The proportional-integral-derivative (PID) is still the most common controller and stabilizer used in industry due to its simplicity and ease of implementation. In most of the real applications, the controlled system has parameters which slowly vary or are uncertain. Thus, PID gains must be adapted to cope with such changes. In this paper, adaptive PID (APID) controller is proposed using the recursive least square (RLS) algorithm. RLS algorithm is used to update the PID gains in real time (as system operates) to force the actual system to behave like a desired reference model. Computer simulations are given to demonstrate the effectiveness of the proposed APID controller on SISO stable and unstable systems considering the presence of changes in the systems parameters. 1. Introduction A challenging problem in designing a PID controller is to find its appropriate gain values (i.e., proportional gain , integral gain , and derivative gain ) [1]. Moreover, in case where some of the system parameters or operating conditions are uncertain, unknown, or varying during operation, a conventional PID controller would not change its gains to cope with the system changes. Therefore a tuning method is needed. Various PID controller tuning techniques have been reported in the literature. It is classified into two groups, offline tuning methods as Zeigler-Nichols method and online tuning methods or adaptive PID. APID can tune the PID gains to force the system to follow a desired performance even with the existence of some changes in system characteristics [2]. Adaptive control has been commonly used during the past decades specially the model reference adaptive control (MRAC). Its objective is to adapt the parameters of the control system to force the actual process to behave like some given ideal model which is demonstrated in [3, 4]. There are two main categories of adaptive control. Indirect. It starts with controlled system identification and then uses those estimated parameters to design the controller as presented in [5–7]. Direct. This is more practical than indirect method. It uses a parameter estimation method to get the controller parameters directly the same as introduced in [8, 9]. An adaptive PID controller is presented in [10] using least square method which is an offline parameter estimation method. On the other hand, an optimal self-tuning PID controller is introduced in [5] using RLS to estimate the model from its dynamic data. RLS is a recursive algorithm for online parameter estimation that is frequently used because it has a fast rate of convergence.
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