### Effects of Adaption Gain in Direct Model Reference Adaptive Control for a Single Conical Tank System

#### Abstract

This paper implement and analysis the effects of direct Model Reference Adaptive Control (MRAC) for a single conical tank system. Classical control strategies fail due to its high nonlinearity, continuously varying area, and loading effects of a single conical tank system. To overcome the shortfalls, this article proposed the MRAC scheme for controlling the level of a single conical tank process. The MRAC can be regarded as an adaptive servo system, in which the desired performance is expressed in terms of a reference model that provides the anticipated response to a command signal. The selection of adaption gain is the most important part in the design of MRAC, particularly in real-time applications. This article analyses the effect of adaption gain from the lower value to upper value. The simulation result shows the higher values of adaption gain improves the system performances and reduces the error when compared with the lower values of adaption gain. To improving the stability and reliability of adaptive control, improved MRAC scheme is proposed with PID controller. This improved version has two loops such as inner loop and outer loop. Inner loop act as a normal feedback with PID controller and outer loop act as an adaptive control for parameter adjustment. This proposed approach shows, better performance than normal MRAC. The entire analyses are simulated in MATLAB R2013a environment.

#### Keywords

#### Full Text:

PDF#### References

Rajesh, R. and Baranilingasen, I., 2017. Modeling and analysis of differential tuning methodology of PID controller for a linearly parameterized non linear system. International Journal for Science and Advance Research in Technology, 3(5), pp.615-620.

Warier, S.R. and Venkatesh, S., 2012, March. Design of controllers based on MPC for a conical tank system. In Advances in Engineering, Science and Management (ICAESM), 2012 International Conference on (pp. 309-313). IEEE.

Vijula, D.A., Vivetha, K., Gandhimathi, K. and Praveena, T., 2014. Model based controller design for conical tank system. International Journal of Computer Applications, 85(12).

El Damatty, A.A., Saafan, M.S. and Sweedan, A.M.I., 2005. Experimental study conducted on a liquid-filled combined conical tank model. Thin-Walled Structures, 43(9), pp.1398-1417.

Lee, M. and Shin, J., 2009. Constrained optimal control of liquid level loop using a conventional proportional-integral controller. Chemical Engineering Communications, 196(6), pp.729-745.

Åström, K.J. and Hägglund, T., 2006. Advanced PID control. In The Instrumentation, Systems, and Automation Society.

Gaing, Z.L., 2004. A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE transactions on energy conversion, 19(2), pp.384-391.

Seborg, D.E., Mellichamp, D.A., Edgar, T.F. and Doyle III, F.J., 2010. Process dynamics and control. John Wiley & Sons.

Seborg, D.E., Edgar, T.F. and Shah, S.L., 1986. Adaptive control strategies for process control: a survey. AIChE Journal, 32(6), pp.881-913.

Monopoli, R., 1974. Model reference adaptive control with an augmented error signal. IEEE Transactions on Automatic Control, 19(5), pp.474-484.

Hsu, L., 1990. Variable structure model-reference adaptive control (VS-MRAC) using only input and output measurements: the general case. IEEE Transactions on Automatic Control, 35(11), pp.1238-1243.

Senjyu, T., Kashiwagi, T. and Uezato, K., 2001. Position control of ultrasonic motors using MRAC and dead-zone compensation with fuzzy inference. In Power Electronics Specialists Conference, 2001. PESC. 2001 IEEE 32nd Annual (Vol. 4, pp. 2031-2036). IEEE.

Stoten, D.P. and Benchoubane, H., 1990. Empirical studies of an MRAC algorithm with minimal controller synthesis. International Journal of Control, 51(4), pp.823-849.

Wu, H. and Deng, M., 2015. Robust adaptive control scheme for uncertain non-linear model reference adaptive control systems with time-varying delays. IET Control Theory & Applications, 9(8), pp.1181-1189.

Zuo, Z. and Wang, C., 2014. Adaptive trajectory tracking control of output constrained multi-rotors systems. IET Control Theory & Applications, 8(13), pp.1163-1174.

Prakash, R. and Anita, R., 2011. Neuro-PI controller based model reference adaptive control for nonlinear systems. International Journal of Engineering, Science and Technology, 3(6), pp.44-60.

