- Consider the PCM distillation column module of Appendix E with the following variables:CVs: Overhead Composition (xD) and Bottom Composition (xB) MVs: Reï¬‚ux Ratio (R) and Vapor
- Repeat Exercise 20.11 for R = diagonal [0.1, 0.1] and: (i) M = 1 and (ii) M = 4.Data From 20.11Consider the PCM distillation column module of Appendix E with the following variables:CVs:
- Repeat Exercise 20.12 for Q = diagonal [0.1 0.1] and(i) M = 1 and (ii) M = 5.Data From 20.11Consider the PCM distillation column module of Appendix E with the following
- Consider Section 24.3.3, where the dynamic properties of a signal transduction were analyzed. Two properties of inter est are the signal duration and the amplitude of the signal.(a)The following
- Recall the Central Dogma for biology, which is depicted in simplified form in the block diagram Fig. E24.7. In this case, it is assumed that nuclear transport can be ignored. Let X denote an
- An interesting motif in biological circuits is a switch, in which the system can change from (effectively) one binary state to another. An analysis of a continuous reaction network reveals a rise to
- Consider the simplified version of the chemotaxis circuit in Fig. 24.10.(a) Derive the conditions for the process gain K that ensure that the receptor activity is always reset to zero and even for
- As a specific biological example for Exercise 24.2 and Fig. E24.2(b),ˆ— the synthesis of tryptophan can be described by the following set of material balances:where k1, k2, k3, and k4
- Consider the block diagram in Fig. E24.2 of the multiple feedback loops involved in the Central Dogma schematic from Fig. 24.3, namely, genetic regulation C1, transnational regulation C2, and enzyme
- In this exercise, treat the components as simple (reactive) chemical species and perform the appropriate (dynamic) material balance. Assume that a messenger RNA mRNA is produced by a constant (basal)
- Data from an actual clinical trial for the closed-loop artificial pancreas is summarized in the following cumulative histograms, where the percentage of blood glucose measurements below a particular
- Recall the artificial pancreas control problem from Section 23.2. In order to regulate blood glucose BG, you have two possible manipulated variables to choose from: pumping insulin FIand pumping
- Consider the diabetic patient in Example 23.3. Your goal is to design an automated device to administer insulin infusion in response to meal disturbances. (a) Considering only the
- A crystallize is used to separate a pharmaceutical product from the fermentation extract. The three manipulated variables are the fines dissolution rate u1, the crystallize temperature u2, and the
- In a rehabilitation training experiment for a neurological patient, a step change in treadmill speed of +2.5 km/h was made. The patient heart rate response HR is given in Fig. E23.4.(a) Derive an
- Gaohua and Kimura (2006) derived an empirical patient model for the manipulation of ambient temperature u (ˆ˜C) to inï¬‚uence the patient€™s brain intracranial
- Consider the granulation model that was given in Example 23.2.(a) Design an MPC controller, using the nominal process model. Initially consider a control horizon of M = 2 and a prediction horizon of
- Consider the fermentor problem in Example 23.1. (a) Design an IMC controller for the first operating point (dilution = 0.202 h-1), and simulate the response to both a +0.5 [g/L] and a -0.5 [g/L]
- In order to improve the reliability of a critical control loop, it is proposed that redundant sensors be used. Suppose that three independent sensors are employed and each sensor works properly 95%
- In a computer control system, the high and low warning limits for a critical temperature measurement are set at the “2-sigma limits,” T̅ ± 3σ̂ T, where T̅ is the nominal temperature and σ̂
- An analyzer measures the pH of a process stream every 15 minutes. During normal process operation, the mean and standard deviation for the pH measurement are x = 5.75 and s = 0.05, respectively. When
- A process (including sensor and control valve) can be modeled by the transfer function,(a) Derive an analytical expression for the response to a unit step change in the input.(b) Suppose that the
- For the transfer functions(a) Derive an analytical expression for the step response to a unit step change. Evaluate the step-response coefficients, {Si}, for a sampling period of Î”t =
- A brewery has the capability of producing a range of beers by blending existing stocks. Two beers (suds and premium) are currently available, with alcohol concentrations (by volume) of 3.0% for suds
- A batch reactor converts component A into B, which in turn decomposes into C:where
- A refnery processes two crude oils that have the yields shown in the table below. Because of equipment and storage limitations, production of gasoline, kerosene, and fuel oil must be limited as shown
