温度控制与PID控制器简介.

Introductions to temperature control

and PID controllers

Process control system.

Automatic process control is concerned with maintaining process vari ables temperatures pressures flows compositions, and the like at some desired operation value. Processes are dynamic in nature. Changes are always occurring, and if actions are not taken, the important process vari ables-those related to safety, product quality, and production rates-will no t achieve design conditions.

In order to fix ideas, let us consider a heat exchanger in which a pr ocess stream is heated by condensing steam.

The purpose of this unit is to heat the process fluid from some inlet temperature, Ti(t, up to a certain desired outlet temperature, T(t. As m entioned, the heating medium is condensing steam.

The energy gained by the process fluid is equal to the heat release d by the steam, provided there are no heat losses to surroundings, iii th at is, the heat exchanger and piping are well insulated.

In this process there are many variables that can change, causing t he outlet

temperature to deviate from its desired value. [21 If this happe ns, some action must be taken to correct for this deviation. That is, the objective is to control the outlet process temperature to maintain its desir ed value.

One way to accomplish this objective is by first measuring the temp erature T(t , then comparing it to its desired value, and, based on this comparison, deciding what to do to correct for any deviation. The flow of steam can be used to correct for the deviation. This is, if the temperat ure is above its desired value, then the steam valve can be throttled ba ck to cut the stearr flow (energy to the heat exchanger. If the temperat ure is below its desired value, then the steam valve could be opened so

me more to increase the steam flow (energy to the exchanger. All of th ese can be done manually by the operator, and since the procedure is f airly straightforward, it should present no problem. However, since in mo st process plants there are hundreds of variables that must be maintaine d at some desired value, this correction procedure would required a trem endous number of operators. Consequently, we would like to accomplish this control automatically. That is, we want to have instnnnents that contr ol the variables wJtbom requring intervention from the operator. (si This is what we mean by automatic process control.

To accomplish ~his objective a control system must be designed and

implemented.

The first thing to do is to measure the outlet temperaVare of the pro cess stream. A sensor (thermocouple, thermistors, etc does this. This se nsor is connected physically to a transmitter, which takes the output from the sensor and converts it to a signal strong enough to be transmitter t o a controller. The controller then receives the signal, which is related to the temperature, and compares it with desired value. Depending on this comparison, the controller decides what to do to maintain the temperatu re at its desired value. Base on this decision, the controller then sends another signal to final control element, which in turn manipulates the ste am flow.

The preceding paragraph presents the four basic components of all control systems. They are

(1 sensor, also often called the primary element.

(2 transmitter, also called the secondary element.

(3 controller, the \"brain\" of the control system.

(4 final control system, often a control valve but not always. Other common final control elements are variable speed pumps, conveyors, an d electric motors.

The importance of these components is that they perform the three basic operations that must be present in every control system. These op erations are

(1 Measurement (M : Measuring the variable to be controlled is us ually done by the combination of sensor and transmitter.

(2 Decision (D: Based on the measurement, the controller must the n decide what to do to maintain the variable at its desired value.

(3 Action (A: As a result of the controller's decision, the system m ust then take an action. This is usually accomplished by the final control element.

As mentioned, these three operations, M, D, and A, must be presen t in every control system.

PID controllers can be stand-alone controllers (also called single loo p controllers, controllers in PLCs, embedded controllers, or software in V isual Basic or C# computer programs.

PID controllers are process controllers with the following characteristi cs:

Continuous process control

Analog input (also known as \"measuremem\" or \"Process Variable\" or \"PV\"

Analog output (referred to simply as \"output\"

Setpoint (SP

Proportional (P, Integral (I, and/or Derivative (D constants

Examples of \"continuous process control\" are temperature, pressure, flow, and level control. For example, controlling the heating of a tank. Fo r simple control, you have two temperature limit sensors (one low and o ne high and then switch the heater on when the low temperature limit s ensor tums on and then mm the heater off when the temperature rises t o the high temperature limit sensor. This is similar to most home air con ditioning & heating thermostats.

In contrast, the PID controller would receive input as the actual tem perature and control a valve that regulates the flow of gas to the heater. The PID controller automatically finds the correct (constant flow of gas to the heater that keeps the temperature steady at the setpoint. Instead of the temperature bouncing back and forth between two points, the tem perature is held steady. If the setpoint is lowered, then the PID controller automatically reduces the amount of gas flowing to the heater. If the se tpoint is raised, then the PID controller automatically increases the amou nt of gas flowing to the heater. Likewise the PID controller would autom atically for hot, sunny days (when it is hotter outside the heater and for cold, cloudy days.

The analog input (measurement is called the \"process variable\" or \" PV\". You want the PV to be a highly accurate indication of the process parameter you are trying to control. For example, if you want to maintain a temperature of + or -- one degree then we typically strive for at least ten times that or one-tenth of a degree. If the analog input is a 12 bit analog input and the temperature range for the sensor is 0 to 400 degre es then our \"theoretical\" accuracy is calculated to be 400 degrees divide d by 4,096 (12 bits =0.09765625 degrees. [~] We say \"theoretical\" beca use it would assume there was no noise and error in our temperature s ensor, wiring, and analog converter. There are other assumptions such a s linearity, etc.. The point being--with 1/10 of a degree \"theoretical\" accur acy--even with the usual amount of noise and other problems-- one degr ee of accuracy should easily be attainable.

