Regelkringen: Dead Time, Open and Closed Control Systems, and Distillation Control

Dode Tijd (Dead Time) Fundamentals

• Definition of Dead Time: Dode tijd is the time that elapses between the moment a corrective organ (e.g., a valve) makes a change at the input of a process and the moment this change is perceptible in the measurement (x) at the output of the process.

• Conceptual Metaphor: It is described as a kind of "delayed reaction" of the process output back to the process input.

• Relation to Distance: The further the measurement point "x" is removed from the control point "y", the larger the dead time will be.

• Concrete Examples:

  • Conveyor Belt: In a transport band system, if a valve at the start (corrigerend orgaan) changes the amount of material, the change at the end of the belt is only visible after a specific delay.

  • Filling Funnel: A change in the valve opening of a funnel (e.g., from $30\%$ to $60\%$) results in a measured change only after the dead time has passed.

• Mathematical Calculation (Fluid Flow):

  • Consider an incompressible liquid moving through a perfectly insulated pipe of length $L$ at a constant velocity $v$.

  • If $L = 60.96\,\text{m}$ and $v = 6.096\,\text{m/s}$, the delay ($td$) in temperature change between input and output is calculated as:         $td = \frac{L}{v} = \frac{60.96\,\text{m}}{6.096\,\text{m/s}} = 10\,\text{s}$

  • Graphically, the temperature change resulting from the corrective organ's action appears exactly $10\,\text{s}$ later.

• Distillation Column Level Example: When the bottom of a distillation column is filled by increasing the feed flow rate, the level in the bottom will only rise some time after the flow rate has been increased.

Impact of Dead Time on Regulation

• Difficulty in Control: Processes with large dead times are significantly harder to regulate.

• Controller Over-Correction: Because the controller does not see the immediate result of its intervention due to dead time, it may continue to adjust or "over-correct."

• Oscillation Risks: By the time the effects are measurable at the output, the controller might have already compensated too much. This causes it to react at "full strength" in the opposite direction to correct its own repeating errors.

• Unwanted Frequency: Dead times can lead to rapid, powerful adjustments that inadvertently create more errors, requiring further regulation.

• Mitigation Strategy: Where possible, dead time should be avoided or minimized, for example, by placing the sensor closer to the corrective organ.

• Characteristic Processes: Dead time is inherent to slow processes such as temperature and level control, and specific measuring devices like a gas chromatograph.

Open Regelsysteem (Open Control Systems)

• Core Principle: The variable expected to cause a disturbance is measured and regulated at the input of the process. This is also called "voorwaartse regeling" (feedforward).

• Functionality:

  • Measurement happens at the process input.

  • The process value itself is NOT measured; instead, the disturbance is measured.

  • The controller takes action based on the disturbance measurement to counteract its effect before it impacts the output.

• Room Heating Example: In an open system, the outside temperature might be measured. If the outside temperature drops, the boiler switches on to heat the room before the inside temperature actually falls.

• Advantages:

  • The controller does not wait for an error to occur in the process before adjusting.

  • It can eliminate errors before they are noticeable in the process.

  • It constitutes a fast regulation method.

• Disadvantages:

  • Disturbances that are not measured cannot be compensated (e.g., an open window or a group of people entering a room).

  • There is no measurement of the absolute result; there is no feedback (terugkoppeling).

  • Requires extensive process knowledge because only one specific disturbance is typically handled.

Open System Case Studies: Heater (Oven)

• Scenario A: Flow Control (Debietregelaar):

  • Sensor (FT): Measures flow of the cold medium.

  • Goal: Maintain correct temperature despite changes in flow rate ($F$).

  • Reaction: If the medium flow decreases (X < W), the valve ($Y$) closes the fuel/steam supply. If the flow increases (X > W), the valve ($Y$) opens further.

  • Limitation: It cannot correct changes in the temperature of the incoming medium.

• Scenario B: Temperature Control (Temperatuurregelaar):

  • Sensor (TT): Measures the temperature of the incoming cold medium.

  • Goal: Anticipate changes in inlet temperature.

  • Limitation: This only works if the flow rate remains constant. A change in the flow of the incoming medium is not perceived by the $TC$ and will not be corrected.

Gesloten Regelkring (Closed Control Systems)

• Core Principle: This involves feedback ("terugkoppeling"). The controller measures the consequence ($x$) of a control signal ($y$) and compares it with the setpoint ($w$).

• Functionality:

  • The measurement occurs at the end of the process.

  • The controller "knows" if its action had the desired effect by looking at the difference between $w$ and $x$.

• Room Heating Example: The sensor measures the actual room temperature. If it is too low, the boiler stays on until the setpoint is reached.

• Advantages:

  • All errors (even unforeseen ones) are eventually regulated.

