## 1 Introduction  
Although novel and effective theories and design methodologies are being continually developed in the digital control field, proportional-integral-derivative (PID) controllers are still the most widely adopted solution for control problems in both academic and industry sectors. The tuning of the parameters of the PID controllers has been proved a hard task and several approaches have been investigated in the past [1; 2] using analytical methods, heuristic methods, such as Ziegler-Nichols (Z-N) rule, frequency response methods, artificial intelligence such as fuzzy logic [3], and iterative learning approaches [4]. Evolutionary algorithms (EA), such as genetic algorithms (GA) [5] and particle swarm optimization (PSO) [6], used in intelligent control applications, have been also proposed as an efficient solution for tuning the PID parameters. The simplicity and speed convenience of evolutionary algorithms force the controller quickly seek out the optimal output value. In this paper, we study the use of an evolutionary algorithm, named Big Bang-Big Crunch (BB-BC) [7], to optimize PID controller gains. BB-BC optimization algorithm is used to minimize performance control measures, integral absolute error (IAE), integral time absolute error (ITAE), integral square error (ISE), and integral time square error (ITSE) while minimizing the system overshoot. The key idea of using BB-BC here can be explained as the transformation of a convergent solution to a chaotic state and then back to a single tentative solution point. BB-BC algorithm has been implemented in various engineering applications, especially where the computational time and convergence time are important factors [8]. Some representative optimization problems, where the efficiency of BB-BC has been demonstrated, are the following: optimal design of truss structures [9], Schwedler and ribbed domes [10], concrete retaining walls [11], fuzzy inverse controllers [12], and fuzzy PID controllers [13]. Moreover, BB-BC algorithm has been adopted in real-time applications where the optimization task is adaptive or must be solved in relatively small sampling intervals. Besides its low computational time and high global convergence speed, another advantage of BB-BC, especially important for auto-tuning processes, is that it does not need gradient information and therefore can operate to minimize naturally defined cost functions without complex mathematical operations. We evaluate the efficiency of BB-BC to tune the parameters of a PID controller used in a second-order heat, ventilation, and air conditioning (HVAC) system. In the HVAC system, the supply air pressure is regulated by the speed of a supply air fan. Increasing the fan speed will increase supply air pressure, and vice versa. The dynamics from the fan variable speed drive to the supply air pressure can be modeled as a second order plus dead time. This process is well established by [PERSON] and [PERSON] [14]. In real applications, however, where both fans and dampers exhibit non-linear properties for different working points, even a well-tuned PID controller may not be able to achieve a desired performance for all set points and process variations. Thus, we investigate how fast and accurate the BB-BC algorithm can tune the PID controller parameters in this HVAC system. To further reduce the optimization latency of the control system, the BB-BC algorithm along with the PID controller, are accelerated using FPGA technology. Up to now, embedded computers, built around programmable microcontrollers, were the dominant computing platform for implementing PID controllers in industrial environments. The last decades, the field programmable hardware technology, also known as field programmable gate arrays (FPGAs), has emerged as an alternative solution for controlling industrial applications.