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Process Control book. Read 3 reviews from the world's largest community for readers. This book has been designed as a textbook for the students of electr. A typical process control system is shown in Figure. Assume the physical variable to be controlled is the temperature. Basically Industrial process control loop. 1. PROCESS CONTROL INTRODUCTION. PROCESS A process denotes an operation or series of operations on fluid or solid materials during which the.
Our BookSleuth is specially designed for you. Subasri rated it really liked it Dec 24, The control system functions to maintain the controlled variable Temperature here as close to the moving set point as required. Cp is modeled as first order. On the other hand the supply of material is sometimes not constant and a flow control is necessary as shown in Fig. Applying unsteady state heat balance for the bulb. Get A Copy.
The precision of the performance of the modeled dynamic process is an advantage which offsets the limiting assumption that the process is linear.
Solution of differential equations Linear 2. Take Laplace transform 2. Step 1: Take inverse Laplace transform. Factorise using partial fraction decomposition 3. Momentum Quite often. Energy and 3. In such cases we select other variables which can be measured conveniently. Thus mass. For most of the processing systems of interest there are only three such fundamental quantities.
The quantity S can be any of the following fundamental quantities: A Set of fundamental dependent quantities whose values will describe the natural state of a given system. Mass of individual components 3. Mass 2. Total mass 2. Total energy 4. A Set of equations in the variables above which will describe how the natural state of the given system changes with time. Consider the system shown in Fig. We have: Whenever an input variable of a system changes. Transport rate equations They are needed to describe the rate of mass.
Kinetic and potential energies of the system respectively.
Kinetic rate equations They are needed to describe the rates of chemical reactions taking place in a system. In this case. The solution of the fundamental quantities.
The time interval is called. Equations of state Equations of state are needed to describe the relationship among the intensive variables describing the thermodynamic state of a system. Reaction and Phase equilibria relationships: These are needed to describe the equilibrium situations reached during a chemical reaction or by two or more phases.
If the state variables donot change with time. By convention. The application of the conservation principle as defined by the above equations will yield a set of differential equations with the fundamental quantities as the dependent variables and time as the independent variable. The state equations with the associated state variables constitute the 'mathematical model' of a process. The ideal gas law and the van der Waals equation are two typical equations of state for gaseous systems.
If y t and f t are interms of deviation variables around a steady state. The resistance associated with the flow of mass. The dead time is an important element in the mathematical modeling of processes and has a serious impact on the design of effective controllers.
Their capacity to store material. Then the transfer function of a first order process is given by. Thus in the case of linear or linearised system. The presence of dead time can very easily destabilize the dynamic behaviour of a controlled system. In other words.
The resistance is associated with the pumps. For such systems the resistance is associated with the transfer of heat through walls. Similarly the temperature response of solid. Cp is modeled as first order. From Equation 1. Then the transfer function is given by: Thus the larger the value of 'A'. As the liquid level goes up. The corollary conclusions are: Refering to the tank level system.
Several features of the plot in Fig. This action works towards the restoration of an equilibrium state steady state. The energy balance at transient state is given by the equation 1.
This is easily seen from the equation 1. Refer Fig. R in the response of first order lag systems is given in Fig. A and static gain KP determined by the resistance to the flow of the liquid. Kp for a step size A.
The ultimate value of the response its value at the new steady state is equal to KP for a unit step change in the input. The value of the response y t reaches The Laplace transform of equation 1. The resistance to the flow of heat from the steam to the liquid is expressed 1 by the term. At steady state the equation 1. The system possesses capacity to store thermal energy and a resistance to the flow of heat characterized by U.
The equation 1. The following assumptions are made to determine the transfer function relating the variation of the thermometer reading T for change in the temperature of the liquid TF. Applying unsteady state heat balance for the bulb.
The expansion or contraction of the glass walled well containing mercury is negligible that means the resistance offered by glass wall for heat transfer is negligible 2. The liquid film surrounding the bulb is the only resistance to the heat transfer. T is the temperature of the mercury in the well of the Thermometer. The temperature of the liquid TF varies with time as shown in Fig.
The mercury assumes isothermal condition throughout. Temperature is assumed constant. Here the following two types of pressure processes will be dealt with: Process with inlet and outlet resistances.
Making a mass balance. Gas storage tank and 2. P F1 F2 Fig.
F1 is inlet flow through resistance R1 with source pressure P1. F2 is output flow through resistance R2 and flowing out at pressure P2. As the flows into and out of the tank are both influenced by the tank pressure.