Prakash, R. and Anita, R., 2010. Robust model reference adaptive PI control. Journal of Theoretical & Applied Information Technology, 14.

Wei, S.U., 2007. A model reference-based adaptive PID controller for robot motion control of not explicitly known systems. International Journal of Intelligent Control and Systems, 12(3), pp.237-244.

Zhang, S., Feng, Y. and Zhang, D., 2015. Application research of MRAC in fault-tolerant flight controller. Procedia Engineering, 99, pp.1089-1098.

Wu, H., 2013. A class of adaptive robust state observers with simpler structure for uncertain non-linear systems with time-varying delays. IET Control Theory & Applications, 7(2), pp.218-227.

Datta, A. and Ioannou, P.A., 1994. Performance analysis and improvement in model reference adaptive control. IEEE Transactions on Automatic Control, 39(12), pp.2370-2387.

Sun, J., 1993. A modified model reference adaptive control scheme for improved transient performance. IEEE Transactions on Automatic Control, 38(8), pp.1255-1259.

Narendra, K. and Annaswamy, A., 1987. A new adaptive law for robust adaptation without persistent excitation. IEEE Transactions on Automatic control, 32(2), pp.134-145.

Ioannou, P.A. and Kokotovic, P.V., 1984. Instability analysis and improvement of robustness of adaptive control. Automatica, 20(5), pp.583-594.

Xin, W., Zhen-Lei, W., Yi-Hui, Z., Li-Xue, L., Jia-Zhen, L. and Hui, Y., 2010, June. Multiple models robust adaptive controller of reduced model. In Proceedings of the 31st Chinese Control Conference.

Narendra, K.S. and Balakrishnan, J., 1997. Adaptive control using multiple models. IEEE transactions on automatic control, 42(2), pp.171-187.

Volyanskyy, K.Y., Haddad, W.M. and Calise, A.J., 2009. A New Neuroadaptive Control Architecture for Nonlinear Uncertain Dynamical Systems: Beyond $sigma $-and $ e $-Modifications. IEEE Transactions on Neural Networks, 20(11), pp.1707-1723.

Nguyen, N.T., 2012. Optimal control modification for robust adaptive control with large adaptive gain. Systems & Control Letters, 61(4), pp.485-494.

Cao, C. and Hovakimyan, N., 2008. Design and Analysis of a Novel ${cal L} _1 $ Adaptive Control Architecture With Guaranteed Transient Performance. IEEE Transactions on Automatic Control, 53(2), pp.586-591.

Yucelen, T. and Haddad, W.M., 2013. Low-frequency learning and fast adaptation in model reference adaptive control. IEEE Transactions on Automatic Control, 58(4), pp.1080-1085.

Stepanyan, V. and Krishnakumar, K., 2012. Adaptive control with reference model modification. Journal of Guidance, Control, and Dynamics, 35(4), pp.1370-1374.

Lee, T.G. and Huh, U.Y., 1997, July. An error feedback model based adaptive controller for nonlinear systems. In Industrial Electronics, 1997. ISIE'97., Proceedings of the IEEE International Symposium on (pp. 1095-1100). IEEE.

Gibson, T.E., Annaswamy, A.M. and Lavretsky, E., 2013. On adaptive control with closed-loop reference models: transients, oscillations, and peaking. IEEE Access, 1, pp.703-717.

Luyben, W.L., 1989. Process modeling, simulation and control for chemical engineers. McGraw-Hill Higher Education.

Ogunnaike, B.A., 1994. Process dynamics, modeling, and control (No. 660.28 O48.).

Marlin, T.E., 1995. Process Control. New York: McGraw-Hill.

Roffel, B. and Betlem, B., 2007. Process dynamics and control: modeling for control and prediction. John Wiley & Sons.

Downs, J.J. and Vogel, E.F., 1993. A plant-wide industrial process control problem. Computers & chemical engineering, 17(3), pp.245-255.

Spong, M.W. and Vidyasagar, M., 2008. Robot dynamics and control. John Wiley & Sons.

Åström, K.J. and Wittenmark, B., 2013. Adaptive control. Courier Corporation.

Landau, I.D., Lozano, R., M'Saad, M. and Karimi, A., 1998. Adaptive control (Vol. 51). New York: Springer.

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution 3.0 License.