- The thermal effciency of a natural gas boiler versus air/fuel ratio is plotted in Fig. E19.2. Using physical arguments, explain why a maximum occurs. Air-to-fuel stoichiometric ratio Figure E19.2
- In Figs. 18.6 and 18.7, look at the different pairings of controllers. Which one has the larger stability region? How does this compare with the preferred pairing indicated by the RGA (is it the same
- Water (F1) is blended with a stream F2 with 40% ethanol to make a whiskey product that is 30% ethanol. Assume F1 = 4 gal/min and F2 = 4 gal/min.(a) Develop a steady-state material balance model for
- A process control engineer has decided to install an automated shower control system in a bathroom of her mansion. The design calls for a system that can deliver 3 gal/min of water at 110∘F by
- For the two input two output process in Example 18.2, use Simulink to check the stability regions in Fig. 18.6 for the 1-1, 2-2 controller pairing. Set Kc1 = 1, and try three values of Kc2(-1,
- Consider the simple block diagram for the feedback control of circadian rhythms (i.e., 24 h) in Fig. 24.5.To simplify things considerably, assume that transcription obeys a first order process with
- The dynamic behavior of a temperature sensor and transmitter can be described by the FOPTD transfer functionwhere the time constant and time delay are in seconds and:T = actual
- The analog exponential flter in Eq. 17-4 is used to flter the output signal from a transfer function G = 1/(2s + 1). The input signal is d(t) = 1 + 0.2 sin t. Compare the responses for no fltering
- It is desired to reduce the concentration of CO2in the ï¬‚ue gas from a coal-fred power plant, in order to reduce greenhouse gas emissions. The efï¬‚uent
- Design a time-delay compensator (Smith predictor) forwhere Gv = Gm = 1 and Î¸ = 1. Show closed-loop responses for unit step set-point and disturbance changes (Gd = Gp). Use an IMC PI
- The cascade reactor control configuration shown in Fig. 16.3 utilizes a measurement of the cooling water temperature. It has been suggested that the temperature of the reactor wall be measured to
- In the introduction to Section 16.4, it is stated that based on a steady-state degrees-of-freedom analysis of a control system, it is not possible to eliminate offset in the controlled variables for
- Figure E16.26 shows cascade temperature control of a polymerization reactor, which uses feed heat exchange to adjust the reactor temperature. Using the instrumentation diagram, explain how this
- Diabetes mellitus is characterized by insufficiency of the pancreas to produce enough insulin to regulate the blood sugar level. In type I diabetes, the pancreas produces no insulin, and the patient
- Consider Figs. 16.3 and 16.4 illustrating cascade control. (a) Suppose you were to apply feedforward control, instead of cascade control, to handle disturbances D1 and D2. Where do you expect
- A water tank heating process shown in Fig. E16.4 controls the outlet temperature at a desired set point TSPby manipulating the steam pressure PSof steam sent to the tank heat exchanger. The steam
- Measurement devices and their dynamics inï¬‚uence the design of feedback controllers. Brieï¬‚y indicate which of the two systems below would have its closed-loop
- Consider the PCM furnace module of Appendix E. Assume that oxygen exit concentration cO2is the CV, air ï¬‚ow rate AF is the MV, and fuel gas purity FG is the DV.(a) Using the
- The distillation column in Fig. 15.8 has the following transfer function model:with Gv = Gm = Gt = 1.(a) Design a feedforward controller based on a steady-state analysis.(b) Design a
- Design a feedforward€“feedback control system for the blending system in Example 15.5, for a situation in which an improved sensor is available that has a smaller time delay of 0.1 min.
- A liquid-phase reversible reaction, A ‡„ B, takes place isothermally in the continuous stirred-tank reactor shown in Fig. E15.8. The inlet stream does not contain any B. An
- Consider the ratio control scheme shown in Fig. 15.6. Each flow rate is measured using an orifice plate and a differential pressure (D/P) transmitter. The pneumatic output signals from the D/P
- Use arguments based on the phase angle in frequency response to determine if the following combinations of G = GvGpGmand Gcbecome unstable for some value of Kc.a.b.c.d.e. |G = G. = K. (4s + 1)(2s +
- Two engineers are analyzing step-test data from a bioreactor. Engineer A says that the data indicate a second-order over damped process, with time constants of 2 and 6 min but no time delay. Engineer
- Determine if the following processes can be made unstable by increasing the gain of a proportional controller Kcto a sufficiently large value using frequency response arguments:a.b.c.d. G,G,Gm 2 s +1
- A perfectly stirred tank is used to heat a flowing liquid. The dynamic model is shown in Fig. E14.4.
