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Sunday, October 4, 2009
Types of Feedback Controls
There are many controlling methods and mechanism used in daily life to control the processing parameters in labs and industry. Here we will discuss a few of them and our main concern will be on temperature controllers specifically. Thus keeping in mind about a temperature controller of an oven, which are the common methods used, we start with the most simple on method which is The ON-OFF control.
The On-Off Control
This is the simplest form of control, used by almost all domestic thermostats. When the oven is cooler than the set-point temperature the heater is turned on at maximum power, suppose it is M, and once the oven is hotter than the set-point temperature the heater is switched off completely. The turn-on and turn-off temperatures are deliberately made to differ by a small amount, known as the hysteresis H, to prevent noise from switching the heater rapidly and unnecessarily when the temperature is near the set-point.
Proportional Control
A proportional controller attempts to perform better than the On-Off type by applying power, W, to the heater in proportion to the difference in temperature between the oven and the set-point. where P is known as the proportional gain of the controller. As its gain is increased the system responds faster to changes in set-point but becomes progressively under damped and eventually unstable. The final oven temperature lies below the set-point for this system because some difference is required to keep the heater supplying power. The heater power must always lie between zero and the maximum M because it can only source, not sink, heat.
Proportional+Derivative Control
The stability and overshoot problems that arise when a proportional controller is used at high gain can be mitigated by adding a term proportional to the time-derivative of the error signal,
This technique is known as PD control. The value of the damping constant, D, can be adjusted to achieve a critically damped response to changes in the set-point temperature.
Proportional, Integral and Derivative Control
Although PD control deals neatly with the overshoot and ringing problems associated with proportional control it does not cure the problem with the steady-state error. Fortunately it is possible to eliminate this while using relatively low gain by adding an integral term to the control function which becomes
where I, the integral gain parameter is sometimes known as the controller reset level. This form of function is known as proportional-integral-differential, or PID, control. The effect of the integral term is to change the heater power until the time-averaged value of the temperature error is zero. The method works quite well but complicates the mathematical analysis slightly because the system is now third-order.
Proportional and Integral Control
Sometimes, particularly when the sensor measuring the oven temperature is susceptible to noise or other electrical interference, derivative action can cause the heater power to fluctuate wildly. In these circumstances it is often sensible use a PI controller or set the derivative action of a PID controller to zero.
Third-Order Systems
Systems controlled using an integral action controller are almost always at least third-order. Unlike second-order systems, third-order systems are fairly uncommon in physics but the methods of control theory make the analysis quite straightforward. For instance, applying the so-called Routh-Hurwitz stability criterion, which is a systematic way of classifying the complex roots of the auxiliary equation for the model, it can be shown that provided the integral gain is kept sufficiently small then parameter values can be found to give an acceptably damped response with the error temperature eventually tending to zero if the set-point is changed by a step or linear ramp in time. Whereas derivative control improved the system damping, integral control eliminates steady-state error at the expense of stability margin.
The On-Off Control
This is the simplest form of control, used by almost all domestic thermostats. When the oven is cooler than the set-point temperature the heater is turned on at maximum power, suppose it is M, and once the oven is hotter than the set-point temperature the heater is switched off completely. The turn-on and turn-off temperatures are deliberately made to differ by a small amount, known as the hysteresis H, to prevent noise from switching the heater rapidly and unnecessarily when the temperature is near the set-point.
Proportional Control
A proportional controller attempts to perform better than the On-Off type by applying power, W, to the heater in proportion to the difference in temperature between the oven and the set-point. where P is known as the proportional gain of the controller. As its gain is increased the system responds faster to changes in set-point but becomes progressively under damped and eventually unstable. The final oven temperature lies below the set-point for this system because some difference is required to keep the heater supplying power. The heater power must always lie between zero and the maximum M because it can only source, not sink, heat.
Proportional+Derivative Control
The stability and overshoot problems that arise when a proportional controller is used at high gain can be mitigated by adding a term proportional to the time-derivative of the error signal,
This technique is known as PD control. The value of the damping constant, D, can be adjusted to achieve a critically damped response to changes in the set-point temperature.
