v CHEG 461 : Process Dynamics and Control Subject: Introduction to Process Control Week 01, Lectures 01 02, Spring 2014 Dr. Costas Kiparissides Content 1. Introduction to Process Dynamics and Control 2. Open loop Versus Closed loop Control Systems 3. Classification of Input and Output Variables 4. Feedback and Feedforward Control Strategies 5. Examples of Closed loop Control Systems 6. Block Diagrams of Controlled Processes 7. Summary and Course Objectives 1
Course Outline ( 1) Chapter 1 Thefirstpartofthecoursecoversthe fundamentals of mathematical modeling and dynamic analysis of physical and chemical processes and in general of dynamic systems. Based on the fundamental (mass, molar and energy) conservation equations, a system of differential and algebraic equations is commonly derived to describe the dynamic behavior of a chemical/physical system. Accordingly, the dynamic response of a system to dynamic changes in the system input variables is analyzed via the solution of the mathematical model describing the dynamic behavior of a given system. Solution of the mathematical model for a process is effected either via analytical mathematical methods (i.e., solution of low order linear ODEs in the time or Laplace domain) or numerically with the aid of available numerical solution tools (i.e., MATLAB, etc.). The above approach is known as open loop dynamic analysis of the chemical and physical systems. Course Outline ( 2) Chapter 1 The second part of the course examines the dynamic behavior of chemical and physical processes in closed loop, that is, under the action of a controller (e.g., feedbackor feedforward, etc.). We will learn how to design and tune a controller (i) to regulate a process output variable (e.g., temperature, concentration, etc.) to a desired value (set point) despite the presence of process disturbances (regulatory control), (ii) to stabilize and operate an open loop unstable process (stabilizing control), (iii) to optimize the performance of a process via the application of trajectory/optimizing control. In particular, we will study the fundamental principles of classical control theory, including the different types of controllers (e.g., proportional (P), proportional/integral (PI) and proportional/integral/derivative (PID), etc.) and analyze quantitatively the dynamic behavior of closed loop control systems. We will learn how to tune a control loop (i.e., acontroller), in theoryandinthelaboratoryonrealsystems. 2
Course Outline ( 3) Chapter 1 Finally, we will learn in the laboratory part of the course how to use computer simulation tools (i.e., MATLAB, SIMULING, ControlStation,etc.)to design and simulate the transient behavior of open loop and closed loop dynamic systems. Specific Course Objectives Specific Course Objectives Describe the fundamentals of modern process control systems including the needs and incentives for process control and its applications. Model the dynamic behavior of chemical processes using differential equations and transfer functions. Solve linear ODEs in the time domain and using Laplace transforms. Analyze the dynamic behavior of first, second and higher order systems and calculate the system s response to changes (i.e., pulse, step, etc.) in the input variables. Understand the differences between linear and non linear dynamic system behavior. Understand the concept and use of feedback controllers (i.e., P, PI, PID). Understand block diagram developments and closed loop transfer functions. Analyze the dynamic response of systems under feedback control. Perform stability analysis of closed loop systems. Carry out Root Locus Analysis of closed loop systems. Understand frequency response analysis of control systems. Perform controllers tuning using fundamental and approximate process models. Demonstrate a conceptual understanding of complex control structures (e.g., feedforward control, cascade control, multivariable process control, etc.). Use software tools such as MATLAB, SIMULINK to design and evaluate open loop and closed loop dynamic systems. 3
Introduction to Process Control In the chemical industry, the design of a control system is essential to ensure: Good Process Operation Process Safety Product Quality Minimization of Environmental Impact Purpose of a Control System 4
Loose Control Costs Money Tight Control: Profitable Operation 5
Decrease of Standard Deviation in CV Increase of Process Profitability 6
Motivation for Process Control DEFINITIONS Process Dynamics and Control Process: The conversion of feed materials to products using chemical and physical operations taking place in some unit or equipment. Process dynamics refers to unsteady state process behavior. Transient operation occurs during important situations such as start up and shut downs, and unusual disturbances or planned transitions from one product to another. Process control refers to maintaining a process at the desired operating conditions, safely and efficiently, despite the presence of process disturbances, by manipulating,e.g., the flow of a material stream or the energy input into a process. 7