- A two-phase feed to the gas-liquid separator (or flash drum), shown in Fig. E13.10, consists of a mixture of two hydrocarbons. Because the vessel pressure P is lower than the feed pressure, the feed
- (a) Using the process, sensor, and valve transfer functions in Exercise 11.21, find the ultimate controller gain Kcuusing a Bode plot. Using simulation, verify that values of Kc> Kcucause
- For the following statements, discuss whether they are always true, sometimes true, always false, or sometimes false. Cite evidence from this chapter.(a) Increasing the controller gain speeds up the
- You are using proportional control (Gc =Kc) for a process with Gv = 4 / 2s + 1 and Gp 0.6 / 50s + 1 (time constants in s). You have a choice of two measurements, both of which exhibit first order
- A data acquisition system for environmental monitoring is used to record the temperature of an air stream as measured by a thermocouple. It shows an essentially sinusoidal variation after about 15s.
- A stirred-tank heating system is shown in Fig. E13.9. Briefly critique these two control strategies. (a) It is proposed that h and T be controlled by manipulating wh and wc using two PI
- Consider the PCM distillation column module of Appendix E. Assume that distillate MeOH composition xDis the CV, that reflux ratio R is the MV, and that they are related by the following transfer
- Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature THCis the CV, that fuel gas flow rate FFGis the MV, and that they are related by the following transfer function
- Consider the FOPTD model in Eq. 12-10 with K = 5, τ = 4, and θ = 3. Design PI and PID controllers using the IMC tuning method with τc = θ = 3. Simulate the closed loop systems for a unit step
- A process stream is heated using a shell and tube heat exchanger. The exit temperature is controlled by adjusting the steam control valve shown in Fig. E12.5. During an open-loop experimental test,
- A process, including the sensor and control valve, can be modeled by the transfer function:(a) If a proportional-only controller is used, what is the maximum value of controller gain Kc that will
- A process has the transfer function, G(s) = 2e−2s / (s + 1). Compare the PI controller settings for the following design approaches:(a) IMC method (τc = 0.2)(b) IMC method (τc = 1.0)(c) ITAE
- Consider the two feedback control strategies shown in Fig. 12.6 (with G = GvGpGm) and the following transfer functions:(a) Design an IMC controller,Gˆ—c, using a filter, f =
- Suppose that the temperature in an exothermic continuous stirred-tank reactor is controlled by manipulating the coolant flow rate using a control valve. A PID controller is used and is well tuned.
- A coolant (specific gravity = 1.2) is pumped through a heat exchanger and control valve at a nominal (desired) flow rate of qd = 0.6 m3/min. The total pressure drop over this heat exchanger
- Consider the evaporator and control system in Figure 13.6.(a) Should each control valve be air-to-open (AO) or air-to-close (AC)?(b) Should each PI controller be direct-acting or reverse-acting? (I/P
- It has been suggested that the liquid flow rate in a large diameter pipeline could be better regulated by using two control valves instead of one. Suppose that one control valve has a large
- The dynamic behavior of a temperature sensor / transmitter can be modeled as a first-order transfer function (in deviation variables) that relates the measured value Tmto the actual temperature,
- Air samples from a process area are continuously drawn through a1∕4-in diameter tube to an analytical instrument that is located 60m away. The tubing has an outside diameter of 6.35 mm and a wall
- A cylindrical storage tank is 2 m tall and 1 m in diameter. A low-level alarm is activated when the liquid level decreases to 0.25 m. Suppose that the tank is initially half full when a slow leak
- The probability of a particular type of sensor functioning properly is 0.95. Consequently, a triply redundant sensor system has been proposed for a critical measurement. Thus, three independent
- For the reliability analysis of the flow control loop in Example 10.4, the DP flow meter is the least reliable component. Suppose that a second, identical flow meter is used in a backup mode so that
- Repeat Exercise 10.7 for the case where the flow meters are triply redundant; that is, there are three identical flow meters with two in the backup mode. How much would the overall system reliability
- Consider the liquid storage tank with a low-level inter-lock, as shown in Fig. 10.4. Suppose that an independent low-level alarm is added, with its set-point value above the value for the low-level
