Ship Three-Axis Turntable Control Based on Fuzzy Inference Variable Universe Huixuan Fu, Yuan Li, Zhongliang Zhang and Yuchao Wang 1 Introduction The three-axis turntable is used to simulate the navigation attitude. Three-axis including roll axis, pitching axis and bow thruster, are driven by three DC torque motor. Compared with the general flight test turntable, its running speed is relatively low, the rotation of each axis is smaller, the set frequency and amplitude is lower [1, 2], so the low-speed performance is the main performance index of ship turntable. With the improvement of turntable precision and low speed performance requirements, high accuracy turntable control [3, 4], improving the speed of rotary table control system performance is to become more important. At present, many domestic and foreign scholars have done a lot of research on the turntable performance problems, they generally considered the turntable performance is mainly affected by the friction torque of the driving motor, especially the turntable will crawl phenomenon at low speed, seriously affecting the low-speed performance of turntable [5]. In order to reduce the impact of friction, a traditional double-loop PID controller has designed [6]. However, during the operation of the turntable system, the frictional torque changes with external factors such as inertia, mechanical wear, lubrication and temperature. Due to the low speed friction torque and the complicated nonlinear factors of the turntable system, it is difﬁcult to solve this problem by traditional control methods based on precise mathematical model. The variable universe fuzzy control algorithm means that the universe of the fuzzy control system can be changed with the error, without changing the number of the control rules, to the universe of the allergic error [7]. The fuzzy logic controller based on variable universe fuzzy controller does not need too much universe expert knowledge, only need to know the general trend of the rule [8]. H. Fu Y. Li Z. Zhang Y. Wang (&) College of Automation, Harbin Engineering University, Nantong Street 145, Harbin, India e-mail: wangyuchao@hrbeu.edu.cn © Springer Nature Singapore Pte Ltd. 2018 Z. Deng (ed.), Proceedings of 2017 Chinese Intelligent Automation Conference, Lecture Notes in Electrical Engineering 458, https://doi.org/10.1007/978-981-10-6445-6_23 201 202 H. Fu et al. According to the characteristics of ship motion, a variable universe fuzzy controller for ship three-axis turntable has been designed. The simulation results showed that the method can improve the turntable performance and control accuracy. 2 Establishment of Turntable and Friction Model At low speeds, the most important effect on turntable performance is the friction disturbance torque. In order to facilitate the modeling and analysis of friction, a simpliﬁed stribeck friction model is used as follows [9]: 8 _ þ ½ðTm Tc Þ=e < Tm sgnðhÞ Tf ¼ ðTm Tc Þ=h_ s þ Kv h_ : Tc þ Kv h_ if if h_ \ h_ s h_ h_ s ð1Þ The linear transformation is as follows: 8 < ðTm Tc Þ=e f ¼ ðTm Tc Þ=h_ s þ Kv : Kv h_ if if h_ \ h_ s h_ h_ s ð2Þ Tf ¼ Tm þ f h_ ¼ Tm þ f x ð3Þ The friction model is substituted to get the direct torque motor model with friction disturbance, as shown in Fig. 1. The ﬁgure Ua shows the input DC voltage, Ia is the armature current, Ra is the armature resistance, La is the armature inductance, TL is the load torque, Tm is the maximum static friction torque, f is the linear friction coefﬁcient, J is the motor shaft inertia, h is the angle value, Tc is Coulomb friction torque, Te is the external force, h_ s is the speed, Kv is the viscosity constant. Fig. 1 Single axis turntable model with friction disturbance Tm f Ua 1 Las + Ra Ia KT TF TL Ke 1 ω (θ ) 1 Js S θ Ship Three-Axis Turntable Control Based on Fuzzy Inference … 203 3 Turntable Fuzzy Control Strategy for Variable Universe According to the characteristics and the feasibility of the ship motion, the variable universe fuzzy control based on fuzzy inference is used to design the control system of the turntable azimuth axis system. The system has two main controller module, one controller module determines the input and output of the universe extension factor, the other determines the control output, the input is both determines by the position error e of the turntable