What Does Process Mean? An Example of Stirred Tank Heater T in, w M Q T, w Inputs T in w Process Output T 8
Process Dynamic Models The dynamic behavior of a process can be in theory analyzed in terms of a mathematical model which includes a system of differential and algebraic equations. The numerical solution of the dynamic process model (and in very limited cases, its analytical solution) provides significant information on the process output responses, that is, the system s dynamic behavior in terms of variations in the process input variables. Open Versus Closed loop Systems In open loop dynamic systems: In the first part of the course we will focus in open loop dynamic systems. We will study the transient behavior of processes. No control mechanism. In closed loop control systems: In the second part of thecoursewewillfocus onthe closed loop control of a process under the operation of an automatic controller. 9
Open Versus Closed loop Systems The Elements of a Control System 10
Control Instrumentation Measurement Sensors: Temperature, pressure, pressure drop, level, flow, density, concentration, etc. Final Control Element: Solenoid, valve, variable speed pump or compressor, heater or cooler, etc. Types of Automatic Controllers: On/off, PID, cascade, feed forward, multivariable, modelbased Smith predictor, sampled data, parameter scheduled adaptive controllers, etc. Control Terminology (1) Controlled Variables: These are the variables which quantify the performance or quality of the final product, whichare alsocalledoutput variables. Manipulated Variables: These input variables are adjusted dynamically to keep the controlled variables at their set points. Disturbances: These are also called "load" variables and represent input variables that can cause the controlled variables to deviate from their respective set points. 11
Control Terminology (2) Set point Change: Implementing a change in the operating conditions. The set point signal is changed and the manipulated variable is adjusted appropriately to achieve the new operating conditions. Also called "servo" control or trajectory control. Disturbance Change: When a disturbance enters a process, it can change the process output variables from their desired values. A control system should be able to return each controlled variable back to its setpoint. This is called regulatory control. Controlled and Manipulated Variables Chapter 1 12
Home Heating Control System Control Objective Measured Process Variable (PV) Set Point (SP) Controller Output (CO) Manipulated Variable Disturbances (D) Home Heating Control System Measurement Computation Action Is house cooler than set point? (T setpoint T house > 0) Action Open Fuel Valve Is house warmer than set point? (T setpoint T house < 0) Action Close Fuel Valve 13
Control Block Diagram General Control Block Diagram 14
Control of a Stirred Tank Heater Continuous stirred tank heater Question: Assume that the inlet temperature, T i (t) changes with time. How can we ensure that T(t) remains at or near the set point temperature? (t) (t) (t) Control of a Stirred Tank Heater (t) Feedback control of stirred tank heater 15
Control Instrumentation Measurement Element: Thermocouple for temperature measurement and transmitter, TT Final Control Element: Electric heater Automatic Controller: For example, PID temperature controller, TC Electrical Transmission Lines Classification of Input Variables Manipulated Variables (MV or Control Variables) Their values can be adjusted freely by an operator or a control mechanism. In the example of the heated tank: the amount of heat added (Q). Disturbance Variables (DV) They actually represent random variations in the input process variables. Their values are not the result of the adjustment by an operator or a controller. They vary in a random and nonpredictable way. In the example of the heated tank: Inlet temperature of inlet water. 16
Classification of Output Variables The output variables can be further distinguished into: Measured output variables or Controlled variables (CV) Their values can be measured with the aid of a measurement element (i.e., sensor) and,thus, can be controlled. In the example of the heated tank: The outlet temperature. Unmeasured output variables They are not or cannot be measured directly. Control Block Diagram 17
Feedback Control Distinguishing feature: Takes corrective action after disturbance enters the process. Advantages: Corrective action is taken regardless of the source of the disturbance. Reduces sensitivity of the controlled variable to disturbances and changes in the process. Disadvantages: No corrective action occurs until after the disturbance has upset the process, that is, until after y(t) differs from y sp. Oscillatory responses, or even instability Example: Heated Stirred Tank (t) (t), Q(t) 18
