Summary and Theory - Essay Example

Summary and Theory An air temperature control system is usually utilized in controlling the immediate air temperature irrespective of the air outside. The air temperature control system exemplifies a first order plus dead-time dynamic and is the most distinctive in the industry. Thus, the dynamic gain must reduce with rising gain to the input. The first order system may be referred to as the time taken by the heater to react to the power input whereas the dead time may be referred to as the time taken by the air to flow from the heater to the thermistor. Basically, the control system assists in saving money since the apparatus is self-regulating which includes reducing power when the immediate air temperature has risen and a lesser amount of power is needed. In an air temperature control system, drawing of the air is first done from the immediate environment, past a heating coil and before the air is released back to the atmosphere, it is passed through a thermistor which records the air temperature. Afterwards, the air is then passed back to the system to finish the closed loop system. The programmable thermistor, which records the heat, is linked to the system so as to regulate the system. This assists in generating a voltage which utilized as an indicator to a controller. The thermistor being a semiconductor device, its resistance varies with a change in temperature. The temperature control system is made up of a digital device that is linked to cooling or heating coil. The device also has a circuit board and a memory chip. The heat that is absorbed by the air is referred to as dynamic heat balance that is determined as the heat going in-the heat coming out written as The number of input voltage for an amplifier is usually assumed. The output voltage is amplified and bears an opposite sign to that of the input as the following equation specifies ,with the e being an error and is established from a comparator circuit as e=r-c and when offset becomes the permanent error that the controller cannot influence. The resistors are set at similar value to the unit amplifier gain (K). There is a process gain in the control system which is the air temperature change per unit of power input. The gain or temperature change at higher air flow ought to be low since a given unit changes as heat input is absorbed by a moderately big mass air flow. The gain ought to be higher at lower air flow since the same unit change in heat input is employed to a lower air flow. Minimal controller tuning is needed for the variable gain. This lab’s experiments will dwell on; Loop elements which deal with the determination of an element’s stable state gain for the thermistor circuit and air heating process and the heater. Distinct elements in the loop in this experiment are usually separated in the industry; however, in this case, they are all put in a single small package which may make them a bit difficult to differentiate. Because of the nearness of the element, the first order times as well as response time are quite short. Establishment of the dynamic, which is utilized in measuring dead time, steady state gain and time constant. Proportional control which is utilized in determining the offset distinctive of the comparative gain by testing the controller on the procedure. Frequency respond-This experiment is just a confirmation of the theory that the frequency response can be predicted from the time constant and that frequency response also is a determinant of loop stability. PROCEDURE 3.1-LOOP ELEMENTS After the process of calibration was finished, the DC power supply was fastened up to the input socket on the air temperature control equipment and the ground. With the blower speed being too low, the DC power supply was regulated to an input voltage of 4V.After the equipment came to a stable state the readings on the digital thermometer (°C), the sensor voltage (V) and of the wattmeter (W) were noted. Stable state was exhibited when there was small to no change in the digital thermometer. There was also an increase of the DC power supply voltage in additions of about 1.0V for a 4.0 V to 10.0 V range. Again the values of the digital thermometer (°C), the wattmeter (W), the sensor voltage (V) and of the wattmeter (W) were taken for every different input voltage. The speed of the blower was then increased to high and repetition of the experiment done for similar values of input voltage utilized with the speed of the blower. The heater’s gain, the air heating procedure as well as the sensor were determined by plotting heater watts against input voltage, air temperature against heater watts, and sensor voltage against air temperature. The graph slopes are the appropriate gains of the elements of the air temperature control apparatus. 