Modelling and Control of a 1st Order Process: Tank Heating - Lab Report Example

MODELLING AND CONTROL OF FIRST ORDER PROCESS Department of Electrical Engineering. Control and Instrumentation Student Name: Student No: Lecturer: Assignment Title: Modeling and Control of a 1st Order Process: Tank Heating Laboratory Report Date of Submission: Control and Instrumentation Abstract This report is related to the work carried-out in the laboratory to test the heating and cooling of a first order system to deduce the parameters of the transfer function that represent the time constant and steady state gain of the process. The first part of the experiment is related to determining these parameters through modeling the process equation and evaluating the transient response of the system output to a unit step change in the input of the system. The process is in the form of a small tank of water with electrical heater. The CPSU (Controller/Power Supply Unit) has a selectable power level of approximately 20 watt and maximum of 100 watt. For this experiment we will need to select the 20 watt setting for the power supply. To perform the transient characteristics recording, the temperature sensor was placed in hot water tank and the output voltage and water temperature was recorded. A multimeter is used to measure the output response voltage of the sensor, while this is transferred into temperature reading using the calibration curve of the temperature sensor that relates the output voltage of the sensor to the surrounding temperature. The first part of the experiment is dedicated to determining the transient characteristics of the first order system. The second part of the experiment is dedicated to designing a proportional controller that can achieve specific transient characteristics of the first order system in terms of time constant and steady state gain. Introduction A control system is an arrangement of physical components connected or related in such a manner as to command, direct, or regulate itself or another system. Control systems abound in our environment. But before exemplifying this, we define two terms: input and output, which help in identifying, delineating, or defining a control system. The input is the stimulus, excitation or command applied to a control system, typically from an external energy source, usually in order to produce a specified response from the control system. The output is the actual response obtained from a control system. It may or may not be equal to the specified response implied by the input. A closed-loop control system is one in which the control action is somehow dependent on the output Temperature sensors are very important sensors in many industrial applications. All heating and cooling systems are equipped with temperature sensors. These sensors are the main element in the feedback control loop for these systems. Also, temperature sensors are used in industry to protect equipment against very high undesirable temperature that could damage the equipment. The performance of temperature sensors and its accuracy is very important for accurate operation of the closed loop control system to maintain the required output temperature or detect undesirable equipment and ambient temperature rise. This is why, temperature sensors have to be calibrated at specific time intervals to guarantee correct signaling to control system. If the temperature sensor is not well calibrated, false signals could be sent to the control system that will not be able to achieve desired output temperature of fail to protect the equipment against temperature rise. Some equipment is very important and any damage could result in severe problems. An example of these equipments is the power transformers and the furnaces. Thermocouples are one of the main equipments used in industry for temperature sensing in many temperature control applications because of being cheap, easy used, and well robust operation. Thermocouples produce a voltage signal in proportional to the applied temperature on the sensor. Thermocouples are mainly a closed thermoelectric circuit between two different types of materials that produce voltage difference when subjected to external temperature source due to difference in thermal coefficient of the materials. One junction is normally kept in a fixed temperature region while the other junction is exposed to contact with the medium which temperature need to be measured. This medium can be any medium, liquid, gas, or chemical component, while the interactions with the thermocouple in any form that can affect its performance or reading is prohibited. For protection purposes, all thermocouple devices are normally supplied with protective coatings or shields that protect them from interaction with environment, while keeping the function for temperature sensing active. Generally, every temperature sensor has a calibration curve as shown in figure (1) that relates its output voltage to the input temperature affecting the sensor surrounding. This curve is very important in designing controller system so that the voltage output can be used to control the required temperature in a certain application so that it fulfills the required control action effectively. The sensor has to be calibrated against its calibration curve from time to time to make sure that there is no deviation from the setting used in the controller. Figure (1): Calibration Curve for the Thermistor. This experiment will test a first order system response to a step input command of its temperature. The system is formed by a water tank and a heating element. The system equation is as follows: The process is a small tank of water with an electrical heater. The CPSU (Controller/Power Supply Unit) has a selectable power level of approx 20 watts and MAX (approx. 100 watts). For this experiment we will select the ~20 watt supply. The theoretical modeling has been dealt with in the tutorial on 1st order systems. The general form of the system equation is (1) where: QH = heater power (W) h = heat transfer coefficient (W/m2 oC) A = effective surface area (m2) TA = ambient temperature (oC) T = instantaneous temperature of the heated material M = mass of heated material (kg) c = specific heat of heated material (J/kg oC) D = differential operator d/dt The quantity is known as the TIME CONSTANT of the process and is a measure of how quickly the temperature responds to the effect of the heater. A system described by equation (1), (a FIRST ORDER equation) will respond in a particular way to the sudden switching ON of the heater. This sudden application of heat is known as a STEP INPUT and equation (1) can be solved for this step input function to give an equation for the resulting temperature with respect to time. This is called the RESPONSE of the system. The significance of the time constant is that it indicates the time at which the temperature of the system reaches 0.632 of its final temperature above ambient. Tables (1) represent the parameters of the system under test. Parameter Value QH 20 Watt A 7x10-3 m2 C 3x103 J/kg/oC TA 18 0c M 50 g =50x10 kg MC/hA =time constant ==636 sec D d/dt T h Table (1) Parameters of the system under test. In the next section, a description of the procedure to do the experiment in the laboratory, obtained results and conclusion for the work will be presented. The work carried-out in this experiment is mainly to deduce experimentally the first order system transient characteristics parameters experimentally for the purpose of controlling these parameters using a closed loop proportional controller. This means that the values are recorded during the change in the heated material over time a result of step input of the heater power. This response will be used to determine the time delay, and the time constant, and the steady state gain to define the characteristics of the first order system. Theoretical background The time response of a system, subsystem, or element is the output as a function of time, usually following application of a prescribed input under specified operating conditions. The unit step response is given by y , ( t ) = /dw(t - 7)u(7)d7, where l ( t ) is a unit step function. In y l ( f ) = \>a( f - 7 ) U( 7 ) d T = /dyb( f - 7 ) d7 0 Now make the change of variable 8 = t - 7 . Then d7 = -do, 7 = 0 implies 8 = t , 7 = t implies 8 = 0, and the integral becomes 3.27. Show that the unit ramp response y , ( t ) of a causal linear system described by the convolution integral is related to the unit impulse response y s ( t ) and the unit step response y , ( t ) by the equation yr( t ) = J;,( 7 ' ) d7' = JrjTy6s w( t - 7 ) = ya( t - 7 ) and 7 changed to t - T ' , The first term can be written as tjdya(7') d7'= tyl(t). The second term can be Integrated by parts, yielding jd.'Ya(.') d7/ =7/yl(7')lb - /;, Read More

