Adaptive PID controller based on online LSSVR with kernel tuning

In this paper, the effects of tuning the kernel bandwidth for an online LSSVM are investigated. LSSVM is used to obtain a model of the system, and based on this model information, an adaptive PID is designed to control the plant. The kernel parameter determines how the measured input is mapped to the feature space and a better plant model can be achieved by discarding redundant or irrelevant features, therefore introducing adaptability in kernel parameters improves modeling performance. The purpose of this paper is to find the optimal kernel bandwidth to improve the modeling performance of the LSSVM and consequently control performance obtained by adaptive PID which is designed based on the Jacobian information attained by the LSSVM. The proposed method has been evaluated by simulations carried out on a continuously stirred tank reactor (CSTR), and the results show that there is an improvement both in modeling and control performances.