The post How PID Controller Works appeared first on MyClassBook.
]]>This mode of the controller is a complex combination of proportional-integral-derivative control modes. PID control mode possesses zero steady state error, oscillations, and high stability. By the addition of the derivative term to PI control mode helps to reduce overshoot, reduce settling time as well as becomes capable of handling sluggish and fast dynamics higher order processes. In this mode, integral terms try to stabilize the lightly damped system, usually, only PD control mode can not do it easily.
Mathematically this is represented as,
Where,
Since, PID control mode can be utilized in many different ways as shown in above equation, which actually helps to define tunable parameters of PID controller.
PID controller has many industrial as well as domestic applications.
The example we are going to consider here is “maintaining the position of booster rocket at the time of taking off”. To replicate this problem in simplified terms, let’s consider launch pad as a cart and rocket as an inverted pendulum. Now, this a classic example of runaway process, i.e. pinch to the pendulum in normal condition will result in instability of the overall system. Such a system either only PI or only PD controller can not stabilize since one can not handle sudden disturbance and another can not handle initial instability. PID controller maintains it’s position by eliminating steady-state error and predicting error trend.
Please visit this article to get more understanding on PID Controller Tuning.
Please watch below video for more understanding on PID Controller in a simple way.
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]]>The post PD Controller (Proportional-Derivative) Controller in Control System appeared first on MyClassBook.
]]>Prediction of the behavior of error will always result in better stability. In order to avoid effects of the sudden change in load, the derivative of the error signal taken in this mode to predict the trend of a controlled variable. So let us see in detail, how does PD Controller work.
Almost all physical processes have transportation lag (Dead Time) in their system (usually due to improper allocation of the sensor) since only proportional controller’s output will react after some time to sudden change in load and which may result in a huge transient error. But, with the addition of a derivative controller, this mode becomes capable of predicting error with consideration of dead time. So that, sudden jerks or spike signals are not given to actuator, hence improves the life span of actuators.
Mathematically this is represented as,
Where,
From the equation, we can say that this mode cannot eliminate the steady state error of proportional controller. However, It can handle fast process load changes as long as the load change steady state error is acceptable.
Maintaining a level of liquid inside the tank is a sluggish and integrating process and many cases due to improper allocation of level sensor (in this case which is measured as a function of flow) result into the significant addition of transportation lag. PD controller mode has the capability to predict future of error, hence the effect of additional dead time is reduced. A sudden change in desired value of level will result in high overshoot in the case of PI control mode, but in the case of PD control mode, this integrating effect will be reduced by addition derivative term with the proportional term.
Please watch below video for more understanding on PD Controller:
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]]>The control mode of PI Controller has a one-to-one correspondence of the proportional mode as well as the integral mode which eliminates that inherent offset. This controller is mostly used in areas where the speed of the system is not an issue. Since proportional controller can not provide new nominal controller’s output in case of new load condition, but in this new configuration necessity of fixed (offset) error has been replaced by the accumulation of error term i.e integral term. Mathematically, this can be represented as,
Where,
Form PI controller’s equation we can say that when an error is zero, but the controlled variable is oscillating about desired value, then integral action tries to eliminate error and reaches desired value.
When an error is not zero and only accumulated error is not sufficient for resulting in the quick ramp up, in that case, the proportional controller reduces rise time and tries to achieve optimal controller’s output at new load conditions.
Flow control of any liquid is a dynamic process, improper prediction of error might result in control value saturation or extended flow of liquid which usually happens when we apply derivative controller to such a system.
In this case, the Proportional controller gives proper ramp up to achieve desired value quickly as well as the occurrence of offset error or steady state error about desired value has been eliminated by the integral term.
Please watch below video for more understanding on PI Controller. In this video, they have explained how we can eliminate steady state error using PI Controller.
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]]>With an integral controller, we can calculate accumulated error, but with the derivative control, we can calculate the ratio of error change per unit time, hence act as a predictor. Derivative controller action responds to the rate at which the difference between desired value and the measured value is changing that is derivative of the error. Mathematically represented as below,
Where,
The derivative controller is not used alone because it provides no output when the error is constant.
