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®
Applications Guide
PID Control
in Tracer Controllers
CNT-APG002-EN
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® Applications Guide PID Control in Tracer Controllers CNT-APG002-EN October 2001
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PID Control in Tracer Controllers This manual and the information in it are the property of American Standard Inc. and shall not be used or reproduced in whole or in part, except as intended, without the written permission of American Standard Inc. Since The Trane Company has a policy of continu- ous product improvement, it reserves the right to change design and specification without notice. The Trane Company has tested the system described in this manual. However, Trane does not guarantee tha
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® Contents Chapter 1 Overview of PID control. . . . . . . . . . . . . . . . . . . . . . 1 What PID loops do . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 How PID loops work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 PID calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Proportional calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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® Contents Chapter 4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Discharge-air temperature control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Building pressure control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Cascade control—first stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Staging cooling-tower fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Set
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® Chapter 1 Overview of PID control This guide will help you set up, tune, and troubleshoot proportional, inte- gral, derivative (PID) control loops used in Tracer controllers. These con- trollers include the Tracer MP580/581, AH540/541, and MP501 controllers. This chapter provides an overview of PID control. What PID loops do A PID loop is an automatic control system that calculates how far a mea- sured variable is from its setpoint and, usually, controls an output to move the measured variab
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® Chapter 1 Overview of PID control How PID loops work A PID loop performs proportional, integral, and derivative calculations to calculate system output. Figure 2 illustrates how a typical PID loop works. The sigma (Σ) symbol indicates that a sum is being performed. The plus (+) symbol indicates addition, and the minus (–) symbol indicates subtraction. Figure 2: PID loop Error + PID calculation HVAC equipment Plant Σ Setpoint – Measured variable (process variable) Conversion function In an
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® PID calculations PID calculations A PID loop performs three calculations: the proportional calculation, the integral calculation, and the derivative calculation. These calculations are independent of each other but are combined to determine the response of the controller to the error. Proportional calculation The proportional calculation responds to how far the measured variable is from the setpoint. The larger the error, the larger the output of the calcu- lation. The proportional calcula
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® Chapter 1 Overview of PID control Figure 4: The effects of proportional bias on system output Proportional bias = 75 Proportional bias = 50 Proportional bias = 25 Error Integral calculation The integral calculation responds to the length of time the measured vari- able is not at setpoint. The longer the measured variable is not at set- point, the larger the output of the integral calculation. The integral calculation uses the sum of past errors to maintain an out- put when the error is zero. L
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® PID calculations Figure 5: Integral output added to proportional output Error ≠ 0 Error = 0 Proportional + integral output when proportional Proportional + integral output has gone to zero output 2 1 Proportional-only output Time The value of the integral calculation can build up over time (because it is the sum of all past errors), and this built-up value must be overcome before the system can change direction. This prevents the controller from over-reacting to minor changes, but can p
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® Chapter 1 Overview of PID control Because of these disadvantages, derivative control is rarely used in HVAC applications (with the exception of steam valve controllers and static pressure control). Derivative control can affect the output in two ways: it slows the output if the derivative gain is negative and increases the output if the derivative gain is positive. Slowing (or smoothing) the actuator motion, sometimes known as dynamic braking, can help if there are many quick changes in t
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® Velocity model Velocity model Trane controllers use a type of PID control known as the velocity model. The velocity model minimizes the problem of integral windup, which occurs when the sum of past errors in the integral calculation is too great to allow the controller to change the output at one of the extremes (see “Integral calculation” on page 4). The velocity model, illustrated in Figure 7, gets its name from the fact that the proportional gain affects the change in error (or error v
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® Chapter 1 Overview of PID control 8 CNT-APG002-EN
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Actuator position (%) ® Chapter 2 PID settings This chapter describes some of the key variables used to set up and tune PID loops. The variables discussed here are: Throttling range Gain Sampling frequency Action Error deadband Throttling range The throttling range is the amount of error it takes to move the output of a system from its minimum to its maximum setting. For example, a throt- tling range of 4°F (2.2°C) means that a controller fully opens or closes an actuator when the
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® Chapter 2 PID settings The throttling range determines the responsiveness of a control system to disturbances. The smaller the throttling range, the more responsive the control. You cannot directly program the throttling range in Tracer con- trollers; rather, the throttling range is used to calculate the gains. Figure 9 shows that as the throttling range increases, the potential error becomes larger. When the output is at 0% or 100%, the error is equal to one-half of the throttling range.
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® Calculating the gains Calculating the gains Table 1 shows recommended initial values for the proportional and inte- gral gains for several applications. Most applications do not require a derivative contribution, so the derivative gain is not shown. We recom- mend using a ratio of 4:1 between the proportional and integral gains, so the proportional gain should be four times as large as the integral gain. You may need to modify the values shown in Table 1 when tuning a PID loop, but try to
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® Chapter 2 PID settings Sampling frequency The sampling frequency is the rate at which the input signal is sampled and the PID calculations are performed. Using the right sampling fre- quency is vital to achieving a responsive and stable system. Problems can arise when the sampling frequency is too slow or too fast in comparison to time lags in the system. Sampling too slowly can cause an effect called aliasing in which not enough data is sampled to form an accurate picture of changes in th
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® Sampling frequency Problems also arise from sampling too quickly. Some systems have natu- rally slow response times, such as when measuring room temperature. Slow response times can also be caused by equipment lags. Since PID loops respond to error and changes in error over time, if the measured variable changes slowly, then the error will remain constant for an extended period of time. If the measured variable is sampled repeatedly during this time, the proportional output remains about
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® Chapter 2 PID settings Calculating the sampling frequency PID loops are carried out by programs, such as process control language (PCL) programs and Tracer graphical programming (TGP) programs. Since the PID calculation occurs when the program executes, the sam- pling frequency and the program execution frequency are generally the same. Note: Tracer controllers have different approaches to using the sam- pling frequency. For Tracer MP580/581 controllers, the sam- pling frequency can be a m
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® Calculating the sampling frequency 6. Calculate two-thirds (66%) of the change in measured variable deter- mined in step 4. Add this value to the initial temperature to deter- mine at what point two-thirds of the total change occurs. In the example, 0.66 × 50°F = 33°F, so two thirds of the total change occurs at 70°F + 33°F = 103°F (0.66 × 28°C = 18°C; 21 + 18 = 39°C). 7. Again, set the analog output to 0% and allow the measured variable to stabilize. The measured variable stabilizes at 70°