Closed loop Artificial Pancreas glucose setpoint r u y Chapter 1 controller pump patient sensor measured glucose Feedforward Control Distinguishing feature: Measures a disturbance and takes corrective action before disturbance enters the process. Advantages: Corrects for disturbance before it upsets the process. Disadvantages: Must be able to measure the disturbance. No corrective action for unmeasured disturbances 19
Example: Heated Stirred Tank (t) (t) (t), Q(t) Example: Stirred Tank Heater Possible Control Strategies 1. Measure T and adjust Q 2. Measure T i and adjust Q 3. Measure T and adjust w 4. Measure T i and adjust w 5. Measure T and T i and adjust Q 6. Measure T and T i and adjust w 7. Place a heat exchanger on the inlet stream Classification of Control Strategies 1 & 3: Feedback control 2 & 4: Feedfoward control 5 & 6: Feedfoward Feedback control 7: Change of design 20
Example: Blending System x 1 (t) w 2 (t) Notation: w 1, w 2 (t) and w are mass flow rates x 1 (t), x 2 and x(t) are mass fractions of component A x(t) w(t) Assumptions: 1. w 1 is constant Example: Blending System 2. x 2 = constant = 1 (stream 2 is pure A) 3. Perfect mixing in the tank Control Objective: Keep x at a desired value (or set point ) x sp, despite variations in x 1 (t). Flow rate w 2 (t) can be adjusted for this purpose. Terminology: Controlled variable (or output variable ): x(t) Manipulated variable (or input variable ): w 2 (t) Disturbance variable (or load variable ): x 1 (t) 21
What value of Overall balance: Design Question w 2 is required to have x x SP? 0 w w w (1-1) 1 2 Chapter 1 Component A balance: wx 1 1 w2x2 wx 0 (1-2) (The over bars denote nominal steady state design values.) At the design conditions, x x SP. Substitute in Eq. 1 2, x x and x2 1, then solve Eq. 1 2 for w2 : xsp x1 w2 w1 (1-3) 1 x SP SP Control Question Chapter 1 Equation 1 3 is the design equation for the blending system. If our assumptions are correct, then this value of keep x at x. But what if conditions change? SP will Control Question. Suppose that the inlet concentration x 1 changes with time. How can we ensure that x remains at or near the set point? x SP As a specific example, if x x and w w, then x > x SP. 1 1 2 2 w 2 22
Some Possible Control Strategies Method 1. Measure x and adjust w 2. Intuitively, if x is too high, we should reduce w 2 ; Manual control vs. automatic control Proportional feedback control law, w2 t w2 Kc xsp x t (1-4) 1. Where K c is called the controller gain. 2. w 2 (t) and x(t) denote variables that change with time t. 3. The change in the flow rate, w 2 t w 2, is proportional to the deviation from the set point, x SP x(t). Blending System: Control Method 1 Chapter 1 23
Some Possible Control Strategies Method 2. Measure x 1 and adjust w 2. Chapter 1 Thus, if x 1 is greater than that w w 2 2 ; x 1, we would decrease w 2 so One approach: Consider Eq. (1 3) and replace x1 and w2 with x 1 (t) and w 2 (t) to get a control law: xsp x t w2 t w1 (1-5) 1 x 1 SP Blending System: Control Method 2 Chapter 1 24
Some Possible Control Strategies Because Eq. (1 3) applies only at steady state, it is not clear how effective the control law in Eq. (1 5) will be for transient conditions. Chapter 1 Method 3. Measure x 1 and x, adjust w 2. This approach is a combination of Methods 1 and 2. Method 4. Use a larger tank. If a larger tank is used, fluctuations in x 1 will tend to be damped out due to the larger capacitance of the tank contents. However, a larger tank means an increased capital cost. Control Strategies for Blending System Table. 1.1 Control Strategies for the Blending System Chapter 1 Method Measured Variable Manipulated Variable Category 1 x w 2 FB 2 x 1 w 2 FF 3 x 1 and x w 2 FF/FB 4 - - Design change 25
Hierarchy of Control Activities Chapter 1 Control System Developments Chapter 1 26
Summary Learn why modeling the dynamic behavior of a process is fundamental to controlling it. Practice methods of collecting and analyzing process data to determine dynamic behavior. Learn what "good" or "best" control performance means for a particular process Understand the computational methods behind PID control and learn when and how to use each form. Learn how controller tuning impacts performance and how to determine values for these parameters. Examples of Control Applications Robotics: Robots perform automated tasks in assembly lines, where precision is important (e.g. welding in automotive industry) and dangerous tasks physically impossible for humans (e.g. military operations, and space explorations) 27
Examples of Control Applications Aerospace Applications: Aircraft or missile guidance and control Space vehicles and structures Examples of Control Applications Intelligent Transportation & Automotive Systems: Marine, Land, Air vehicles Platoon of cars in Automated Highway Systems Warning systems for trains, railroad crossings, Automatic landing systems for planes, flight control systems Air traffic control, highway traffic control, Ship steering, etc etc Professor Costas Kiparissides Chemical Engineering Department CHEMG 461 28