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]]>The post Integral Controller In Control System appeared first on MyClassBook.
]]>As we know that, the proportional controller tells us how far to move, to achieve zero error, whereas integral controller tells us how fast to move to achieve zero error. The proportional controller cannot guarantee zero error in case of a transient change in load dynamics of the system, whereas integral control accumulates positive and negative errors and tries to eliminate steady state error.
Integral action is provided by summing the error over time, multiplying that sum by a gain, and adding the result to the present controller output. You can see that if the error makes random excursions above and below zero, the net sum will be zero, so the integral action will not contribute. But if the error becomes positive or negative for an extended period of time, the integral action will begin to accumulate and make changes to the controller output.
Mathematically it can be represented as,
Where,
If we differentiate above equation then,
Above equation shows that when an error occurs, the controller begins to increase or decrease its output at a certain rate that depends on the size of the error and the integral time constant. If the error is zero, then controller output will not change. If there is a positive error, the controller output begins to ramp up at a rate determined.
There are no specific applications where integral control used individually since integral controller alone will cause transient overshoot and which may result in actuator saturation (means actuator cannot be operated beyond this limit).
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]]>Mathematically this can be represented as
Where,
It indicates that, if the error is zero, the output is constant and equal to P0 and if there is an error, for every 1 % error, a correction of Kp % is added to or subtracted from P0, depending on the sign of error.
Thermostat used in room temperature control expands or compress it’s bimetallic spring as per temperature variation in the room and gives corresponding control signal to heater coil.
Another example is heat exchanger system,
E.g. If the controller’s output will increase with falling outlet temperature of the heat exchanger until there is enough steam flow admitted to the heat exchanger to prevent the temperature from falling any further. But in order to maintain this greater flow rate of steam (for greater heating effect), an error must develop between the measured temperature and desired temperature. In other words, the process variable (temperature) must deviate from desired value in order for the controller to call for more steam, in order that the process variable does not fall any further than this. This necessary error between the measured value and desired value is called ‘offset’ or residual error.
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]]>The post Types of Controllers in Process Control System appeared first on MyClassBook.
]]>In this universe, there are several types physical changes exists, among those changes, which are under our bounded observation is known as process and device by which we can obtain desired response from that process is commonly known as the controller.
Historically, two position controller was abundantly used among the controllers, since it has only two possible positions i.e. 0% or 100%. A simple example of this type of controller is a relay.
Whenever the measured value of the controlled variable is less than desired value i.e. potential difference between two terminal of the coil of relay then, normally open contact gets closed or normally closed contact gets opened.
Similarly, if the measured value is equal to desired value then, there is no change in state.
Room heater, if the temperature of the room goes below the desired temperature then, the heater turns ON and if the temperature is above the desired temperature then heater turns OFF.
This controller’s output changes at fixed rate when the difference between desired value and the measured value exceeds neutral zone. Mathematically, it can be represented as,
Where,
By integrating equation (1) we get,
Where p(0) is initial controller’s output.
This indicates that current controller’s output keeps a history of previous control outputs. In many cases, such a kind of information is not available.
Unlike single speed controller, it’s ‘KF’ values increases or decreases as per deviation exceeds certain limits. It means that for large error (|desired value – measured value|) will have large ‘KF’ value and vice versa.
In self-regulating processes such as liquid flow rate control in the pipe (as shown in below diagram) a single speed floating controller is used. The load is determined by the inlet and outlet pressures Pin and Pout, and the flow is determined in part by the pressure P, within the DP cell and control valve. This is an example of a system with self-regulation. We assume that small control valve opening has been found to maintain the desired flow rate inside the pipe. If larger than the neutral zone, the valve begins to open or close at a constant rate until an opening is found that supports the proper flow rate at the new load conditions. Clearly, the rate is very important, because especially fast process lags cause the valve to continue opening or closing beyond that optimum self-regulated position.
In upcoming articles, we will learn about Continuous controllers, till then if you like this article, share it with your friends, like our Facebook page and subscribe to our newsletter for future updates. Have a nice day!
