A Practical Approach to Accurate Temperature Control
Precise control of a thermal system requires time, care, and expense. Highly sensitive measuring instruments and indicators, as well as frequent recalibration in service, are required to know how good the control is. One basic question of a user of a thermal system is whether the temperature control is accurate enough to produce a product or operate a process satisfactorily? Eliminating the last degree or fraction of a degree of temperature deviation is costly and should be done only for sound practical reasons. Good temperature control can be achieved using standard instruments.
What Affects Control Accuracy?
System bandwidth and constancy of mean temperature are the overall measures of control accuracy. They are affected by many factors including:
- Temperature gradients: the range of temperature variation throughout the system at any given instant.
- Thermal lag: the time delay for a temperature change in one part of the system.
- Location of the controller's sensing element relative to heat source and load.
- Response speed and sensitivity of the controller; they determine its suitability for a given application.
- Heat balance: the capacity of the heat source in relation to heat demand from the work, plus heat losses; improper balance can destroy control.
If the temperature in a thermal system is measured at some instant, starting at the heater and progressing outwards toward the edge of the system, the temperature decreases as measurements are made farther away from the heat source. The gradual drop in temperature is called a thermal gradient. Every operating thermal system has a gradient at all times.
Consider a system containing a heater, sensing element, and a workload. If you place a sensitive temperature indicator at various points in the system and record the temperatures existing at the beginning, middle, and end of the operating cycle, you would obtain three different temperature curves (figure 1). These represent the temperature gradient in the system at three instants during its continuous cyclic change from minimum to maximum slope.
Measurement and control of temperature must allow for thermal gradients. Because temperature varies along the gradient, it is important to measure temperature as close as possible to the location to be controlled. A measurement instrument placed between the work and the heater usually provides higher temperature readings than the temperature in the work area.
Similarly, the controller set point must be adjusted according to its relative location. The closer to the heater, the larger the offset necessary to keep the heater from shutting off too soon.
Although thermal gradients are inevitable and necessary, excessive gradients can be troublesome. Thermal gradients can be reduced by:
- Balancing heater capacity against heat demand.
- Setting and locating the sensing element properly to control the duration of the heat cycle.
- Insulating the system to reduce heat loss.
The delay in heat distribution through a system, which exists to some extent in every system, is called thermal lag. It is influenced by the distance between the heat source and the work, and the resistance to heat flow and heat capacity of the heat transfer medium.
Thermal lag hinders accurate control because it handicaps the controller. It withholds information about temperature changes in the system from the controller for a certain interval, which may be as much as several minutes in some instances. Therefore, the lag can prevent the sensing element from the sensing heat demand soon enough to deliver heat when needed. It also can delay the arrival of heat at the sensing element for too long a time period so the heater delivers more heat than the system requires. The result in the former case is temperature undershoot; in the latter case, temperature overshoot. Both can produce an undesirably large system bandwidth (figure 2).
In a rapidly changing system, thermal lag can produce misleading information while evaluating controller performance. In certain systems, the lag can be so large that when the sensing element is placed between the heat source and the work area, the controller might call for heat because of a lower temperature in its location, while the temperature at the work is just starting to increase as a result of the previous heating cycle.
The heat-transfer medium has great effect on the amount of thermal lag. Various media, listed in order of preference for close control (there may be overlap between individual materials in difference classes) include:
- Well-agitated liquids
- Rapidly moving air
- High-diffusivity metals
- Low-diffusivity solids
- Stagnant air
- Stagnant liquids
In most instances, the choice already is determined by the cost, size, and application for the thermal system.
A controller performs no better than the system permits. Thermal lag is one of the major factors in handicapping the controller. Lag can be reduced by proper choice of heat-transfer material, and it can be further reduced by correctly matching the controller with the application and by placing the components correctly in the system. Correct placement is essential, because widely different control accuracies are obtained for a given heat source, controller and thermal load depending on the relative locations of the components (see Sidebar "Preferred component location").