This is why, temperature sensors have to be calibrated at specific time intervals to guarantee correct signaling to control system. If the temperature sensor is not well calibrated, false signals could be sent to the control system that will not be able to achieve desired output temperature of fail to protect the equipment against temperature rise. Some equipment is very important and any damage could result in severe problems. An example of these equipments is the power transformers and the furnaces.

Thermocouples are one of the main equipments used in industry for temperature sensing in many temperature control applications because of being cheap, easy used, and well robust operation. Thermocouples produce a voltage signal in proportional to the applied temperature on the sensor. Thermocouples are mainly a closed thermoelectric circuit between two different types of materials that produce voltage difference when subjected to external temperature source due to difference in thermal coefficient of the materials.

One junction is normally kept in a fixed temperature region while the other junction is exposed to contact with the medium which temperature need to be measured. This medium can be any medium, liquid, gas, or chemical component, while the interactions with the thermocouple in any form that can affect its performance or reading is prohibited. For protection purposes, all thermocouple devices are normally supplied with protective coatings or shields that protect them from interaction with environment, while keeping the function for temperature sensing active.

Generally, every temperature sensor has a calibration curve as shown in figure (1) that relates its output voltage to the input temperature affecting the sensor surrounding. This curve is very important in designing controller system so that the voltage output can be used to control the required temperature in a certain application so that it fulfills the required control action effectively. The sensor has to be calibrated against its calibration curve from time to time to make sure that there is no deviation from the setting used in the controller.

Figure (1): Calibration Curve for the Thermistor. This experiment will test a first order system response to a step input command of its temperature. The system is formed by a water tank and a heating element. The system equation is as follows: The process is a small tank of water with an electrical heater. The CPSU (Controller/Power Supply Unit) has a selectable power level of approx 20 watts and MAX (approx. 100 watts). For this experiment we will select the ~20 watt supply. The theoretical modeling has been dealt with in the tutorial on 1st order systems.

The general form of the system equation is (1) where: QH = heater power (W) h = heat transfer coefficient (W/m2 oC) A = effective surface area (m2) TA = ambient temperature (oC) T = instantaneous temperature of the heated material M = mass of heated material (kg) c = specific heat of heated material (J/kg oC) D = differential operator d/dt The quantity is known as the TIME CONSTANT of the process and is a measure of how quickly the temperature responds to the effect of the heater.

A system described by equation (1), (a FIRST ORDER equation) will respond in a particular way to the sudden switching ON of the heater. This sudden application of heat is known as a STEP INPUT and equation (1) can be solved for this step input function to give an equation for the resulting temperature with respect to time. This is called the RESPONSE of the system. The significance of the time constant is that it indicates the time at which the temperature of the system reaches 0.632 of its final temperature above ambient.

Tables (1) represent the parameters of the system under test. Parameter Value QH 20 Watt A 7x10-3 m2 C 3x103 J/kg/oC TA 18 0c M 50 g =50x10 kg MC/hA =time constant ==636 sec D d/dt T h Table (1) Parameters of the system under test.

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