A first order system with multiple resistances Refer Fig. If there are several inlets and outlets the system is still first order one. The effluent flow rate Fo is determined by a constant-displacement pump and not by the hydrostatic pressure of the liquid level h. Either of them could be the controlled variable or the load variable or both could be load variables if the controller acts to change R1 or R2.
In the tank discussed under section 1. As a matter of fact. Processes with integrating action mostly commonly encountered in a chemical process are tanks with liquids. A pure capacitive process will cause serious control problems.
But any small change in the flow rate of the inlet steam will make the tank flood or run dry. But this is not true for a large number of components in a chemical process. Since we can vary the value of h. Such an 'adaptive procedure' can be used successfully if the time constant and the static gain of a process change slowly.
This example is characteristic of what can happen to even simple first-order systems. The general first order transfer function.
If the rate of change is constant it is called linear ramp. We will discuss here the response of a first order system with a linear ramp forcing function in the input. Hence the response for the remaining four forcing functions will be discussed here. It is defined as the difference between input variable x t and the response y t at steady state. Time Lag: It is defined as the time taken by the response to reach the value of the input.
C2 and C3 in equation 1. In Fig 1. For example. A second order system is one whose output. An output may change. In this section we will discuss about the second order systems and in section 1. If equation 1. Case A: Thus we can distinguish three cases. Let us examine each case separately. For a unit step change in the input f t. As it was the case with first-order systems. But when compared to a first-order response we notice that the system initially delays to respond and then its response is rather sluggish.
It must be emphasized that almost all the underdamped responses in a chemical plant are caused by the interaction of the controllers with the process units they control. We notice that a second-order system with critical damping approaches its ultimate value faster than does an over damped system. The underdamped response is initially faster than the criticalled damped or over damped responses. The oscillatory behaviour becomes more pronounced with smaller values of the damping factor.
This oscillatory behaviour makes an underdamped response quite distinct from all previous ones. Although the under damped response is initially faster and reaches its ultimate value quickly. From the plots we can observe the following: Overshoot is the ratio between the maximum amount by which the response exceeds its ultimate value A and the ultimate value of the response.
Case C: Under damped Response. Critically damped response. Decay Ratio: The decay ratio is the ratio of the amounts above the ultimate value of two successive peaks. Period of Oscillation: The time elapsed between two successive peaks is called the period of oscillation T.
Good understanding of the underdamped behaviour of a second-order system will help tremendously in the design of efficient controllers. The time needed for the response to reach this situation is known as the response time Refer Fig. For practical purposes. Two First Order System in series: Non-Interacting When material or energy flows through a single capacity. From Fig. The faster the response of the system.. If on the other hand.
In Fig. It is defined as the time required for the response to reach its final value for the first time Refer Fig. Rise Time: This term is used to characterize the speed with which an underdamped system responds. Response Time: There is a series of liquid flow elements which are non-interacting. It is quite possible that all capacities are associated with the same processing unit. Equation 1. This sequential solution is characteristic of non interacting capacities in series.
When a system is composed of two non interacting capacities. From equation 1. For the case of N noninteracting systems [Fig K P 2 Equation The transfer functions for the two tanks are: This system represents interacting capacities or interacting first-order systems in series. Also the multiple capacities need not correspond to physically different units.
The mass balances yield. It is to be noted that the two capacities do not interact when the inlet temperature changes. Let us analyse the characteristics of an interacting system with two interacting tanks Refer Fig. It is easy to show that these two capacities interact when the inlet flowrate changes. Interacting tanks The stirred tank heater. The larger the value of A1R2.
Equations 1. Comparing equation 1. Since the response is overdamped with poles p1 and p2 given by equation 1. They occur rather rarely in a chemical process. Since resistance and capacitance are characteristic of the first order systems. When the pressures at the top of the two legs are equal. To know the dynamic P lan e C response of the levels in the two legs.
Recall also that the fluid velocity and acceleration are given by. Externally Mounted Level Indicator: The system of the tank-displacer chamber has many similarities with the manometer.
A change in pressure p1 of a processing unit will make the pressure p2 change at the end of the capillary tube. The position of the sensing diaphragm is detected by capacitor plates on both sides of the diaphragm. A reference pressure will balance the sensing diaphragm on the other side of this diaphragm. The position of the stem or. These forces are: The position of the stem is determined by the balance of all forces acting on it. Consider a typical pneumatic valve shown in Fig.
It is a system that exhibits inherent second order dynamics. C is the friction coefficient between stem and packing.
Although it is not encountered in ordinary liquid. Consider the mass. The following general conclusions can be made regarding the basic characteristics of the capacities in series for a step change in the input. N Noninteracting Capacities in Series a The response has the characteristics of an overdamped system. We can identify the following three capacities in series.