- Using the failure rate data in Table 10.1, evaluate the reliability and mean time between failures for the high-pressure interlock in Fig. 10.4. Assume that the failure rate for the solenoid switch
- A plasma etching batch process has a process gain of E Ȧ/min (but no dynamics). The manipulated variable is the etch time, so the controlled variable is the film thickness. There are no time
- Derive the characteristic equation for a control system with the following transfer functions: Gc= Kc,Is the system stable for (a) Kc = 9, (b) Kc = 11, (c) Kc = 13? Gm 0.5 |G,G, : s+3* (s +
- Suppose a control system is modeled by GvGp = 0.25 / (s + 1)3 , Gm = 4, and Gc = Kc. Find the maximum value of Kc for a proportional controller for which the system is stable, using direct
- A control system has the following transfer functions in its block diagram (see Fig. 11.8): Gc=1, Gv = 2, Gd = Gp= 2 / s(s + 4), Gm= 1. For a unit step change in Ysp, determine (a)
- A PI controller is to be used in a temperature control system for a bioreactor. For nominal conditions, it has been determined that the closed-loop system is stable when τI = 10 min and −10 <
- A process is described by the transfer functionFind the range of controller settings that yield stable closed-loop systems for:(a) A proportional-only controller.(b) A proportional-integral
- Consider the block diagram of a feedback control system in Fig. 11.8, where Km= 1, Gp= 1 / s + 1, Gd= 0, Gv= Kveˆ’s, Gc= 1, and Gm= 1. A control engineer claims that the process will
- It is desired to control the exit temperature T2of the heat exchanger shown in Fig. E11.18 by adjusting the steam flow rate ws. Unmeasured disturbances occur in inlet temperature T1. The dynamic
- A process control system contains the following transfer functions:(a) Show how GOL (s) can be approximated by a FOPTD model;Find K,Ï„, and Î¸ for the open-loop process transfer
- For the control system based on the standard feedback control configuration in Fig. 11.8determine whether the value of a affects the stability of the closed-loop system. Assume Kc > 0. You do not
- The set-point of the control system under proportional control (Kc= 5) undergoes a step change of magnitude 2. For (a) Determine when the maximum value of y occurs.(b) Determine the offset.(c)
- Consider proportional only control of the level control system in Fig. 11.16. The level transmitter has a span of 10 ft. and a zero of 15 ft. Recall that the standard instrument ranges are 4 to 20 mA
- A control system has Gv = Gm = 1 and a second-order process Gp with Kp = 2, τ1 = 4 min, and τ2 = 1 min, which is to be controlled by a PI controller with Kc = 2 and τI = τ1 = 4 min (i.e., the
- Consider a third-order process with Gm = Gv = 2 and Gp = Gd = 2 / (s + 2)3.(a) Find the roots of the characteristic equation for a proportional controller Gc = Kc for Kc = 1, 8, and 27. Classify each
- Consider the schematic diagram of a controlled blending process shown in Fig. 8.1. The control objective is to control the mass fraction of the exit stream, x, by adjusting inlet flow rate, w2, using
- A hot liquid is cooled by cold water in a counter-current heat exchanger: shown in Fig. E8.15:Temperature Th2 is to be controlled by adjusting flow rate, wc. The temperature sensor/transmitter (TT)
- A steam-heated evaporator used to concentrate a feed stream by evaporating water is shown in Fig. E8.14. The massfraction of solute in the exit stream x is measured and controlled by adjusting the
- Consider the liquid storage system in Fig. E8.13. Suppose that q1must be kept constant, and, consequently, h2is to be controlled by adjusting q2. Suppose that the q2control valve is fail-close.
- Consider a standard feedback control system where each component is functioning properly. Briefly indicate whether you agree or disagree with the following statements: (a) For proportional-only
- Consider the simulation results for PID control in Figs. 8.15 and 8.16. Note that the uIresponse in Fig. 8.16 changes monotonically. Do you think this feature is typical of uIresponses for other PID
- What differential equation model represents the parallel PID controller with a derivative filter? (a) Repeat for the series PID controller with a derivative filter.(b) Simulate the time response
- An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t = 0, the error signal is increased at the
- An electronic PI temperature controller has an output p of 12 mA when the set point equals the nominal process temperature. The controller response to step change in the temperature set point of 2.5