PID Modeling and Level Control of Multiple Liquid Vessel - Math Problem Example

Abstract - In industrial control system liquid levels in multiple tanks is usually difficult for controllers to know the amount of liquids that is within those tanks. This paper undertook the responsibility of doing modeling of a system which will determine the water levels and control the water/liquid entry into the tanks. PID controller system is designed for four tanks. Simulation was carried out for the control system. Index Terms: PID controller, sensor, water level indicator, Matlab. I. Introduction PID is an industrial control system that are applied in manufacturing industries to maximize on the efficiency of production, supervision, as well as data acquisition amongst other aspects of controlled systems. It industrial application such as liquid level control in nuclear power generation plant, food processing and chemical processing PID Control system designed will consider the flow rate of water and the height in the four tanks. It will control the water pump in such a manner that the levels of water in all the tanks are known[6]. The plant will have feedback loop that that measures the variable, SetPoint that converts feedbacks to a voltage. There is also Error Signal that alerts about differences between SetPoint and measured variables. The disturbances and Controller to supply power, read Set Point, process the error, and give the output to the Plant [12]. II. PROCESS The process will have equations which will solve all acts as parameters for water levels in the tanks. The re will be a single input as well as a single output and the tanks will not be in a linear position for control to be efficient. The water levels will be determined by letters such as H1, H2, and H3. The coefficient for the tanks will be. The feedback signal to the computer ensures that there is information regarding the controller that is being relayed. This signal is usually appositive signal and it is relayed when the desired results as been attained. These sensors are capable of sensing any changes in setpoints. With these, any water level beyond the set level will cause signals to be sent to the computer. These signals cause automatic disturbances in controller thereby stabilizing the water level. The set up uses a process controller, which uses a self contained process of heating simulation with an inbuilt controller function [4]. In this set up, the method that was utilized involved altering parameters under investigations and measuring their corresponding effects on the water level changes, these were then compared with the set values so at to generate a control signal that could enable regulation of the electrical power supply. The justifications for this industrial control process is based on the fact that most if not all industrial processes require energy utilization, but of late these have become so expensive that maximum utilization has become a key consideration[7]. There is a need to therefore formulate ways and methods of ensuring such processes attain maximum utilization of the available resources at a controlled approach. Such settings would more often give a better combination of various parameters under investigations that could be unified to give the best result in any controlled industrial process. III Mathematical modeling In designing this system the laws of mass conservation will be used. Where time will be held constant and the following mass flow rate formula will be applicable. The design will have 4 water Tanks, two pumps, Water level indicator, Sensor and Microcontroller. Tank 1 Tank 2 Tank 3 Tank 4 Taking the above equations and do first and second order configuration to have transfer function as shown below; This will be used in designing the controller. The designed PID controller is as shown below; Figure 1: last two tank system control The simplified PID controller diagram in word is as follows; Figure 2: Extract of one tank IV Results and Discussion The following were the outcome of simulation that took place after running the program. The simulation model showed water level in the tank 4. Figure 3: The Coupled Tank The above result shows the response of liquid level in tank 4 with respect to change in water level in other tanks when the controller not is used. In steady state, the controller behaves as digital controller, and during transients it uses a continuous-time digital signal processor to achieve time-optimal response. The compensators were designed using analogue frequency response design methods, based upon open-loop frequency response criteria of phase margin (PM) and gain crossover frequency (cg). The design method assumed second order relationships between open-loop frequency and closed-loop time response