Three classes of higher-order systems are most often encountered.. Heat Capacity of the mixture in the tank It is easy to show that these capacities interact. The content of the tank is a mixture of components A and B is being cooled by constant flow of cold water circulating through the jacket..
Heat capacity of the coolant in the jacket N Interacting Capacities in Series Interaction increases the sluggishness of the overall response If we extend the same procedure to N capacities first-order systems in series Here again.
Heat capacity of the cold water in the jacket. It is expected that the response of the coolers to input changes will be overdamped and rather sluggish. Each tray has material and heat capacities. From the physics of distillation and absorption it is easy to see that the 2N capacities interact.
Both systems have a number of trays. Total material capacity of the tank 2. This is because the input change has to travel through a large number of interacting capacities in series.
On the contrary. We can represent such system by a series of two systems as shown in Fig. For the first-order system we have the following transfer function: Virtually all physical processes will involve sometime delay between the input and the output.
Consider a first-order system with a deadtime td between the input f t and the output y t. But this is not true and contrary to our physical experience. At each boiler load there is a different volume. The water level in the steam drum is related to. Ref Fig. Processes with deadtime are difficult to control because the output does not contain information about current events. An example of such a process is boiler water level control system. The control of feed water therefore needs to respond to load changes and to maintain water by constantly adjusting the mass of water stored in the system.
On the other hand. As a consequence. Therefore if the drum volume is kept constant. This property is called 'Inverse Response' and it causes an effective delay in control action. Such behaviour is the net result of two opposing effects and can be explained as 1 follows referring to Fig 1. Equilibrium is restored within seconds.
With constant heat supply. If the condition above is not satisfied. The result of the two opposing effects is given by [Refer Fig 1. The cold feedwater causes a temperature drop which decreases the volume of the entrained steam bubbles. This leads to a decrease of the liquid level of the boiler water.
The above drum level control example demonstrates that the inverse response is the result of two opposing effects Two opposing effects result from two different first-order processes. Table Systems with inverse response are particularly difficult to control and require special attention.. In general. In all cases we notice that when the system possesses an inverse response.. Consequently it is necessary to manipulate the variables of the process in such a manner that the behaviour of the process insures obtaining the desired composition.
Idlies making in kitchen is one of the simplest example of batch process. The purpose of such processes is to produce one or more products at a a given composition. The degrees of freedom are usually well-defined.
The product composition desired is that at the end of the processing period and thus cannot be measured during the process. Maximum production and best economy result when the variables of the process are properly manipulated.
Batch processes are most often of the thermal type where materials are placed in a vessel or furnace and the system is controlled for a cycle of temperatures under controlled pressure for a period of time.
Batch or Hood annealing of steel rolled coils. Batch processes are nearly always defined by temperature. A process computer may be used to insure a relationship among variables providing best operation. In short production rate quantity. The manipulated variable m is adjusted by the control valve and hence the valve position is indirectly represented for manipulated variable. The normal action of integral response is to shift the proportional band to urge the temperature toward the set point.
Let us take a batch process where the temperature controlled variable C is raised slowly to the set point v and maintained for a particular period of time. Fixed product flow rate usually requires flow controllers at several points of entering and leaving materials. Product composition is best insured by measuring product composition and controlling it by manipulating one of the degrees of freedom of the process. Since the valve is already fully open.
The temperature cycles about the setpoint before becoming stable. The gradual closing of the valve can be accomplished only by a corresponding deviation of the variable from the setpoint. Continuous processes possesses a number of degrees of freedom given by the number of variables and defining relations for the system.
If the process reaction rate is large or if lags are not small. Notice that the initial overshoot of temperature.
The large initial overshoot is due to the action of integral response. Heating and rolling of steel ingots or billets. When the processing begins. Offset in the final value may be eliminated by means of integral response. These variables are generally the temperature. When the temperature reaches the lower edge of the proportional band.
Usually the purpose of the process is to produce one or more product at a a given composition. As long as proportional sensitivity is high. Best economy is accomplished by maintaining all process variables in a predetermined relation such that the highest efficiency.
During the heating up period the temperature is. With most processes a gradually decreasing valve setting is required in order to balance energy offset. Offset may be eliminated by means of integral response. Sundaresan and Krishnaswamy method. Skamath Created Date: Apply knowledge of mathematics and science to process dynamics Download our process control by krishnaswamy eBooks for free and learn more about process control by krishnaswamy.
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My resume. The purpose of process control is to reduce the variability in final. Farooq x. Ty food tech credit Sridhar Krishnaswamy Created Date. It third year syllabus Release of dr k s krishnaswamy's book. Control Spring University of Kentucky.
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