicator or directionality of the process gain. CN is obtained by calculating the ratio of the maximum singular value to the minimum singular value of the gain matrix. Gain Matrix If CN is large (CN >10), K is ill-conditioned. If CN is one, K is perfectly conditioned.

The graphical representation of the condition number is showed next:

Dynamic Simulations

Simulation is the imitation of the operation of a real - world process or system over time. Simulation is used to describe and analyze the behavior of a system, ask "what if" questions about the real system, and aid in the design of real systems. In order to do a simulation is necessary to have a model of the process, and sometimes to develop the model to simulate is costly and time consuming and therefore is a hard task to carry out.

However to develop the model is essential part of the simulation. What if ….. Dynamic simulation predicts how process variables change with time when moving from one steady-state to another or during a transient upset.

Optimization of plant operations Application Areas of Dynamic Simulation Process Design Analysis Off line systems On line systems Quasi on line systems Education, Training/Control System Development Advancement of plant operations /Optimization Optimization of plant operations The results obtained from the dynamic simulator in the online system are feed back to the actual plant in real-time. The results obtained from the dynamic simulator are applied to simulated plants Results obtained from the dynamic simulator in the system are not immediately applied to actual plant operations.

Contributions of Dynamic Simulation Process Design The dynamic response of the process without corrective action by a person or control system is important in the analysis of many process design. Proper use contributes to designing processes that are easily maintained near the desired operating conditions. In addition a simulation can help to ensure that all of the equipment for a new plant is consistently sized

What if analysis Evaluate changes to the process equipment, feed materials and operating conditions faster and lower costs trough modelling than through experimentation. Evaluate the response of the system when changes in operating conditions and equipment are made

Process control design A control strategy study can be as simple as determining the optimal tuning constants for a controller or as complicated as designing an advanced control strategy for the entire plant. In general to determining the effectiveness of a process control and develop a control strategy.

Process Control Development Strategy Determinate how disturbances propagate trough the system. Investigate the relative sensitivity of process variables to process upsets. Investigate process and control loops interactions. Determine the effect of equipment sizing or arrangements changes on disturbances rejections and overall operability. Determine the effects of ambient conditions on the process.

Compare the dynamic performance of alternatives control strategies. Perform control-loop tuning. Investigate star-up, shut-down, low, mid, max throughput operations.

Training The operators need training in how to control the process. Training courses teach how to use the Control System to control "a" plant, and simulation can be used to train operators on how to operate "their" plant during a startup or emergency.

What if… changes to the process equipment, feed materials and operating conditions ?? Real Plant Two options Faster Simulation Dynamic simulation technology plays a very important role in achieving safer and optimal plant operations.

Glossary

Control System A control system is a system of integrated elements whose function is to maintain a variable process at a desirable value or within a range of desired value. Input Control system input is the stimulus applied to a control system from an external source to produce a specified response from the  control  system. Output Control system output is the response to the input applied.

Open-Loop system An   open-loop  control  system  is a control system in which the control action is independent   of   the   output. Open Closed-Loop A closed-loop control system is one in which control action is dependent on the output Time Delay It represents the time to have a response of the system.

Offset Error between the new set point and the new steady state controlled variable value. Ultimate period Period of oscillation of the system at the margin of stability Ultimate Gain Controller gain that brings the system to the margin of stability at the critical frequency

Spam Is the difference between the largest measurement value made by the sensor/transmitter and de lowest value Zero Is the lowest reading available from the sensor/ transmitter. Accuracy Is the difference between the value of the measured variable indicate by the sensor and its true value.

Process measurement dynamic It indicates how quickly the sensor responds to changes in the value of the measured variable. Calibration Involves the adjustment between the sensor output and the predicted measurement Repeatability Is related to the difference between the sensor readings while the process conditions remains constant

Noise Is the variation in a measurement of a process variable which does not reflect real changes in the process variables. It is caused by electrical interference, mechanical vibrations or fluctuations within the process. Set Point It is the desirable value of the controllable variable

QUIZ

1.- A dynamic model is : a) A mathematical representation of a real process. which describes approximately its behavior respect to time. b) A mathematical representation of a real process which describes its behavior without consider the variation on time.

2.- A dynamic state differs from steady state: a) Accumulation term is not included in variation equations to built a model. b) Accumulation term is included in variation equations c) There is no difference between them

3.- To control process is important because: a) To transform raw materials in manufactured products. b) To decrease the variability of key variables of the process without forget the objectives of the control system.

4.- A characteristic of feedback : a) It uses an input to influence the output to the system. b) It uses an output to influence the input to the system. c) It is just a process control concept

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Now you know different basics concepts about process control CONGRATULATIONS! Now you know different basics concepts about process control