measures. These assumptions were invested to determine their reasonableness in the system. Having obtained the required compensators in analogue form, a digital equivalent was evaluated. The performance of the continuous-time and discrete-time controllers was compared Figure 4: Performance of PID Controller The figure above shows performance of the system. It indicates that integral controller overshoots before stabilizing thus eliminating steady state error. The figure below shows bode diagram for the frequencies of PID controller. In implementing Simulink inherent bandwidth restrictions that are as result of natural sampling effect are avoided using a digital controller that has a transient response. In this case a steady state, the controller functions as voltage-mode controller where it uses specific continuous-time digital signal processor to achieve output voltage recovery in the optimal time[9]. An important feature to note concerning the decomposition process is that it is what makes it possible for the samples in the original signal to be reordered. However, the re-ordering of these samples is supposed to follow a specific pattern which is determined by the binary equivalents of each sample. This algorithm that involves the rearrangements of the order of the time domain samples through the counting in binaries that have been flipped from left to right[6]. There are also special cases whereby the algorithm is only applicable to periodic signals if one wants the sampled input to also become periodic. This phenomenon is referred to as spectral leakage. In the case, which happens frequently, whereby the sampled signal is not periodic, there will result discontinuities in the periodic signal that has been processed by the system. This discontinuity can also occur when an integer number of periods are not sampled. The eventual effect of this is that the energy that is contained in the signal will end up leaking from the signal frequency bin into the other frequency bins that are adjacent to it, hence the term spectral leakage. The result of this leakage is errors in the amplitudes of the frequency spectrum display. Due to these amplitude errors, the overall effect will be a case whereby small frequency peaks that occur very close to larger ones will end up being obscured. Thus, in order to reduce the effects of this spectral leakage, a process known as windowing which basically utilizes window functions can be used V Conclusion PID controller system for water tank levels was designed using Matlab Simulink. The parameters for the tanks were based on time and water levels. There was minimum time and maximum time and water levels. References [1] J. Astrom and T. Hagglund, “Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins,” Automatica, vol. 20, no. 5, pp. 645-651, 1984. [2] P. Aravind, M.Valluvan and M.Lavanya. “Auto Tuning PID Controller for Multi-tank Process” International Journal of Computer Applications (0975 – 8887), Volume 84 – No 4, December 2013 NGL-006-69-3, Nov. 15, 1987 [3] I. Isa, B. Meng, Z. Saad and N. Fauzi, 'Comparative study of PID controlled modes on automatic water level measurement system', in IEEE 7th International Colloquium on Signal Processing and its Applications (CSPA), 2011, pp. 237-242. [4] V. Aggarwal, M. Mao and U. o'Reilly, 'A Self-Tuning Analog Proportional-Integral-Derivative (PID) Controller', in First NASA/ESA Conference on Adaptive Hardware and Systems, 2006. AHS 2006, 2006. [5] J. G. Ziegler and N. B. Nichols, “Optimum Settings for Automatic Controllers,” ASME Trans., vol. 64, pp. 759-768, Nov. 1942. [6] J. G. Ziegler and N. B. Nichols, “Process Lags in Automatic Control Circuits,” ASME Trans., pp. 433-444, July 1943. [7] L. Wang, Computer Controlled System Design and Implementation, 1st ed. Springer, 2015, p. 17. [8] V. Hajare and B. Patre, 'Design of PID controller based on reduced order model and Characteristic Ratio Assignment method', in IEEE International Conference on Control Applications (CCA), Hyderabad, India, 2013, pp. 1270 - 1274.W. B. Field, “Adaptive Three-Mode Controller,” ISA J., vol. 9, no. 2, pp. 30-33, 1962. [9] Y. Nishikawa, N. Sannomiya, T. Ohta, and H. Tanaka, “A Method for Auto-TunLig of PID Control Parameters,” Automatica, vol. 20, no. 3, pp. 321-332, 1984. [10] P. Gawthorp and P. Nomikos, 'Automatic tuning of commercial PID controllers for single-loop and multiloop applications', IEEE Control Systems Magazine, no. 1, pp. 34 - 42, 1990. [11] Rajagopalen, A.S. Identification of an Effective Controller for a Stirred Tank Heater Process. International Journal of Engineering and Advanced Technology, Volume-3, Issue-1, October 2013 [12] Dzolkafle, M. B. Implementation of PID controller for controlling the liquid level of the coupled Tank system, 2013. Read More