3.2-PROCESS DYNAMICS This section of the experiment had the adjustment of the blower to low speed. Connection was done of the waveform generator to the air temperature control instrument, to the input socket and grounded. Setting of the voltage was done at about 9 Vs. Adjusting of the signal generator to the square was done and the input signal set to 2 V.A connection was made between the air temperature instrument and the output sensor signal to the channel 1 and 2 on the oscilloscope, which was later grounded and turned on. The time constant, dead time as well as steady time were recorded when the output and input signals could be viewed on the oscilloscope. The dead time was determined by observing the length from peak to peak of the output and input waves. A stable state gain was calculated by pitching the change in the output signal by the variation of the input signal. The gain’s absolute product from the first experiment was determined and recorded in table 3.2.1 3.3-PROPORTIONAL CONTROL The amplifier’s terminals were linked with the 10 KΩ resistors. The voltage of the sensor was linked to the amplifiers’ input socket. The other potentiometer terminals were linked to the -15V power supply and consequently grounded. The determination of set point and sensor voltages confirmed that the amplifier output was a subtraction of the 2, implying that the circuit was appropriately built. In addition, the amplifier feedback terminals were linked to the potentiometer socket and the 10 KΩ resistors. The input voltage was adjusted to 0.5V.The gain amplifier output led to similar scale of the product gain and a voltage with the opposite sign. After all the tests to ascertain that the comparator was linked and functioning correctly, both the heater input and sensor output were linked to the controller output. Adjustment was done to the bias potentiometer watching the controller’s output voltage to ensure its indicated zero so as to indemnify a controlled set point. Introduction of a set point was done and measurement of the sensor voltage and the controller output change was done. This process was done again and again with increments from a gain of 1 to 4.Original offset was eliminated through adjusting the bias. Experimental and calculated results are illustrated in table 3.3.1. 3.4-FREQUENCY RESPONSE Frequency responses were observed in this section of the experiment. Since the comparator was not utilized in this section of the experiment, it was disengaged. Nevertheless, the signal generator was joined to the trainer input; together with the sensor output were joined to oscilloscope’s channels 1 and 2.Adjustment to blow speed was raised and the output of the sensor was regulated to 2.96V.In addition, the signal generator was adjusted to generate a sine wave. A low frequency of 0.1Hz was positioned to start the experiment. By use of the oscilloscope the run stop button was triggered off to generate the wave on the screen. Recording of the frequency, period, lag and output voltage was done. The theoretical and experimental phase and gain were determined together with the frequency which was converted by use of the provided equations. The recorded and calculated are as illustrated in table 3.4.1 For the damping ratio, the needed gain for quarter-amplitude damping was determined by use of this the formula , where Kc represents controller gain and Gol symbolizes the amplitude at which the output phase lag was -180 degrees. After the gain was determined, the needed resistance of the potentiometer was determined by use of the equation , where Kc is the gain, Rc is the needed potentiometer resistance, and R3 is 10,000 Ω. Connection of the oscilloscope and controller to the apparatus with the gain determined in stage 1-2 that we set. Introduction of a disturbance to the loop at a fast blower speed was done. Calculation of the damping ratio was done by use of the oscilloscope and the damping results are as illustrated in table 3.4.3. DISCUSSION: The first of this experiment should be checked at 3.1.1 and 3.1.2.It becomes clear while examining the slope (i.e. gain) of the heater against input voltage is negative, whereas the air temperature against the heater watts and sensor voltage against air temperature have gains and slopes that are positive. These relationships were discovered to be linear ones. As watts rises, the quantity of heat generated by the electrical heater also rises. In normal circumstances, an assumption is made such that when there is a rise in input voltage, the heater watts also rises. Nevertheless, this pattern does not happen in this particular experiment. A decrease in the heater watts led to a decrease in the temperature of the sensor. This is because of the fact that less heat was being generated by the heater. As the input voltage rose, the sensor voltage also reduced. This information implies that as the temperatures reduces; the output voltage to the blower assembly from the sensor also reduces. Numerous features also change when the blower speed changes from low to high blower speed. As the blower speed rises, the temperature and voltage of the sensor reduces considerably. This observation implies that as the rate of air flow rises, the temperature at which the air exits the channel reduces. The dead time, time constant as well as stead-state gain were calculated for both high and low blower speeds. As illustrated in table 3.2.1, the time constant was larger for the low blower speed. This implies that the high blower speeds reacts more rapidly than the low blower rate. In regard to dead time, it was discovered that the dead time was larger for the high blower than the low blower speed. Thus, the high blower speed has a quicker reaction but a bigger dead time than the slow blower speed due to the fact that air exiting the heater reaches the thermistor