There is little problem with control if the heat source, sensing element and work are grouped into a compact area. The short heat path from the heater enables the sensing element to respond quickly to temperature increases at the heater and cycle frequently, minimizing overshoot. However, intimate grouping of system components is not feasible in a majority of cases due to the relatively large size of the system and because the heat source is at some distance from the work area. The issue then is where to place the sensing element, because moving it away from either the heater or load affects control is some manner. Placement of the sensing element when the work and heat source are separated requires a compromise between the smallest bandwidth and constant mean temperature at the work area-both cannot be achieved at the same time. It is necessary to decide which of the two types of accuracy is more important for the particular system.
Importance of cycling frequency
Precise performance of on/off controls requires frequent cycling of the heat source. Rapid cycling produces a series of short bursts of heat that approximates a steady heat input at the load. By comparison, infrequent cycling causes prolonged heating intervals in which large quantities of heat enter the system. This results in a wide variation in the thermal gradient during the operating cycle and unwanted increases in the system bandwidth.
Even though rapid cycling reduces bandwidth, excessive cycling decreases the life of contacts and mechanical components of controllers, relays, heaters, and other cycle components. Cycling frequency can be reduced by moving the sensing element away from the heat source and by increasing the thermal lag to the element by some artificial means, such as insulating the element. Solid-state devices can be switched rapidly without the mechanical problems of wear and servicing. However, the initial installation costs are somewhat higher.
Liquid and gas systems
In liquid baths and ovens where the heat demand is primarily steady, locating the sensing element fairly close to, and above, the heat source minimizes bandwidth. Slowly moving convection currents take too long to reach an element placed too far from the heater (figure 3a). By the time the controller can turn off the heater, too much heat already has been generated with inevitable overshoot. Agitation and/or distribution of the heat sources over the bottom of the tank helps shorten the lag in heat transfer, increases temperature uniformity and improves control. However, the narrowest bandwidth is obtained by placing the sensing element closer to the heater (figure 3b), which further reduces thermal lag, while the agitator promotes uniform mixing and reduces heat gradients.
Generally, the best location for the sensing element in ovens is fairly close to the heating elements to reduce the transfer lag of the convection currents (figure 3c). It may have to be moved closer to the center of a large oven (where the heat source also is large) to lower temperature offset to a point where the temperature will be more representative of that of the entire oven. Where feasible, blowers should be installed to prevent temperature stratification and eliminate stagnant air pockets around the sensing element, which can insulate it and slow its response. Multiple heaters or coils are preferable because they distribute the heat faster and more uniformly than a single concentrated source.
Insulation is important
Proper insulation reduces heating costs while improving control accuracy and also minimizes temperature gradients within the system. Reduction of gradients also lowers the offset required for the controller setpoint, and produces a narrower system bandwidth as the heaters cycle.
For optimum temperature control with minimum heat input, thermal conductivity within a system should be high with low conduction of heat away from the system; the system should be thermally insulated from supporting structures that could carry away heat and increase the gradient. This is particularly important where the heated mass is relatively small compared with the supporting structure; for example, a heated platen in a large press.
Types of control action
Four types of control action are:
- On/off (two position)
- Proportioning (throttling)
- Proportioning plus integral (automatic reset)
- Proportioning plus integral plus derivative (rate)
The control element (heater, valve, etc.) with on/off control is either on or off; or open or closed; no intermediate position is possible. As a result, the size of the corrective action has no relation to the amount of temperature deviation. Full heat (or other action) is supplied regardless of whether the temperature is 2 or 20 degrees below the setpoint. The heat stays on until the controller senses that the system temperature corresponds to the setpoint (or more accurately, the higher limit of the controller's operating bandwidth).
The end result of two-position control is that the system temperature oscillates continuously above and below an average system temperature. The size or amplitude of these oscillations determines the system's bandwidth, and they are governed by many design factors.
Most on-off controllers have a fixed operating differential, but in some more elaborate controllers, the operating differential can be varied to suit the application. Operating differential is the "dead zone," or the difference between the temperatures at which the controller opens and closes its contacts. The chief advantage of increasing the operating differential is to decrease the cycling rate and, thus, the wear on the switches, heaters and other cycled components. However, reduced cycling affects control.
Because the system bandwidth is strongly influenced by cycling frequency, the operating differential of a controller, if adjustable, should be increased judiciously. The best choice is the one which reduces the cycling frequency of the equipment as much as possible without producing an excessive temperature bandwidth in the system.
