Abstract—Now-a-days PID (proportional-integral-derivative) controller is used in every type of small or large industries. For this the digital PID controller is so popular. But it is necessary to design and tune the PID controller in a proper method for applying the plant. The paper represents a method of tuning a digital proportional-integral-derivative (PID) controller. The name of the method is Steepest Gradient Descent Method (SDGM). It is an iterative method. The SDGM method is very simple, easy to use and each iteration is very fast. It is also a guaranteed method to find the minima through numerous times of iterations as long as it exists. By applying this optimization method PID controller is tuned both of digital and analog process. In the paper by applying the method of some plant the comparison result of analog and digital are shown. From the comparison it is found that the digital scheme is preferable than analog scheme. Index Terms—PID controller, SDGM. I. INTRODUCTION The first controllers with proportional, integral, and derivative (PID) feedback control action became commercially available during the 1930s. The 1940s saw widespread acceptance in industry of pneumatic PID controllers, and their electronic counterparts entered the market in the 1950s. Digital hardware has been routinely used since the 1980s with significant impact on process control. Even several decades after three-mode controllers were introduced; the vast majority of controllers used in the chemical process industry are based on PI/PID models [1]. The popularity of these controllers has led to research on tuning methods, resulting in hundreds of publications on this topic. Ziegler-Nichols tuning relations and Cohen-Coon tuning rules are among the earliest published methods. Tuning relations based on error criteria are more recent model-based tuning rules, which offer improvements over earlier tuning methods. Tuning rules also exist for unstable processes as well as for tuning in the presence of plant model mismatch [2]. Despite the numerous approaches available for controller tuning, surveys indicate that poorly tuned control loops are abundant in industry. In general, the gain scheduling of the PID controllers is an optimization problem. The method of steepest descent (SDGM) is also known as The Gradient Descent, which is basically an optimization algorithm to find the local minimum of a function. By applying the SDGM to the PID controller, the controller is tuned and applied to some conventional plant then the digital and analog results are compared to the paper. II. PID CONTROLLER PID controller consists of Proportional Action, Integral Action and Derivative Action. It is by far the most common control algorithm. PID controller’s algorithm is mostly used in feedback loops [1]. PID controllers can be implemented in many forms. It can be implemented as a stand-alone controller or as part of Direct Digital Control (DDC) package or even Distributed Control System (DCS). The latter is a hierarchical distributed process control system which is widely used in process plants such as pharmaceutical or oil refining industries [3]. The schematic diagram of the PID controller is given below. Such set up is known as non- interacting form or parallel form. Fig. 1. Schematic of the PID controller - non-interacting form [3] A. 2.1 Proportional Control The proportional controller output uses a ‘proportion’ of the system error to control the system. However, this introduces an offset error into the system. (1) where, is the error signal of the system and K P is the gain of the P controller B. Integral Control The integral controller output is proportional to the amount of time there is an error present in the system. The integral action removes the offset introduced by the proportional control but introduces a phase lag into the system. (2) where, K I is gain of the integral controller. C. Derivative Control The derivative controller output is proportional to the rate of change of the error. Derivative control is used to reduce/eliminate overshoot and introduces a phase lead action that removes the phase lag introduced by the integral action. (3) Application of SDGM to Digital PID and Performance Comparison with Analog PID Controller M. M. Israfil Shahin Seddiqe and Sobuj Kumar Ray Manuscript received February 7, 2011; revised September 30, 2011. M. M. Israfil Shahin Seddiqe is with Rajshahi University of Engineering and Technology (RUET), Rajshahi, Bnagladesh .(e-mail: mmisrafil@gmail. com) Sobuj Kumar Ray is with International University of Business Agriculture and Technology. (e-mail: sobuj_kumar_ray@yahoo.com) International Journal of Computer and Electrical Engineering, Vol. 3, No. 5, October 2011 634