Process Controls Lecture Notes Fall 2021

  Table of Contents

Solutions for Chapters 1-14 Solutions for Module 5.4 and Module 5.5 Solution for Module 16, Discrete PI Example

Chapter 1 Solutions 1.1

•  Braking Force •   Gear Selection Input Variables – Disturbances:

i.  Driving a car 

Pleasee see either jogging, cycling, stir Pleas stirred red tank heater, or household thermostat for a representative answer. ii.  Two sample favorite activities:

Jogging 

(a)   Objectives: •   Jog intensely intensely (heart (heart rate at 180bp 180bpm) m) for 30 min. •   Smooth Smooth chang changes es in joggin joggingg in inte tensi nsity ty and speed. (b)  Input Variables: •   Jogging Rate – Manipulated input •   Shocking Shocking surprises (dogs, cars, etc. etc.)– )– Disturbance (c)  Output Variables: •  Blood Oxygen level – unmeasured •  Heart beat – measured •   Breathing rate – unmeasured (d)  Constraints: •  Hard: Max Heart Rate (to avoid heart attack → attack  →  death) •   Ha Hard rd:: Bl Blood ood oxyg oxygen en mi mini nimu mum m an and d maximum •  Soft: Time spent jogging (e)   Operating characteristics: Continuous during period, Semi Batch when viewed over larger time periods. Safety, environm environment ental, al, economic economic factors: factors: (f)   Safety Potential for injury, overexertion Control: Feedback/ eedback/F Feedforwa eedforward rd system. system. (g)   Control: Oxygen level, heartbeat, fatigue all part of  determ determini ining ng action action aft after er the fact. Path, Path, weather are part of feedforward system Cycling 

(a)   Objectives: •   Ensure stability (don’t crash) •   Enjoy ride •  Prevent mechanical failure (b)  Input Variables – Manipulated: •   Body Position •   Steering

•   Weather •   Path Conditions •  Other people, animals (c)  Output Variables – Measured: •   Speed •   Direction •   Ca Caloric loric Output Output (via electronic electronic monitor) Output Variables – Unmeasured: •  Level of enjoyment •  Mechanical integrity of person and bicycle •   Aesthetics (smoothness of ride) (d)   Constraints – Hard: •  Turning radius •  Mechanical limits of bike and person •  Maximum fatigue limit of person Constraints – Soft: •  Steering dynamics that lead to instability before mechanica mechanicall failure (i.e. you crash, the bike doesn’t break) Terrai errain n and wea weather ther can limit enjoy• T ment level. (e)   Operation: Operation: Contin Continuous: uous: Steering, Steering, weigh weightt distribution, terrain selection within a path, ped pedal al fo forc rcee Semi Semi ba batc tch: h: Gear Gear sele select ctio ion, n, braking force Batch: Tire pressure, bike selection, path selection (f))   S Safe afety ty,, en envir vironm onmen ent, t, econom economics ics:: Saf Safet ety: y: (f Stability and mechanical limits prevent in jury to rider and others Environment: Trail ero erosio sion, n, noi noise se Economic Economics: s: Health Health costs, costs, maintenance costs (g)   Control Structure: Feedback: Levels of exertion, bike performance are monitored and ride is adjusted after the fact FeedForward: Path is seen ahead and ride is adjusted accordingly. iii.  A stirred tank heater

(a)   Objectives •  Maintain Operating Temperature •   Maintain flow rate at desired level (b)  Input Variables:

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•  Manipulated: Added heat to system •   Disturbanc Disturbance: e: Upst Upstream ream flow rate and conditions (c)   Output Output Variables ariables – Measured: Measured: Tank fluid temperature, Outflow (d)  Constraints: •   Hard: Hard: Max infl inflow ow and outflow outflow as per pipe size and valve limitations

•  Soft: Max or minimum temperature for comfort conditions: Contin Continuous uous heating (e)   Operating conditions: adjustment, continuous temperature reading. (f))  Safety, Environmental, Economic consider(f ations ations:: Saf Safet ety: y: heater heater may may be an electr electriical or burning burning hazard Economics: Economics: Heat Heating ing costs Environmental: Energy consumption.

•   Soft: Fluid temperatur temperaturee for operati operating ng objective

(g)   Control System: Feedback; temperature is mon monito itored red,, heatin heatingg rate rate is adj adjust usted ed aft after er (e)   Operati Operating ng con condit dition ions: s: Con Contin tinuou uouss fluid fluid the fact. flow adjustment, continuous heating adjustment vii.  Air traffic control  (f)  Safety, Environmental, Economic considerPlease Please see either jogging, cycling, stirred stirred tank ations: Safety: Tank overflow, failure could heater, or household thermostat for a represencause injury Economics: Heating costs, spill tative answer. costs, process quality costs Environmental: Energy consumption, contamination due to 1.2 spills of hot water (g)  Control System: Feedback: Temperature is a.  Fluidized Catalytic Cracking Unit monitored, monit ored, heat heating ing rate is adjus adjusted ted Feedi.  Summary of paper: forward: forward: Upstr Upstream eam flow velocit velocity y is used to predict future tank state and input is adA fluidiz fluidized ed cat cataly alytic tic cra crack cking ing unit unit (F (FCCU CCU)) is  justed accordingly. accordingly. on onee of th thee typ ypic ical al an and d co comp mple lex x proce process sses es in iv.   Beer fermentation 

Please see either jogging, cycling, stir Please stirred red tank heater, or household thermostat for a representative answer. v.  An activated sludge process 

Pleasee see either jogging, cycling, stir Pleas stirred red tank heater, or household thermostat for a representative answer. vi.   A household thermostat

(a)   Objectives: •   Maintain comfortable temperature •   Minimize energy consumption (b)  Input Variables: • Manipulated: Outside Temperature setting en•    Disturbance: temperature, ergy transmission transmission betw between een house and environment (c)  Output Variables: •   Measured: Thermostat reading

petroleum refining. Its principal components are a reactor and a generator. The reactor executes cata catalytic lytic cracking cracking to produce lighter lighter petro-oil petro-oil products. product s. The regenerator regenerator recharge rechargess the cataly lyst st and feeds feeds it ba back ck to the react reactor or.. In this paper, the authors test their control schemes on a FCCU model. The model is a nonlinear multiinput/multi-output (MIMO) which couples time varying and stoc stochasti hasticc processes. processes. Consi Considerab derable le co comp mput utat atio ion n is need needed ed to use use mod model el pred predic ic-tiv tivee process process con control trol algorithms algorithms (MPC). Standard PID control control giv gives es inferior performance. performance. A simplified MPC algorithm is able to reduce the number of parameters and computational load while still performing better than a PID control method. ii.   F Familiar amiliar Terms: Terms: Constraint, nonlinearity, nonlinearity, con-

trol trol perform performanc ance, e, MPC, MPC, unmeas unmeasure ured d dis distur tur-bance rejection, modeling, simulation.

b.  Reactive Ion Etching 

Please see FCCU for a representative answer.

•   Unmeasured: Comfort level level (d)  Constraints:

c.   Rotary Lime Kiln 

Please see FCCU for a representative answer.

•   Hard: Max heating heating or cooling duty of  d.   Continuous Drug Infusion  Please see FCCU for a representative answer. system 1-2