Key Engineering Materials Online: 2014-08-11 SSN: 1662-9795, Vol. 621, 357-364 doi:10.4028/www.scientific.net/kem.621.357 2014 rans ech Publications, Switzerland Oil emerature Control System PD Controller Algorithm Analysis Research on Sliding Gear Reducer Yongmei Wang 1,a, Xigui Wang 2,3,b 1 Deartment of Motorcar Engineering, Heilongjiang nstitute of echnology, Harbin 150036, China 2 Mechatronics school, Harbin nstitute of echnology, Harbin 150001, China 3 703 Research of nstitute, Harbin 150078, China a wyr20091207@126.com, b wymwxg2004@126.com Keywords: Lubricating oil, PD controller, emerature, Analysis, Research Abstract. With the develoment of comuter technology, communication technology, electronic technology and automatic control technology, comuter control technology widesread alication, has been widely used in iron and steel, etroleum, chemical, electric ower, building materials, machinery manufacturing, automotive, textile, transortation and other industries. Controlled by comuter, we can realize the control of high reliability, rocess visualization, remote monitoring, data storage and rocessing. he simulation of PD control algorithm, and focuses on the study and analysis of the digital PD control algorithm, the marine gear lube oil temerature control system model, the three arameters of digital PD: roortional coefficient, integral constant, differential constant on the control system erformance was also analyzed. ntroduction With the develoment of comuter technology, communication technology, electronic technology and automatic control technology, comuter control technology widesread alication, has been widely used in iron and steel, etroleum, chemical, electric ower, building materials, machinery manufacturing, automotive, textile, transortation and other industries. Controlled by comuter, we can realize the control of high reliability, rocess visualization, remote monitoring, data storage and rocessing. his aer will combine the shi control system for seed reducer lubrication system oil amount of functional requirements, carry out research and Analysis on the theory of digital PD control algorithm. Device for lubricating system oil PD control algorithm for shi gear reducer PD control is the control algorithm, the deviation ratio of differential, integral outut of a, PD control can achieve very satisfactory control erformance in many industrial objects. Digital PD control is roduced with the develoment of the comuter, is based on the simulation of PD control of the traditional, and joined the comuter control technology evolved. Simulation of PD aeared earlier, it is carried on the PD oeration outut by using the simulation of discrete element. he basic mathematical exression analog PD controller for the [1] [2]: 1 de( t) u( t) K (1 e( t) dt D ) (1) dt ye in ut ()- he outut of the PD controller; et ()- he PD controller's inut (difference set and feedback); K - Proortional coefficient PD controller; - he integral time constant PD controller (min); - Differential time constant PD controller (min); D All rights reserved. No art of contents of this aer may be reroduced or transmitted in any form or by any means without the written ermission of rans ech Publications, www.tt.net. (D: 130.203.136.75, Pennsylvania State University, University Park, USA-06/03/16,07:52:44)
358 Manufacturing Automation echnology and System On the Eq. 1 is the Lalace transform, the transfer function can be obtained for analog PD controller: Us ( ) 1 D( s) K (1 Ds) E() s s So K K, KD K D Us () K D() s K KDs E() s s, the transfer function of analog PD controller, can be written as: ye in K - ntegral coefficient PD controller; KD - he differential coefficient of PD controller; Analog PD controller block diagram as shown in Fig. 1. (2) (3) K + R(s) E(s) K U(s) controlled Y(s) 被控对象 s object - + KDs Fig. 1 Analog PD controller block diagram Digital and traditional PD control simulation of PD control of different oints in the comuter or microrocessor relaces analog chi PD oeration function, only need to rogram the PD algorithm through software, using the comuter or microrocessor, can realize PD control oeration outut, and enhance the flexibility of PD control algorithm to a great extent. Due to the digital signals that the comuter can only deal with discrete, and the controlled object feedback signal is generally the analog signal is similar to the current, voltage. herefore, must the analog signal into digital signal rocessing comuter can receive the signal discretization, namely, the rocess of discretization is divided into three stes: samling, quantization, coding. On the other hand, the comuter can only outut discrete digital signals, and control signals can be received by the general object into analog signals, therefore, must be discrete signal change of the outut of a comuter into a continuous analog signal, the rocess is divided into two stes of decoding and maintain. Signal switching structure of comuter control system as shown in Fig. 2. Samling Quantification Code Comuter Decoding Kee Controlled object Fig. 2 Signal switching structure diagram of comuter control system Samling the continuous signals into discrete signal a oint in time, the exression of discrete signal samling the outut to:
