Journal of Process Control, Vol.21, No.4, 620-626, 2011
Classification of dynamic processes and PID controller tuning in a parameter plane
A quadruplet, defined by the ultimate frequency cop, the ultimate gain k(u), the angle phi of the tangent to the Nyquist curve at the ultimate frequency and the gain G(p)(0), is sufficient for classification of a large class of stable processes, processes with oscillatory dynamics, integrating and unstable processes G(p)(s). From the model defined by the above quadruplet, a two parameter model G(n)(s(n)) is obtained by the time and amplitude normalizations. Two parameters of G(n)(s(n)), the normalized gain rho and the angle phi, are coordinates of the classification rho-phi parameter plane. Model G(n)(s(n)) is used to obtain the desired closed-loop system performance/robustness tradeoff in the desired region of the classification plane. Tuning procedures and tuning formulae are derived guaranteeing almost the same performance/robustness tradeoff as obtained by the optimal PID controller, applied to G(p)(s) classified to the same region of the classification plane. Validity of the proposed method is demonstrated on a test batch consisting of stable processes, processes with oscillatory dynamics, integrating and unstable processes, including dead-time. (C) 2010 Elsevier Ltd. All rights reserved.