quicker than the low blower speed. The quicker velocity of the air from the high blower speed may have led to the transfer of heat to take longer than air that is moving slowly. The steady-state gain was determined by use of the formula, .Thus, the low blower speed had a higher steady-state gain than the high blow speed. On the basis of the above conclusions from the first section of the lab, a low blower speed has a higher voltage sensor than a high blower speed sensor voltage. Thus, the output voltage is higher for the low blower speed. Nevertheless, the low blower speed has got a higher gain when similar input is utilized. The steady-state gain is thus higher than the gains determined in the initial experiment. In section 3.3, analysis was done for every section of the controller so that a deeper and accurate understanding of the controller functions could be gained. Thus, the comparator can be viewed as a summing amplifier which takes care of the error between the set point and sensor voltages. Thus the gain amplifier is utilized in increasing the voltage by a specific multiple. The gain on the controller can be determined by use of the formula, ,where Rc is the potentiometer resistance, which can be controlled and R3 is a 10,000Ω resistance. The gain amplifier’s output is the input voltage and increases a bias voltage that is indicated by a potentiometer. Afterwards, the sign reversal part of the gain controller then changes the voltage’s sign from positive to negative, or vice versa. Thus as tables 3.3.1 and 3.4.1 illustrates the offset temperature and voltage was determined by getting the difference between the absolute difference of the before and after sensor voltages and absolute difference of the before and after set point voltages. The line of the best fit equation was used in determining the offset temperature of the input voltage against temperature. An increase in the controller gain, led to a corresponding decrease in the voltage and temperature offset. Therefore the equation can be utilized in determining the offset. Nonetheless, there are restrictions to this statement, for loop could turn unstable if gain rises to a considerably higher value. Thus for section 3.4, tables 3.4.3 together with graphs 3.4.1 and 3.4.2 should be referred for the next discussion. As the frequency increased, there were numerous factors that changed considerably. Both the amplitude gain and the output voltage reduced. Moreover, the lag reduced and the phase lag reduced considerably as the frequency increased. The following equation was used in determination of the gain in decibels; db= 20logG, where G was the output amplitude. Thus, the hypothetical phase lag was calculated to be a mixture of the reg phase and the dead phase. The dead time is determined in table 3.2.1 and frequency measured in rad/s. On the other hand, the reg phase was calculated to be negative arc tan of multiplying the frequency by the time constant, illustrated in table 3.2.1.The hypothetical gain was determined by use of the formula where K represents the steady=state gain found in table 3.2.1, is the time constant, and is the frequency in rad/s. It is also crucial to bear in mind that all of the time constant sand steady state gain constants emanate from the high blower speed. Prediction can be made of the frequency reaction from the dynamic factors for the hypothetical values since they are the same with the values calculated through experimentation. The Bode diagram can also be used in determination of the frequency response. This is because the Bode diagram illustrates a stable relationship between the gain, phase lag and frequency.As shown in graphs 3.4.1 and 3.4.2, the Bode diagrams illustrate a pattern that is the same as the graphs depicted in fig 1.20 in the Engineering 2434 laboratory manual. There exists an exponential relationship between the phase lag and the frequency in graph 3.4.1.A linear relationship is established between the frequency and the gain the moment the frequency reaches about 1Hz.In addition, the Bode diagrams indicate that as the frequency rises, the phase and gain reduce. The controller gain required for quarter-amplitude damping can be determined by the formula where Kc is the controller gain and Gol is the amplitude gain at which creates a -180 phase lag as illustrated as table 3.4.3.Employing the dynamic amplitude gain to establish the controller gain, the damping ratio was calculated and found to be 0.0209.On the other hand the experimental value is about 0.25 or quarter amplitude damping. The difference between the experimental and theoretical values is most likely influenced by experimental and human error. This portion of this experiment indicates that 180 phase lag amplitude gain can be utilized in determination of the appropriate gain that will develop quarter-amplitude damping. Moreover, when there was a change in blower speed, the gain developed a damping ratio near 0.25.However,the damping ratio of the low blower speed was determined to be 0.236.Nevertheless,a new gain in amplitude at -180 phase lag should be redetermined to establish the controller gain required for either a faster or slower speed. Thus, this experiment has stresses that the amplitude gain required to have quarter-amplitude damping differs with the blower speed employed. Read More