CHEE 434/821 Process Control II Some Review Material

1. CHEE 434/821Process Control IISome Review Material Winter 2006 Instructor: M.Guay TA: V. Adetola

2. Introduction 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

3. Introduction • What is the purpose of a control system? “To maintain important process characteristics at desired targets despite the effects of external perturbations.” Processing objectives Safety Make $$$ Environment... Perturbations Market Economy Climate Upsets... Plant Control

4. Introduction What constitutes a control system? Combination of process sensors, actuators and computer systems designed and tuned to orchestrate safe and profitable operation. Control Plant

5. Introduction • Process Dynamics: • Study of the transient behavior of processes • Process Control • the use of process dynamics for the improvement of process operation and performance or • the use of process dynamics to alleviate the effect of undesirable (unstable) process behaviors

6. Introduction What do we mean by process? A process, P, is an operation that takes an INPUT or a DISTURBANCE and gives an OUTPUT INPUT: (u)Something that you can manipulate DISTURBANCE: (d) Something that comes as a result of some outside phenomenon OUTPUT: (y) An observable quantity that we want to regulate u y P d Information Flow

7. Examples • Stirred tank heater M Tin, w T, w Q Inputs Output Tin w Process T Q

8. Examples • The speed of an automobile Force of Engine Friction Inputs Output Friction Engine Process Speed

9. Examples e.g. Landing on Mars

10. Examples e.g. Millirobotics Laparoscopic Manipulators

11. Introduction • Process A process, P, is an operation that takes an INPUT or a DISTURBANCE and gives an OUTPUT INPUT: (u)Something that you can manipulate DISTURBANCE: (d) Something that comes as a result of some outside phenomenon OUTPUT: (y) An observable quantity that we want to regulate u y P d Information Flow

12. Control What is control? • To regulate of a process output despite the effect of disturbances e.g. • Driving a car • Controlling the temperature of a chemical reactor • Reducing vibrations in a flexible structure • To stabilize unstable processes e.g. • Riding a bike • Flight of an airplane • Operation of a nuclear plant

13. Benefits of Control • Economic Benefits • Quality (waste reduction) • Variance reduction (consistency) • Savings in energy, materials, manpower • Operability, safety (stability) • Performance • Efficiency • Accuracy • robotics • Reliability • Stabilizability • bicycle • aircraft • nuclear reactor

14. Control What is a controller? Process • A controller is a system designed to regulate a given process • Process typically obeys physical and chemical conservation laws • Controller obeys laws of mathematics and logic (sometimes intelligent) e.g. - Riding a bike (human controller) - Driving a car - Automatic control (computer programmed to control) Controller

15. Block representations • Block diagrams are models of the physical systems Process Input variables Output variables System Physical Boundary Transfer of fundamental quantities Physical Mass, Energy and Momentum Abstract Operation

16. Control • A controlled process is a system which is comprised of two interacting systems: e.g. Most controlled systems are feedback controlled systems The controller is designed to provide regulation of process outputs in the presence of disturbances Disturbances Outputs Process Action Observation intervene monitor Controller

17. Introduction What is required for the development of a control system? 1. The Plant (e.g. SPP of Nylon) Nylon Gas Make-up Reheater Vent Relief Pot Dehumidifier Steam Heater Blower Water

18. Introduction What is required? 1. Process Understanding • Required measurements • Required actuators • Understand design limitations 2. Process Instrumentation • Appropriate sensor and actuator selection • Integration in control system • Communication and computer architecture 3. Process Control • Appropriate control strategy

19. Example • Cruise Control Friction Process Speed Engine Controller Human or Computer

20. Classical Control • Control is meant to provide regulation of process outputs about a reference, r, despite inherent disturbances • The deviation of the plant output, e=(r-y), from its intended reference is used to make appropriate adjustments in the plant input, u d r e u y + Controller Process - Classical Feedback Control System

21. Control • Process is a combination of sensors and actuators • Controller is a computer (or operator) that performs the required manipulations e.g. Classical feedback control loop d Computer Actuator r e y + C A P - Process M Sensor

22. Examples • Driving an automobile Driver Steering r e y + C A P - Automobile M Visual and tactile measurement Actual trajectory y Desired trajectory r

23. Examples • Stirred-Tank Heater Tin, w Heater Q T, w TC Thermocouple Tin, w Controller Heater e y TR + C A P - Tank M Thermocouple

24. Examples • Measure T, adjust Q Controller: Q=K(TR-T)+Qnominal where Qnominal=wC(T-Tin) Q: Is this positive or negative feedback? Tin, w Controller Heater e T + C A P TR - Tank M Thermocouple Feedback control

25. Examples • Measure Ti, adjust Q Ti M C A P DQ + Q Qi + Feedforward Control

26. Control Nomenclature • Identification of all process variables • Inputs (affect process) • Outputs (result of process) • Inputs • Disturbance variables • Variables affecting process that are due to external forces • Manipulated variables • Things that we can directly affect

27. Control Nomenclature • Outputs • Measured • speed of a car • Unmeasured • acceleration of a car • Control variables • important observable quantities that we want to regulate • can be measured or unmeasured Disturbances Other Process Control Manipulated Controller

28. Example wi, Ti Pc L wc, Tci h T wc, Tco Po wo, To T • Variables • wi, wo: Tank inlet and outlet mass flows • Ti, To: Tank inlet and outlet temperatures • wc: Cooling jacket mass flow • Pc: Position of cooling jacket inlet valve • Po: Position of tank outlet valve • Tci, Tco: Cooling jacket inlet and outlet • temperatures • h: Tank liquid level