In proportioning (P) control, the controller recognizes the deviation from the setpoint and proportions the corrective action to the size of the deviation. The proportioning action occurs when the system temperature falls within a range of temperatures known as the proportioning band. The preferred temperature is at the approximate center of this band.
The benefit of proportioning control is that the system temperature does not oscillate continuously around the preferred value, as it does with on/off control. Because the corrective action is tailored to the size of the deviation to be corrected, the system has less opportunity to overshoot or undershoot. This action is particularly helpful in systems that cycle work frequently-where the system is cooled down by the addition of cold material and then must be brought up to temperature quickly. Under these conditions, the temperature tends to overshoot in each recovery cycle, and the throttling action of proportioning control is most helpful in combating this tendency.
Ideally the proportioning band for a particular system should be just wide enough to accommodate the time lags in the system. The proportioning band for a given system is established by operating the system at the preferred temperature with the controller functioning in the on/off control mode at minimum differential, noting the limits of overshoot and undershoot encountered. Then, set the proportioning band to just exceed these temperature excursions.
There is an inherent limitation in proportioning control. The size of the corrective action depends only on the size of the difference between the system temperature and the setpoint. However, this corrective action fits only one set of equilibrium conditions. A proportioning controller cannot correct the valve position without a change in sensing element temperature. This results in the system being controlled at progressively lower temperatures, having, in effect, a "droop."
However, the nature of proportioning control prevents the droop from going below the lower limit of the proportioning band under normal operating conditions. Thus, a narrowing of the band reduces droop. Droop can be corrected by resetting the setpoint above or below the original setting and by rotating a manual reset adjustment (if provided) so the system stabilizes at the preferred temperature.
Droop also can be corrected by adding integral action, or automatic reset, to the controller. In the proportioning plus integral (PI) variation, the integrator adds a signal to the proportional output, which corrects for the inherent droop found in a proportional, or P-type controller. This is accomplished by taking the integral of the error between the actual temperature and desired temperature with respect to time. The integral function acts primarily on steady state errors that exist over a period of time. Controllers having antireset wind-up have the ability to suppress the integral function to within a set percent of the proportional band. This alleviates too much integral on start-up, which can cause overshoot.
Controllers having proportioning plus integral plus derivative (PID) function have the characteristics of PI-type controllers, but take the derivative of the error between actual temperature and desired temperature with respect to time. The derivative is an anticipatory function that senses the temperature rate of rise and fall and adjusts the control output to reduce over/undershoot. Note that a derivative time that is too long can cause the controlled temperature to oscillate.
SIDEBAR: Preferred component location
In practice thermal systems are not purely steady or variable, they usually are predominantly one or the other. For such systems, the following guidelines will be helpful: where the heat demand is relatively steady, the sensing element should be placed closer to the heat source; where the demand is largely variable, it should be nearer to the work area (see figure).
A. Heater, sensing element and load grouped together. Excellent control. Good when thermal load changes frequently. Slight thermal lag. System inertia low due to small mass of heat-transfer medium. Rapid cycling speeds system recovery from thermal gradients.
B. Modification of (A) for a larger system. Heater separated from load, thermostat extended between (possible only for liquid-filled bulbs and differential expansion thermostats that are sensitive along their entire length versus at a single point). One end of bulb next to heater, the other near the load; bulb equally responsive to temperature changes in either area.
C. Heater distant from load, sensing element near heater. Produces narrow bandwidth at the load in steady system because controller quickly responds to rapid cycling. Not good in variable system due to long heat-transfer path between load and sensing element.
D. Thermostat between heater and load. General-purpose compromise between (C) and (E) in installations where heat demand alternately is steady and variable. Centrally located sensing element responds to changes at both the load and heater without excessive lag.
E. Sensing element at load, heater distant. Not recommended for steady systems because of lag resulting from long heat path between heater and element. Arrangement shortens delay in sensing changes in load heat requirements in variable system, so temperature expected to remain fairly constant.
F. Heater at load, thermostat distant. Poor control because sensing element too far from heater and load to respond to changes in either one without excessive lag. Arrangement emphasizes that improper placement of element could make it impossible for controller to maintain even fair control.