Proportional, Integral and Derivative Control
Although PD control deals neatly with the overshoot and ringing problems associated with proportional control it does not cure the problem with the steady-state error. Fortunately it is possible to eliminate this while using relatively low gain by adding an integral term to the control function which becomes
where I, the integral gain parameter is sometimes known as the controller reset level. This form of function is known as proportional-integral-differential, or PID, control. The effect of the integral term is to change the heater power until the time-averaged value of the temperature error is zero. The method works quite well but complicates the mathematical analysis slightly because the system is now third-order.
Proportional and Integral Control
Sometimes, particularly when the sensor measuring the oven temperature is susceptible to noise or other electrical interference, derivative action can cause the heater power to fluctuate wildly. In these circumstances it is often sensible use a PI controller or set the derivative action of a PID controller to zero.
Third-Order Systems
Systems controlled using an integral action controller are almost always at least third-order. Unlike second-order systems, third-order systems are fairly uncommon in physics but the methods of control theory make the analysis quite straightforward. For instance, applying the so-called Routh-Hurwitz stability criterion, which is a systematic way of classifying the complex roots of the auxiliary equation for the model, it can be shown that provided the integral gain is kept sufficiently small then parameter values can be found to give an acceptably damped response with the error temperature eventually tending to zero if the set-point is changed by a step or linear ramp in time. Whereas derivative control improved the system damping, integral control eliminates steady-state error at the expense of stability margin.
Labels: differential equations used in temperature controlling and modelling, matlab programs for PID tuning, the gain and controls used for controlling temperature, tuning of pid
Proportional, Integral AND Derivative (PID) controller
A Proportional, Integral AND Derivative (PID) controller is an interesting method and mechanism to control the output by viewing input and is mostly used in industrial control applications but now a days its application are very common and we see it working in every controller. A PID controller can be used for regulation of speed of automobile or AC motors , DC motors or servo motors and stepper motors, temperature of furnace or oven or water baths used in laboratories and hospitals, flow of fluids in industry, pressure and other process variables very common in industry. It is viewed that the Field mounted PID controllers are normally placed close to the sensors or the control regulation devices and be monitored centrally using a SCADA system.For example The Temperature Control using a Digital PID controller on boiler in any industry where boiler are used.
A typical PID temperature controller application could be to continuously vary a regulator which can alter a process temperature (for example, but it could be any process parameter or variable). If we take a basic temperature controller in our mind which works on PID mechanism, then we can say that This may be a pulsed switching device for electrical heaters or by opening and closing a gas valve, it depends upon what is the heating source in that particular application. Generally speaking, A heat only PID temperature controller uses a reverse output action, i.e. more power is applied when the temperature is below the set-point and less power when above. PID control for injection and extrusion applications often employ additional cooling control outputs and usually require multiple controllers.
A PID controller is sometimes called a three term controller also. It reads the sensor signal, normally from a thermocouple or RTD, and converts the measurement to engineering units e.g. Degrees C. It then subtracts the measurement from a desired set point to determine an error. The complete PID controller involves very basic section built in which starts from sensor, sensor interface circuitry, ADCs, micro-controllers, output interfacing circuitry, heater or boiler and the display.
The error is acted upon by the three terms, which are Proportional, Integral AND Derivative (P, I & D) simultaneously, The working principles of each of the term is explained below:
PID Controller Theory
The following section examines PID controller theory and provides further explanation of the question `how do PID controllers work'. The function of PID depends upon three gains (effecting factor ) of three parts known as Proportional gain, Integral gain and Derivative gain.
Proportional (Gain)
The error is multiplied by a negative (for reverse action) proportional constant P, and added to the current output. "P" represents the band over which a controller's output is proportional to the error of the system. E.g. for a heater, a controller with a proportional band of 10 deg C and a setpoint of 100 deg C would have an output of 100% up to 90 deg C, 50% at 95 Deg C and 10% at 99 deg C. If the temperature over-shoots the set-point value, the heating power would be cut back further. Proportional only control can provide a stable process temperature but there will always be an error between the required setpoint and the actual process temperature.