29. Example Variables Inputs Outputs Disturbances Manipulated Measured Unmeasured Control wi Ti Tci wc h wo To Pc Po Task: Classify the variables

30. Process Control and Modeling • In designing a controller, we must • Define control objectives • Develop a process model • Design controller based on model • Test through simulation • Implement to real process • Tune and monitor d r e u y Controller Process Model Design Implementation

31. Control System Development Control development is usually carried out following these important steps Define Objectives Develop a process model Design controller based on model Test by Simulation Implement and Tune Monitor Performance Often an iterative process, based on performance we may decide to retune, redesign or remodel a given control system

32. Control System Development • Objectives • “What are we trying to control?” • Process modeling • “What do we need?” • Mechanistic and/or empirical • Controller design • “How do we use the knowledge of process behavior to reach our process control objectives?” • What variables should we measure? • What variables should we control? • What are the best manipulated variables? • What is the best controller structure?

33. Control System Development • Implement and tune the controlled process • Test by simulation • incorporate control strategy to the process hardware • theory rarely transcends to reality • tune and re-tune • Monitor performance • periodic retuning and redesign is often necessary based on sensitivity of process or market demands • statistical methods can be used to monitor performance

34. Process Modeling • Motivation: • Develop understanding of process • a mathematical hypothesis of process mechanisms • Match observed process behavior • useful in design, optimization and control of process • Control: • Interested in description of process dynamics • Dynamic model is used to predict how process responds to given input • Tells us how to react

35. Process Modeling What kind of model do we need? • Dynamic vs. Steady-state • Steady-state • Variables not a function of time • useful for design calculation • Dynamic • Variables are a function of time • Control requires dynamic model

36. Process Modeling What kind of model do we need? • Experimental vs Theoretical • Experimental • Derived from tests performed on actual process • Simpler model forms • Easier to manipulate • Theoretical • Application of fundamental laws of physics and chemistry • more complex but provides understanding • Required in design stages

37. Process Modeling • Dynamic vs. Steady-state • Step change in input to observe • Starting at steady-state, we made a step change • The system oscillates and finds a new steady-state • Dynamics describe the transitory behavior 65 Steady-State 1 60 55 Output Steady-State 2 50 45 40 50 100 150 200 250 300 0 Time

38. Process Modeling • Empirical vs. Mechanistic models • Empirical Models • only local representation of the process (no extrapolation) • model only as good as the data • Mechanistic Models • Rely on our understanding of a process • Derived from first principles • Observing laws of conservation of • Mass • Energy • Momentum • Useful for simulation and exploration of new operating conditions • May contain unknown constants that must be estimated

39. Process Modeling • Empirical vs Mechanistic models • Empirical models • do not rely on underlying mechanisms • Fit specific function to match process • Mathematical French curve

40. Process Modeling • Linear vs Nonlinear • Linear • basis for most industrial control • simpler model form, easy to identify • easy to design controller • poor prediction, adequate control • Nonlinear • reality • more complex and difficult to identify • need state-of-the-art controller design techniques to do the job • better prediction and control • In existing processes, we really on • Dynamic models obtained from experiments • Usually of an empirical nature • Linear • In new applications (or difficult problems) • Focus on mechanistic modeling • Dynamic models derived from theory • Nonlinear

41. Process Modeling • General modeling procedure • Identify modeling objectives • end use of model (e.g. control) • Identify fundamental quantities of interest • Mass, Energy and/or Momentum • Identify boundaries • Apply fundamental physical and chemical laws • Mass, Energy and/or Momentum balances • Make appropriate assumptions (Simplify) • ideality (e.g. isothermal, adiabatic, ideal gas, no friction, incompressible flow, etc,…) • Write down energy, mass and momentum balances (develop the model equations)

42. Process Modeling • Modeling procedure • Check model consistency • do we have more unknowns than equations • Determine unknown constants • e.g. friction coefficients, fluid density and viscosity • Solve model equations • typically nonlinear ordinary (or partial) differential equations • initial value problems • Check the validity of the model • compare to process behavior

43. Process Modeling • For control applications: • Modeling objectives is to describe process dynamics based on the laws of conservation of mass, energy and momentum • The balance equation 1. Mass Balance (Stirred tank) 2. Energy Balance (Stirred tank heater) 3. Momentum Balance (Car speed) Flow Out Rate of Accumulation of fundamental quantity Flow In - = Rate of Production +

44. Process Modeling • Application of a mass balance Holding Tank • Modeling objective: Control of tank level • Fundamental quantity: Mass • Assumptions: Incompressible flow Fin h F

45. Process Modeling Total mass in system = rV = rAh Flow in = rFin Flow out = rF Total mass at time t = rAh(t) Total mass at time t+Dt = rAh(t+Dt) Accumulation rAh(t+Dt) - rAh(t) = Dt(rFin-rF ),

46. Process Modeling Model consistency “Can we solve this equation?” Variables: h, r, Fin, F, A 5 Constants: r, A 2 Inputs: Fin, F 2 Unknowns: h 1 Equations 1 Degrees of freedom 0 There exists a solution for each value of the inputs Fin, F

47. Process Modeling Solve equation • Specify initial conditions h(0)=h0 and integrate

48. Process Modeling • Energy balance Objective: Control tank temperature Fundamental quantity: Energy Assumptions: Incompressible flow Constant hold-up M Tin, w T, w Q

49. Process Modeling • Under constant hold-up and constant mean pressure (small pressure changes) • Balance equation can be written in terms of the enthalpies of the various streams • Typically work done on system by external forces is negligible • Assume that the heat capacities are constant such that

50. Process Modeling After substitution, Since Trefis fixed and we assume constant r ,Cp Divide by r CpV