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]]>The post Double beam filter photometer appeared first on MyClassBook.
]]>It consists of a source of light (tungsten filament lamp), lens to make the light beam parallel, filter of wavelength selection, cuvette with sample holder for keeping the solution to be analyzed, mirror for incident the part of light beam onto reference photocell, two photocells (one as reference and other as measuring), potentiometers for zero and span adjustments and a recording device (galvanometer).
In double beam photometer, the light rays from the source are made parallel and passed through a filter. It is divided into two parts; one part passes through the sample solution cuvette and falls on the measuring photocell and the other part passes directly onto the reference photocell. The galvanometer receives opposing currents from the two photocells.
1) With the lamp off, the galvanometer is adjusted to zero mechanically.
2) The potentiometer R1 is adjusted for T=1 or A=0.
3) Then with lamp on blank solution is placed in the light path of measuring photocell and potentiometer R2 is adjusted until the galvanometer reads zero.
4) The solution to be analyzed is then placed in the light path of measuring photocell and R1 is adjusted until the galvanometer reads zero, keeping R2 unchanged. The absorbance or transmittance can be read directly on the scale of potentiometer R1. Since the potentiometer R1 is calibrated in terms of transmittance and absorbance.
In double beam filter photometer errors due to fluctuations of the lamp intensity are minimized also the scale of potentiometer R1 can be made much larger in size than the scale of meter in single beam filter photometer.
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]]>It consists of a source of light (tungsten filament lamp), lens to make the light beam parallel, filter of wavelength selection, cuvette with sample holder for keeping the solution to be analyzed , detector (photocell) and reading device (galvanometer or micro-ammeter).
The tungsten filament lamp gives the light radiation. This light is incident on the lens which makes it a parallel beam of light. This parallel beam of light is passed through the sample solution after passing through a filter. The sample absorbs some light energy, transmitting the other. This transmitted light falls on the photocell that generates the photocurrent. This photo-current is recorded by the galvanometer or micro ammeter which is having transmittance scale, since the photometer is directly proportional to the transmitted light, the transmittance scale is linear.
Steps in experiment:
1) With photocell darkened, the meter is adjusted to zero by zero adjustment.
2) The blank or reference solution is inserted in the path of light beam and light intensity is adjusted by means of rheostat in series with lamp. With this adjustment the meter reading is brought to 100 scale divisions.
3) Solutions of both standard and unknown samples are inserted in place of blank and the reading of the specimen relative to the blank is recorded.
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]]>The post High Pressure Liquid Chromatography (HPLC) appeared first on MyClassBook.
]]>In this post we are going to learn construction and working of high pressure liquid chromatography and some basic types of high pressure liquid chromatography (HPLC).
Basically a high pressure liquid chromatography (HPLC) is a method used to separate the components in a mixture to identify and quantify each component.
A high pressure liquid chromatography consists of following major components:
In HPLC (High Pressure Liquid Chromatography) the sample to be analyzed is injected in the column as the mobile phase. This mobile phase flows over the stationary phase in the column. This causes separation of the sample components. These components leave the column at different time and reach at the detector. The detector detects the components and gives the signal to the recorder. The recorder shows the chromatograph as shown in the figure.
The peak position determines the component and the peak amplitude determines the concentration of the compound in the sample.
There are three methods of sample injection as follows:
In this method the sample is introduced through a self sealing elastomeric septum, for this purpose micro syringe designed to withstand pressure up to 1500 psi are used. In stop flow injections, the flow of solvent is stopped momentarily and a fitting at the column head is removed. Then the sample is injected directly onto the head of column packing. After replacing the fitting, the system is again pressurized. This method is simple but the reproducibility of the result can’t be obtained.
The diagram shows sampling loop configuration. These valve devices are the integral part of high pressure liquid chromatography (HPLC) equipment and have interchangeable loops providing a choice of sample sizes from 5 to 500ul. Sampling loops of this type permit the introduction of samples at pressure up to 7000psi. Micro sample injection valves with sampling loops having volumes of 0.5 to 5 ul are also available.
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