The analog output is often simply referred to as \"output\". Often this is given as 0~100 percent. In this heating example, it would mean the v alve is totally closed (0% or totally open (100%.

The setpoint (SP is simply--what process value do you want. In this example--what temperature do you want the process at?

The PID controller's job is to maintain the output at a level so that t here is no difference (error between the process variable (PV and the setpoint (SP.

In Fig. 3, the valve could be controlling the gas going to a heater, t he chilling of a cooler, the pressure in a pipe, the flow through a pipe, t he level in a tank, or any other process control system. What the PID c ontroller is looking at is the difference (or \"error\" between the PV and t he SP .

It looks at the absolute error and the rate of change of error. Absolute error means--is there a big difference in the PV and SP or a little differ ence? Rate of change of error means--is the difference between the PV or SP getting smaller or larger as time goes on.

When there is a \"process upset\setpoint quickly changes--the PID controller has to quickly chan ge the output to get the process variable back equal to the setpoint. If y ou have a walk-in cooler with a PID controller and someone opens the door and walks in, the temperature (process variable could rise very qui ckly. Therefore the PID controller has to increase the cooling (output to compensate for this rise in temperature.

Once the PID controller has the process variable equal to the setpoi nt, a good PID controller will not vary the output. You want the output to be very steady (not changing . If the valve (motor, or other control ele ment is constantly changing, instead of maintaining a constant value, thi s could cause more wear on the control element.

So there are these two contradictory goals. Fast response (fast chan ge in output when there is a \"process upsethe PV is close to the setpoint.

Note that the output often goes past (over shoots the steady-state output to get the process back to the setpoint. For example, a cooler m ay normally have its cooling valve open 34% to maintain zero degrees (after the cooler has been closed up and the temperature settled down. If someone opens the cooler, walks in, walks around to find something, then walks back out, and then closes the cooler door--the PID controlle r is freaking out because the temperature may have raised 20 degrees! So it may crank the cooling valve open to 50, 75, or even 100 percent-to hurry up and cool the cooler back down--before slowly closing the co oling valve back down to 34 percent. Let's think about how to design a PID controller. We focus on the difference (error between the process variable (PV and the setpoint (SP. There are three ways we can view the error. The absolute error This means how big is the difference between the PV and SP. If th ere is a small difference between the PV and the SP--then let's make a small change in the output. If there is a large difference in the PV and SP--then let's make a large change in the output. Absolute error is the \"proportional\" (P component of the PID controller. The sum of errors over time Give us a minute and we will show why simply looking at the absol ute error (proportional only is a problem. The sum of errors over time is important and is called the \"integral\" (I component of the PID controller. Every time we run the PID algorithm we add the latest error to

the su m of errors. In other words Sum of Errors = Error 1 q- Error2 + Error3 + Error4 + .... The dead time Dead time refers to the delay between making a change in the outp ut and seeing the change reflected in the PV. The classical example is

getting your oven at the right temperature. When you first mm on the he at, it takes a while for the oven to \"heat up\". This is the dead time. If y ou set an initial temperature, wait for the oven to reach the initial tempe rature, and then you determine that you set the wrong temperature--then it will take a while for the oven to reach the new temperature setpoint. This is also referred to as the \"derivative\" (D component of the PID con troller. This holds some future changes back because the changes in the output have been made but are not reflected in the process variable ye t. Absolute Error/Proportional One of the first ideas people usually have about designing an autom atic process controller is what we call \"proportional\". Meaning, if the diffe rence between the PV and SP is small--then let's make a small correctio n to the output. If the difference between the PV and SP is large-- then let's make a larger correction to the output. This idea certainly makes s ense. We simulated a proportional only controller in Microsoft Excel. Fig.4 i s the chart showing the results of the first simulation (DEADTIME = 0, p roportional only: Proportional and Integral Controllers The integral portion of the PID controller accounts for the offset prob lem in a proportional only controller. We have another Excel spreadsheet that simulates a PID controller with proportional and integral control. He re (Fig. 5 is a chart of the first simulation

with proportional and integral (DEADTIME :0, proportional = 0.4. As you can tell, the PI controller is much better than just the P cont roller. However, dead time of zero (as shown in the graph is not comm on.

Derivative Control Derivative control takes into consideration that if you change the out put, then it takes tim for that change to be reflected in the input (PV.Fo r example, let's take heating of the oven. If we start turning up the gas flow, it will take time for the heat to b e produced, the heat to flow around the oven, and for the temperature s ensor to detect the increased heat. Derivative control sort of \"holds back \" the PID controller because some increase in temperature will occur wit hout needing to increase the output further. Setting the derivative consta nt correctly allows you to become more aggressive with the P & I const ants.