  • Can handle very complex processes.

• Disadvantages:

  • It only begins to work after a measurable error has occurred in the process (reactive).

  • It is slower than open systems because it must wait for the disturbance to affect the output.

Comparison Summary: Open vs. Closed

• Open (Voorwaarts):

  • Focuses on one specific disturbance.

  • Very fast.

  • Small dead time (regulation happens before the process).

  • Requires deep process knowledge.

• Closed (Teruggekoppeld):

  • Considers the result of all disturbances.

  • Much slower.

  • Dode tijd is a significant factor.

• Hybrid (Cascade Control): In practice, a combination is often used. A feedforward (open) system handles the primary major disturbance, while a feedback (closed) loop mops up all other remaining errors.

Destillatiekolom: Construction and Operation

• Objective: Separation of components based on volatility or boiling point ($HK$ = Hoogkoker/High Boiler; $LK$ = Laagkoker/Low Boiler).

• Internal Structure: The column is filled with plates or packing to facilitate separation.

• Thermal Dynamics: Vapor moves upward, giving off heat to liquid on the plates. The low boiler ($LK$) evaporates. Higher parts of the column contain higher concentrations of $LK$.

• Zones:

  • Rectificatiezone (Rectification): The section above the feed ($F$) entry.

  • Strippingzone (Stripping): The section below the feed ($F$) entry.

• Top Subsection (Condenser):

  • Goal: Condense top vapor for volume reduction and provide reflux ($R$).

  • Reflux: Returning part of the condensed liquid to the column to ensure only the low boiler evaporates and to keep plates/packing wetted. This is vital for top product purity.

  • Temperature: The top temperature must match the boiling point of the low boiler. If it is too high, high boilers ($HK$) are reaching the top.

• Bottom Subsection (Reboiler):

  • Goal: Keep the bottom product boiling to drive $LK$ upward.

  • Thermosifon: A method of circulating bottom product based on mass density differences, though pumps are also used.

Control Strategies for Distillation Columns

• Bottom Temperature Regulation:

  • Measures temperature at the bottom.

  • Controls the steam supply valve to the reboiler.

  • Often implemented as a cascade control to eliminate fluctuations in steam flow.

• Reflux Flow Regulation:

  • Measures temperature on the top plate ($SP = \text{boiling point } LK$).

  • Controls the reflux supply valve ($R$). High reflux is expensive (requires re-evaporation) but ensures purity.

• Top Product Drainage:

  • Level control ($LC$) on the reflux drum/accumulator. If the level is too high, the drainage valve opens further.

• Feed Flow Regulation ($FC$):

  • Ensures consistent, stable distillation by providing a steady inflow.

• Differential Pressure Regulation ($\Delta p$):

  • Measures the pressure difference between the bottom (higher due to hydrostatic pressure) and the top. A large $\Delta p$ indicates fouling or vapor blockages.

• Purity Control Case Study:

  • If too much bottom product ($HK$) is in the top vapor, the top temperature will be Higher.

  • Solution: The $TRC10$ (Temperature Recording Controller) will measure the high temperature and open the reflux valve further.

Temperature Profile and Tray 3 Control

• In certain column designs, the temperature at "the third plate" ($TRC2$) is identified as the most suitable point for process regulation.

• Scenario 1: Temperature on Plate 3 too low:

  • Indicates the mixture contains too much top product ($LK$).

  • Action: Increase heat by opening the steam supply valve to the reboiler.

• Scenario 2: Temperature on Plate 3 too high:

  • Indicates the mixture contains too much bottom product ($HK$).

  • Action: Decrease heat by closing the steam supply valve further.

Case Studies in Control Loops

• Liquid Level Control (Inlet/Outlet):

  • Regulating level by adjusting the outlet flow is a closed regulation because the sensor measures the level (result) to adjust the valve.

  • Regulating level by adjusting the inlet flow is also a closed regulation for the same reason.

• Dead Time in Piping (Case Study 2):

  • If a sensor and valve are far apart in a pipeline, it is a closed loop with significant dead time. The distance determines the delay magnitude.

• Dryer Process (Case Study 5):

  • Natte voeding (wet feed) is dried using air/steam and a blazer.

  • Option 1: Simple outlet temperature control via $TIC$ (Temperature Indicating Controller) on the steam valve.

  • Option 2: Outlet temperature control based on flow measurement ($FIC$) to handle throughput variations.

• pH Neutralization (Case Study 6):

  • Wastewater is neutralized to $pH = 7$ using $NaOH$ ($50\%$) and $HCl$ ($36\%$).

  • Uses an $AT$ (Analysis Transmitter) and $AC$ (Analysis Controller) to adjust the acid/base valves based on the measured outcome.