This paper proposes a constitution method for an adaptive PID control system that follows a non-stationary system. Because a PID controller has various practical benefits that are easy to implement, unnecessary of controlled model and highly robust, it is the most common control system in industrial world even today. However, its main drawback is that tuning is time consuming because each parameter is determined empirically based on trial-and-error, which is especially noticeable in a multi-input multi-output (MIMO) system composed of multiple PID controllers with interference between control input and controlled output. Other methods have been proposed, including the Ziegler-Nichols ultimate sensitivity method, but it cannot deal with a MIMO system. Additionally, methods using optimization exist, but they cannot provide online tuning for non-stationary systems during operations due to the numerous tuning parameters and repeated computations. In this study, we introduce a computationally efficient optimization method called the Simultaneous Perturbation Stochastic Approximation (SPSA) and investigate its performances when applied to a PID control system. We also propose an online parameter tuning method for the controller by improving the standard SPSA algorithm. The efficiency of proposed method is demonstrated by applying it to a MIMO system, which has some interference.