Fuzzy Adaptive PID Controller Design

TELKOMNIKA ISSN: 1693-6930  Mathematical Modeling and Fuzzy Adaptive PID Control of Erection … Feng Jiangtao 257

3. Fuzzy Adaptive PID Controller Design

We adopt fuzzy adaptive PID control method in erection process to enhance control performance. PID control is connected with fuzzy control and then the parameters of PID control method can change based on circumstance [13]. Fuzzy adaptive PID control method can make full use of operators’ successful nonlinear experience and excellent effect of PID control. It can improve precision and achieve better effect compared with PID control and fuzzy control. The differential equation of PID control is as follows [14].     P I T TD u kT K e kT e kT e kT T T T      11 Where k is sampling number. T is sampling period. ukT is output signal. K P is propotional coefficient. T I is integral time constant. T D is differential time constant. The structure of fuzzy adaptive PID controller is shown in Figure 3. Fuzzy logic controller is used to change the parameters of PID controller. Its input variables are error et and error change rate ct and output variables are △ K P , △ K I , △ K D , which are respectively added to initial values K P0 , K I0 and K D0 . Figure 3. The Structure of Fuzzy Adaptive PID Controller Figure 4. Membership Function Cure of Input All of the variables are implied as linguistic values and defined with seven linguistic values which are: NB-negative big, NM-negative medium, NS-negative small, ZO-zero, PS- positive small, PM-positive medium, PB-positive big [15]. The domain of error et is [-x e , x e ] and the domain of error change rate ct is [-x c , x c ]. The domain of fuzzy subset is {-6, -5, -4, -3, -2, - 1, 0, 1, 2, 3, 4, 5, 6}. Triangular shape function is chosen as input membership function which is shown in Figure 4 [16]. The relationships between et, ct and K P , K I , K D are summarized through much operating experience [17]. 1. When et is relatively large, K P should be adopted relatively large value to speed up the system response and reduce time constant with damping coefficient. K D should be adopted Electro-hydraulic proportional valve Fuzzy Inference Module P K  I K  D K    F uz zy PID controller de dt D efuz zi fi ca tion Fuzzy rules P P P I I I D D D K K K K K K K K K       ec K e K P G I G D G Sensor Hydraulic cylinder E EC ect et et ut ct ZO PS PM PB 1.0 NS NM NB 2 4 6 -2 -4 -6 et  ISSN: 1693-6930 TELKOMNIKA Vol. 15, No. 1, March 2017 : 254 – 263 258 relatively small value to avoid out of range control at the beginning. To avoid large overshoot, remove the integral action. 2. When et is medium, K P should be adopted relatively small value to minimize response overshoot. The value of K D is important and should be adopted medium value. The value of K I should be appropriately increased. 3. When et is relatively small, K P and K I should be adopted relatively large value to have good steady state and avoid oscillation at equilibrium point. The value of K D should be appropriate. Based on the above relationships and the impact of ct, fuzzy control rules are obtained in Table 1 through theoretical analysis. Table 1. Fuzzy Control Rules △K P △K I △K D e NB NM NS ZO PS PM PB c NB PBNBNS PBNBPS PMNMPB PMNMPB PSNSPB ZOZOPM ZOZONS NM PBNBNS PBNBPS PMNMPB PSNSPM PSNSPM ZOZOPS NSZOZO NS PMNBZO PMNMPS PMNSPM PSNSPM ZOZOPS NSPSPS NSPSZO ZO PMNMZO PMNMPS PSNSPS ZOZOPS NSPSPS NMPMPS NMPMZO PS PSNMZO PSNSZO ZOZOZO NSPSZO NSPSZO NMPMZO NMPBZO PM PSZONB ZOZOPS NSPSNS NMPSNS NMPMNS NMPBNS NBPBNB PB ZOZONB ZOZONM NMPSNM NMPMNM NMPMNS NBPBNS NBPBNB Take the first rule as an example, the above rule can be interpreted as “if e is NB and c is NB, then △ K P △ K I △ K D are PBNBNS ”. Mamdani algorithm is introduced as fuzzy implication relation [18]. , , = min , R a u A U a u A a U u A a U u     12 Triangular shape function is chosen as output membership function which is shown in Figure 5 [19]. Figure 5. Membership Function Cure of Output Centroid is chosen as defuzzification method [20], which calculates the area center of the fuzzy set membership function curve surrounded by the horizontal coordinate. The horizontal coordinate value of the center is chosen as the representative value of the fuzzy set. The membership function of F set is Au on the domain U and the horizontal coordinate u corresponding to the area center is calculated by the following formula [21]. U U A u udu u A u du    13 ZO PS PM PB 1.0 NS NM NB 2 4 6 -2 -4 -6 △ K P TELKOMNIKA ISSN: 1693-6930  Mathematical Modeling and Fuzzy Adaptive PID Control of Erection … Feng Jiangtao 259 4. Simulation and Results 4.1. Modeling Erection Mechanism in Simulink