【正文】
nditioning systems (HVAC systems) are typical nonlinear timevariable multivariate systems with disturbances and uncertainties. A new fuzzy control strategy based on the PID parameters tuning to control HVAC systems is proposed in this paper. It takes full advantage of mature technologies of PID controller to improve the design of fuzzy controller. The mathematical analytical expression of parameters between fuzzy controllers and gains coefficients of PID controllers is got based on the structure analysis of fuzzy controllers. and the fuzzy controller is designed through gains tuning of PID controller based the analytical relations. Then this fuzzy controller was applied into temperature control in HVAC systems. The simulation test results showed it is effective and pared with the conventional PID control, the proposed fuzzy control algorithm has less overshoot, shorter setting time and better robustness etc.Index Terms Fuzzy control, Structure analysis, Robustness, HVAC systemsI. INTRODUCTIONModern process control problems in the process industries are dominated by nonlinear timevarying behavior, disturbances and uncertainties[1]. However more than 90% plants are controlled by the wellestablished PID controllers in industrial automation and process until today[2]. Morover, conventional PID controllers have gone through a technological evolution because many sophisticated algorithms have been used to improve its work under difficult conditions. Especially fuzzy logic inferences and neuron network based on selftuning schemes of PID controllers have also been proposed to enhance the control performance. Qiang Bi et al gave an advanced autotuning PID controller then applied it into HVAC systems successfully[3]. Hanxiong Li proposed an improved robust fuzzyPID controller with optimal fuzzy reasoning [4]. But they can not change the linear essence of PID controllers.Fuzzy logic control technique basedon the concept of the fuzzy algorithm by Zadeh in 1973 has been successfully applied in many engineering areas since the pioneer work of Mamdani in 1974[5, 6]. Fuzzy controllers possess advantages of strong robustness, better global control effects etc and no need mathematical model. But fuzzy controller design is still more a matter of art than technology and can not play the main role in industrial processes.In order to absorb the advantages of existing two bination of fuzzy and PID controllers, a novel idea to design PID controllerbased fuzzy controller is attempted to be proposed in this paper. At first we get the mathematical relation of parameters of fuzzy controller and linear gains of PID controllers based on the structure analysis of fuzzy controller. And then the simulation results show the effective performance of this fuzzy controller and experiment tests results indict that the proposed fuzzy control approach is effective for the temperature control of air handling unit in HVAC systems.II. DESIGN OF FUZZY CONTROLLER OF BASED ON PID PARAMETERSIt is assumed that the process under control can be modeled as the following first order plus dead time (FOPDT) dynamics in figure 1:It is easy to design the PID controller for it, so that the gain coefficients can be achieved respectively. P I D Kp ,Ki ,Kd design of nominal fuzzy controller In order to design the PID parameters basedon fuzzy controller, at first the simplest structure of twoinput single output nominal fuzzy controller is given. At any given time instance n with a sampling time Ts, the two input variables of fuzzy controller, error state variable and error change are defined as e(n)=y(n)r(n) and △e(n)=△e(n)△e(n1). And its output variable u(n) is the control signal of process.Generally the membership functions of two input Variables e,△e used triangular shapes and the membership functions of output variables u used singleton fuzzy sets. The membership functions of input variables e,△e are defined in figure 2. The fuzzy inference rulebases in nominal controller use the following four rules: Design of normalized factorsThe fuzzy controller in figure 3 is used to control the above FOPDT process. The nominal fuzzy controller is used in each fuzzy controller. But the input variables of fuzzy controller e(n),△e(n ) are normalized by the normalized Gei and G△ei before fuzzification,while i=1,2. The output variables of fuzzy controller u(n),△u(n) arenormalized by the normalized factors Gu and G△u after defuzzification. That is, e* △ Gei △e(n),△e* △ G△ei △△e(n),u(n) △ Gu △u*,△u(n) △ G△u △△u * (2) where i =1,2 and e, △e, u *,△u *△ [1,1].The membership functions of both input variables e*,△e*and output variables u *,△u * are each defined the same as before. Both of two fuzzy inference rulebases use the nominal fuzzy rules. In fuzzy controller 2, the output variable u * is instead of △u * in fuzzy rules. In fuzzy inference logic algorithms, if AND operation uses “product”, OR operation uses “max”, IMPLICATION operation use “min”. The defuzzification uses centre of gravity method. When arbitrary input variables e(n),△e(n) act on the fuzzy control system,passing through normalizing, fuzzification, fuzzy reasoning and defuzzification, the outputs of fuzzy controllers are as follows:In order to simplify calculation, we chooseThen the whole output of fuzzy controller isIn order to correspond towards conventional PID controllers, we chooseThen the fuzzy controller can be transformed intoIt is a PID controller in style, but it is a fuzzy control at a certain sampling time in nature. Then we can take good use of these equations to design the fuzzy controller on base of parameters tuning of PID controllers. First of all, since the gains tuning of PID controller service for fuzzy controller, we regard the error normalized factor Ge as a free variable for a while, and (7) can be changed into following equal styles: Tuning of normalized factorsIn fact, the prominent cha