A DATA-DRIVEN PID CONTROLLER FOR FLEXIBLE JOINT MANIPULATOR USING NORMALIZED SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATION

N.M.Z.A. Mustapha, M.H. Suid, R.M.T. Raja Ismail, A.N.K. Nasir, M.A. Ahmad, M.Z. Mohd Tumari, J.J. Jui

Abstract


This paper presents a data-driven PID controller based on Normalized Simultaneous Perturbation Stochastic Approximation (SPSA). Initially, an unstable convergence of conventional SPSA is illustrated, which motivate us to introduce its improved version. The unstable convergence always happened in the data-driven controller tuning, when the closed-loop control system became unstable. In the case of flexible joint manipulator, it will exhibit unstable tip angular position with high magnitude of vibration. Here, the conventional SPSA is modified by introducing a normalized gradient approximation to update the design variable. To be more specific, each measurement of the cost function from the perturbations is normalized to the maximum cost function measurement at the current iteration. As a result, this improvement is expected to avoid the updated control parameter from producing an unstable control performance. The effectiveness of the normalized SPSA is tested to the data-driven PID control scheme of a flexible joint plant. The simulation result shows that the data-driven controller tuning using the normalized SPSA is able to provide a stable convergence with 76.68 % improvement in average cost function. Moreover, it also exhibits lower average and best values for both norms of error and input performances as compared to the existing modified SPSA.A DATA-DRIVEN PID CONTROLLER FOR FLEXIBLE JOINT MANIPULATOR USING NORMALIZED SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATION

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References


S. Ishizuka and I. Kajiwara, I., "Online adaptive PID control for MIMO systems using simultaneous perturbation stochastic approximation", Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 9, no. 2, pp. JAMDSM0015-JAMDSM0015, 2015.

M. Almaraashi, R. John, A. Hopgood and S. Ahmadi, "Learning of interval and general type-2 fuzzy logic systems using simulated annealing: Theory and practice", Information Sciences, vol. 360, pp.21-42, 2016.

X. Liu and T. Lan, "Adaptive Neural Gradient Descent Control for a Class of Nonlinear Dynamic Systems with Chaotic Phenomenon", Mathematical Problems in Engineering, vol. 2015, pp. 1-6, 2015.

J.C. Spall, Stochastic optimization, Handbook of computational statistics, Springer Berlin Heidelberg, Berlin, 2012, pp. 173-201.

V. Aksakalli and M. Malekipirbazari, "Feature selection via binary simultaneous perturbation stochastic approximation", Pattern Recognition Letters, vol. 75, pp.41-47, 2016.

C. Antoniou, C.L. Azevedo, L. Lu, F. Pereira and M. Ben-Akiva, "W-SPSA in practice: Approximation of weight matrices and calibration of traffic simulation models", Transportation Research Procedia, vol. 7, pp. 233-253, 2015.

M.A. Ahmad, S. Azuma and T. Sugie, "Identification of continuous-time Hammerstein systems by simultaneous perturbation stochastic approximation", Expert Systems with Applications, vol. 43, pp. 51-58, 2016.

J. Mateo, A.M. Torres, M.A. García and J.L. Santos, "Noise removal in electroencephalogram signals using an artificial neural network based on the simultaneous perturbation method", Neural Computing and Applications, vol. 27, no. 7, pp.1941-1957, 2016.

S. Azuma, I. Baba and T. Sugie, "Broadcast Control of Markovian Multi-Agent Systems", SICE Journal of Control, Measurement, and System Integration, vol. 9, no. 2, pp. 103-112, 2016.

J.C. Spall, "A one-measurement form of simultaneous perturbation stochastic approximation", Automatica, vol. 33, no. 1, pp. 109–112, 1997.

J.C. Spall, "Adaptive stochastic approximation by the simultaneous perturbation method", IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1839–1853, 2000.

J.L. Maryak and D.C. Chin, "Global random optimization by simultaneous perturbation stochastic approximation", in Proceedings of the 2001 Winter Simulation Conference, Arlington, USA, 2001, pp. 307–312.

S. Azuma, M. Selman Sakar and G.J. Pappas, "Stochastic source seeking by mobile robots", IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2308–2321, 2012.

M.A. Ahmad, S. Azuma and T. Sugie, “Performance analysis of model-free PID tuning of MIMO systems based on simultaneous perturbation stochastic approximation”, Expert Systems with Applications, vol. 41, no. 14, pp. 6361-6370, 2014.

Y. Tanaka, S. Azuma and T. Sugie, "Simultaneous Perturbation Stochastic Approximation with Norm‐Limited Update Vector", Asian Journal of Control, vol. 17, no. 6, pp.2083-2090, 2015.

M.A. Ahmad, M.Z. Mohd Tumari, and A.N.K. Nasir, “Composite fuzzy logic control approach to a flexible joint manipulator”, International Journal of Advanced Robotic Systems, vol. 10, no. 58, pp. 1-9, 2013.




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