and the error rate ec [10]. Figure 2 is the principle block diagram of variable universe fuzzy control system. Three-axis turntable input variables in e universe for X1 = ½E; E, the universe of another input variable ec is X2 = ½EC; EC, the universe of output variable u is Y = ½U; U. The fuzzy division of Xi is A = f Aij g, the fuzzy division of Y is B = f Bj g, fuzzy control rules are as follows [11]: ð4Þ If e is A1j and ec is A2j then u is Bj The peak point of Aij is xij the peak point of Bj is yj the algorithm based on fuzzy control is essentially a piecewise interpolation function, and the interpolation function is Fðe; ecÞ, then the above rule can be transformed into the following formula: uðe; ecÞ ¼ Fðe; ecÞ , XY Aij ðxi Þyj ð5Þ The input and output universe changes expressed as follows: X1 ðxÞ ¼ ½aðxÞE; aðxÞE X2 ðxÞ ¼ ½bðxÞEc; bðxÞEc YðxÞ ¼ ½cðxÞU; cðxÞU ð6Þ In formula (6), X1 , X2 , Y are the initial universe, X1 ðxÞ, X2 ðxÞ, YðxÞ are the variable universe.aðxÞ, bðxÞ, cðxÞ respectively for the input variables e, ec, universe scaling factor, u is output variables. e ec de / dt ec e Fuzzy inference ( x) ( x) Fuzzy controller Tm (x) f Ua 1 La s Ra Ia KT _ 1 Js TL Ke Fig. 2 Functional block diagram of turntable FI-VUFC system TF () 1 S 204 H. Fu et al. The initial control rules Rð0Þ ¼ R, the initial ﬁeld X1 = ½E; E, X2 ¼ ½EC; EC, Y ¼ ½U; U, on the basis of the linear basis are fAi gð1 i pÞ , fBj gð1 j qÞ , fCij gð1 i p; 1 j qÞ , the peak value of E ¼ x11 \x12 \ \x1p ¼ E, EC ¼ x21 \x22 \ x2p = EC, U¼ y11 \y12 \ \ypq ¼ U, so that x1i ð0Þ ¼ x1i , x2j ð0Þ ¼ x2j ,yij ð0Þ ¼ yij , membership functions are deﬁned as Ai ðx1 ðkÞ; kÞ, Bj ðx2 ðkÞ; kÞ, the following steps are get the dual input single output controller: Step 1. Initialize Input x1 ð0Þ 2 X1 ; x2 ð0Þ 2 X2 to get the output: yð1Þ ¼ Fðx1 ð0Þ; x2 ð0ÞÞ ¼ p X q X Ai ðx1 ð0ÞÞBj ðx2 ð0ÞÞyij ð0Þ ð7Þ i¼1 j¼1 Step 2. The yð1Þ is applied to the controlled object to get the output of the system, and then feedback to the system and reference input, the controller input x1 ð1Þ; x2 ð1Þ x1i ð1Þ ¼ aðxð1ÞÞx1i ð0Þ ð8Þ x2j ð1Þ ¼ bðx1 ð1Þ; x2 ð1ÞÞx2j ð0Þ ð9Þ yij ð1Þ ¼ Fðx1i ð1Þ; x2j ð1ÞÞ ¼ p X q X As ðx1i ð1ÞÞBt ðx2j ð1ÞÞyst ð0Þ ð10Þ s¼1 t¼1 Step K. The yðkÞ is applied to the controlled object to get the output of the system, and then feedback to the system and reference input, the controller input x1 ðkÞ; x2 ðkÞ. Similarly: x1i ðkÞ ¼ aðx1 ðkÞÞx1i ð0Þ ð11Þ x2j ðkÞ ¼ bðx1 ðkÞ; x2 ðkÞÞx2j ð0Þ ð12Þ yij ðkÞ ¼ Fðx1i ðkÞ; x2j ðkÞÞ ¼ p X q X As ðx1i ðkÞÞBt ðx2j ðkÞÞyst ð0Þ ð13Þ s¼1 t¼1 From the above formula, the adaptive fuzzy control strategy of the double input and single output are: Ship Three-Axis Turntable Control Based on Fuzzy Inference … yðk þ 1Þ ¼ p X q X p X q X 205 Ai ðx1 ðkÞ=aðx1 ðkÞÞÞ s¼1 t¼1 i¼1 j¼1 As ðaðx1 ðkÞx1i ð0ÞÞ Bj ðx2 ðkÞ=bðx1 ðkÞ; x2 ðkÞÞÞ Bt ðbðx1 ðkÞ; x2 ðkÞÞx2j ð1Þyst ð0Þ ð14Þ when x1 ðkÞ ! 0; x2 ðkÞ ! 0, yðk þ 1Þ ! 0. 4 Scaling Factor Selection The core of variable universe is the selection of scaling factor. The size of the scaling factor determines the shape of the universe. It directly affects the performance of variable universe fuzzy control. According to the deﬁnition, scaling factor meet the following conditions [11]: (1) Scaling factor based on function model According to the deﬁnition and properties, the scaling factor is expressed as a function of the output variable. The commonly input and output scaling factor s are as follows [6]: aðxÞ ¼ s j xj ; s [ 0 aðxÞ ¼ 1 k expðkx2 Þ E s1 s2 j xj j yj cðx; yÞ ¼ ; 0\s1 ; s2 \1 E Ec ð15Þ The formula above is a practical mathematical model derived from the relationship between fuzzy rules and scaling factor, and it can be used as a general conclusion. Because of this, the ﬁxed function model is used to describe the uncertainty of the change of the scaling factor, which will cause a certain deviation. (2) Scaling factor based on fuzzy inference The scaling factor based on fuzzy inference is to adjust the flexibility factor by another fuzzy control. The input universe extension factor is only related to e ec, which is divided into fuzzy NB, NM, NS, ZO, PS, PM, PB. To input universe scaling factor aðxÞ, bðxÞ for B, M, S, Z, respectively, represent “universe to adjust”, “universe to small adjustment”, “on the ﬁeld to zero adjustment” are as follows. The new universe is ½E0 ; E0 , ½EC 0 ; EC 0 , ½U 0 ; U 0 , the fuzzy control of output control is divided into NB, NM, NS, ZO, PS, PM, PB. On the basis of this universe, the fuzzy rules of the output control quantity of the variable universe fuzzy controller are Table 1. 