Integral Gain or Reset Gain
The error is integrated (averaged) over a period of time, and then multiplied by a constant I, and added to the current control output. I represents the steady state error of the system and will remove setpoint / measured value errors. For many applications Proportional + Integral control will be satisfactory with good stability and at the desired setpoint.
Derivative Gain (Rate of change gain)
The rate of change of the error is calculated with respect to time, multiplied by another constant D, and added to the output. The derivative term is used to determine a controller's response to a change or disturbance of the process temperature (e.g. opening an oven door). The larger the derivative term, the more rapidly the controller will respond to changes in the process value.
Tuning of PID Controller Terms
The P, I and D terms need to be "tuned" to suit the dynamics of the process being controlled. Any of the terms described above can cause the process to be unstable, or very slow to control, if not correctly set. These days temperature control using digital PID controllers have automatic auto-tune functions. During the auto-tune period the PID controller controls the power to the process and measures the rate of change, overshoot and response time of the plant. This is often based on the Zeigler-Nichols method of calculating controller term values. Once the auto-tune period is completed the P, I & D values are stored and used by the PID controller.
A typical PID temperature controller application could be to continuously vary a regulator which can alter a process temperature (for example, but it could be any process parameter or variable). If we take a basic temperature controller in our mind which works on PID mechanism, then we can say that This may be a pulsed switching device for electrical heaters or by opening and closing a gas valve, it depends upon what is the heating source in that particular application. Generally speaking, A heat only PID temperature controller uses a reverse output action, i.e. more power is applied when the temperature is below the set-point and less power when above. PID control for injection and extrusion applications often employ additional cooling control outputs and usually require multiple controllers.
A PID controller is sometimes called a three term controller also. It reads the sensor signal, normally from a thermocouple or RTD, and converts the measurement to engineering units e.g. Degrees C. It then subtracts the measurement from a desired set point to determine an error. The complete PID controller involves very basic section built in which starts from sensor, sensor interface circuitry, ADCs, micro-controllers, output interfacing circuitry, heater or boiler and the display.
The error is acted upon by the three terms, which are Proportional, Integral AND Derivative (P, I & D) simultaneously, The working principles of each of the term is explained below:
PID Controller Theory
The following section examines PID controller theory and provides further explanation of the question `how do PID controllers work'. The function of PID depends upon three gains (effecting factor ) of three parts known as Proportional gain, Integral gain and Derivative gain.
Proportional (Gain)
The error is multiplied by a negative (for reverse action) proportional constant P, and added to the current output. "P" represents the band over which a controller's output is proportional to the error of the system. E.g. for a heater, a controller with a proportional band of 10 deg C and a setpoint of 100 deg C would have an output of 100% up to 90 deg C, 50% at 95 Deg C and 10% at 99 deg C. If the temperature over-shoots the set-point value, the heating power would be cut back further. Proportional only control can provide a stable process temperature but there will always be an error between the required setpoint and the actual process temperature.
Integral Gain or Reset Gain
The error is integrated (averaged) over a period of time, and then multiplied by a constant I, and added to the current control output. I represents the steady state error of the system and will remove setpoint / measured value errors. For many applications Proportional + Integral control will be satisfactory with good stability and at the desired setpoint.
Derivative Gain (Rate of change gain)
The rate of change of the error is calculated with respect to time, multiplied by another constant D, and added to the output. The derivative term is used to determine a controller's response to a change or disturbance of the process temperature (e.g. opening an oven door). The larger the derivative term, the more rapidly the controller will respond to changes in the process value.
Tuning of PID Controller Terms
The P, I and D terms need to be "tuned" to suit the dynamics of the process being controlled. Any of the terms described above can cause the process to be unstable, or very slow to control, if not correctly set. These days temperature control using digital PID controllers have automatic auto-tune functions. During the auto-tune period the PID controller controls the power to the process and measures the rate of change, overshoot and response time of the plant. This is often based on the Zeigler-Nichols method of calculating controller term values. Once the auto-tune period is completed the P, I & D values are stored and used by the PID controller.
Labels: autotune PID, HMI touchscreen operator panels and SCADA software, single loop integrity, The Tracker 300 series of PID Controllers are fully configurable by PC software, universal input
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