206 Table 1 Fuzzy rules of output control H. Fu et al. ec/e NB NM NS ZO PS PM PB NB NM NS ZO PS PM PB NB NB NM NM NS NS ZO NB NM NM NS NS ZO PS NM NM NS NS ZO PS PS NM NS NS ZO PS PS PM MS NS ZO PS PS PM PM NS ZO PS PS PM PM PB ZO PS PS PM PM PB PB 5 Simulation Analysis The parameter values of the azimuth axis of the turntable are respectively: La = 0.02, Ra = 12.1, KT = 4.11, Ke = 4.11 Considering the friction disturbance torque of the turntable, according to the friction model established in the second section, the empirical data Tm = 2 N m, Tc = 1.5 Nm, h_ s = 0.05, Kv = 0.4. The simulation curves of the turntable are as shown in Fig. 3. In Fig. 3, the blue curve is Stribeck nonlinear friction torque curve, and the red curve is a linear friction torque curve drawn by the piecewise function model. It can be seen from the curve that the linear curve is better than the real value of the friction torque model, and it can be used for simulation analysis. The rotation inertia of the azimuth axis of the turntable is J = 1. In order to compare the control effect of the variable universe fuzzy controller, a simulation model of PID control and a simulation model of fuzzy PID are established respectively. The results of the three controllers are compared under light load and load respectively. 2.1 Fig. 3 Friction disturbance moment of turntable Stribeck friction curve Friction torque (N.m) 2 Linear friction curve 1.9 1.8 1.7 1.6 1.5 0 0.05 0.1 0.15 Time (s) 0.2 0.25 0.3 Ship Three-Axis Turntable Control Based on Fuzzy Inference … 1.4 Fuzzy variable universe Fuzzy PID PID 1.2 Angular velocity (rad/s) Fig. 4 Control system step response in fractional load of three different control strategies 207 1 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) 1.4 Fuzzy variable universe Fuzzy PID PID 1.2 Angular velocity (rad/s) Fig. 5 Control system step response in heavy load of three different control strategies 1 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) The input is rðtÞ ¼ 1ðtÞ, under the interference of the linear friction torque shown in Fig. 3, the inertia J = 1, simulated under the condition of fractional load, the three control strategies angular velocity simulation results are shown in Fig. 4. Other conditions do not change, so that the moment of inertia J = 5, the simulation results of the simulation of their respective angular load, as follows. As can be seen form Figs. 4 and 5, in the low speed conditions, three kinds of control strategy performance is not the same, the conventional double loop PID algorithm has a long dynamic response process, the adjusting time is long and there are some static error, a greater overshoot under load. Fuzzy PID has a better dynamic performance, but there are some overshoot and the low speed performance is not so good. The low speed response curve of the fuzzy variable universe control algorithm is good, the response time is fast, the overshoot is small and the static precision is high. Compared with the previous three control strategies, the fuzzy control algorithm has better low-speed performance. From the different load conditions, the fuzzy variable universe control algorithm is better than the fuzzy PID control algorithm and PID algorithm. 208 H. Fu et al. 6 Conclusions This paper designed a variable universe fuzzy controller for ship three-axis turntable. According to the low speed characteristics of the marine turntable, the fuzzy control based on the fuzzy inference is used to realize the variable universe. Compared with the PID algorithm and fuzzy PID algorithm, the variable universe fuzzy control based on fuzzy reasoning has good low-speed and fastness, and the adaptability is also good when the load changes which veriﬁes the superiority of variable universe fuzzy control in low speed control for turntable. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No. 51409064, No. 51409062). References 1. Liu S, Zhang Y, Yu C et al (2012) Three-dimensional fuzzy control for ship electric propulsion turbine. 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