Key Engineering Materials Vol. 621 359 f ( t) f ( t) ( t k ) 1 k0 ye in f() t - he inut signal is samled; ( t k )- Unit imulse function (when t k, ( t k ) 1); Schematic diagram is as shown in Fig. 3 discretization rocess. (4) Analog signal Discrete signal Fig. 3 he sketch ma of samling rocess Quantification is based on the range of the inut signal and the A/D chi number, digital content on the size of the discrete signal. he minimum value can be calculated by the following formula to quantify: u q umin 2 1 (5) max n ye in umax u min - he maximum value of the inut signal; - he minimum value of the inut signal; n - he conversion of A/D number; nteger signal quantization are q, therefore to quantify the rocess will generate a random q q quantization error, quantization error of range e. By Eq. 5 can be seen, the inut signal 2 2 range is smaller, the greater the number of bits of A/D conversion, quantization error roduced smaller, quantitative results more close to the actual value. Coding is the signal to digital values of the binary coded decimal number, would be equivalent to the binary code, for comuter rocessing. n actual control system, analog samling, quantization, coding signal by comuter or digital chi hardware. But the signal samling time oint, namely the signal in what time samling, through software rogramming. he samling time can be eriodic, can also be non-eriodic. n general, for the sake of convenience, we usually use eriodically samled. Periodic samling intervals called samling eriod, samling eriod selection, not too big, not too small. On the one hand, samling eriod selection must conform to the undistorted signal conditions, the exressions are: s 2max hat is max ye in s - he samling frequency ( Hz ); - he samling eriod ( s ); - he highest frequency of the signal ( Hz ); max n the ractical engineering system, normally s 10 max, that is On the other 5max hand, the samling eriod if too small, before and after the two samled signal changes very little, but will cause the comutation burden for comuter hardware. (6)
360 Manufacturing Automation echnology and System n order to use comuter software for PD oerations, must be discretized on signal. Make t k, k 0,1,2, deviation, integral, differential can be searated into the following exressions. e( t) e( k ) (7) e( t) dt e( m) k m0 de( t) e( k ) e[( k 1) ] dt he Eq. 7, 8, 9 into Eq. 1-1, available digital PD control algorithm for: (8) (9) [ ( ) ( 1)] ( ) { ( ) k D e k e k u k K e k e( m) } m0 (10) Eq. 10 as the location algorithm of digital PD, the exression can be seen, the outut of the controller uk ( ) is not only relevant and current bias, and is related to all deviations e( m),(0 m k 1) in front, need to save the comutation of large amount of data, occuy more memory. n addition the outut uk ( ) corresonds the osition of the actuator, once the comuter failure, the outut of a high mutation uk ( ), the actuator osition roduces large mutations, may cause serious accidents in roduction. Since the algorithm defects in the above two asects, their alication in ractical engineering is relatively small. Aiming at the digital osition PD algorithm, it uts forward the imrovement methods, resulting in a digital PD incremental algorithm. According to equation (10) outut can draw time controller, given as follows: 1 [ ( 1) ( 2)] ( 1) { ( 1) k D e k e k u k K e k e( m) } m0 (11) According to equation (10), (11) can be drawn, incremental control outut u( k ), given as follows: u( k) u( k) u( k 1) D 2D D KP[(1 ) e( k) (1 ) e( k 1) e( k 2)] (12) he digital PD algorithm, the PD controller at any moment, only outut value u( k ). f the actuator is integral element, such as a motor, it can directly outut to the object; if the actuator without integral element, can be outut to the controlled object by formula u( k) u( k 1) u( k ). PD incremental algorithm has the following advantages of [3] [4]: (1) the comuter failure, the outut is 0, executive agencies do not move, the object osition remains unchanged. (2) the outut is only related to the last two values, the calculation is relatively simle. Effects of PD arameters on the erformance of the control system he rincile and algorithm of PD control is introduced, it can be seen from the PD control, the outut is only associated with the following arameters: roortional coefficient( K ), integral time constant ( ), differential time constant ( D ), samling eriod ( ), deviation ( ek ( )), effect of P
Key Engineering Materials Vol. 621 361 samling eriod on the system has been a qualitative analysis on the section, the deviation is a dynamic value, reflects the difference between the inut and outut. his section will be combined with the shi gear lube oil temerature control system model of PD gear, three arameters that influence the erformance of the control system are analyzed. Marine gear oil temerature control system is a comlex system. he temerature control system has a very rominent characteristic: the system is lag relatively large, this brings a challenge to the system debugging. he temerature control system in general by the controller, solid state relay, heater and temerature sensor, temerature control system structure diagram as shown in Fig. 4. Controller Solid state relay Heater Medium Outut temerature emerature transmitter Fig. 4 emerature control system structure diagram By the structure block diagram of control system can transfer function structure diagram for the system, as shown in Fig. 5. Rs () Ds () G h (s) Gs () Cs () H() s Fig. 5 he transfer function of the system structure diagram Ds () as the transfer function of the controller, the secific exression deends on the tye of s 1 e control. Gh () s is the transfer function of the zero order holders. Gs () as the s temerature of the transfer function of the controlled object, the general exression for [5] [6]: s Ke Gs () ( 1s 1)( 2s 1) (13) n the formula (13), 1, 2 reflect the temerature system inertia size, inertia is greater, the greater the value. he delay characteristics of reflect the temerature system. For convenience s e of the analysis, ake Gs (). Hs () is the feedback channel transfer function, ( s1)(0.5s1) ake Hs. () is the samling eriod, ake 1s. he transfer function of the structure as shown in Fig. 6 temerature control system is simlified. Rs () Ds () 1 e s s s e ( s1)(0.5s1) Cs () Fig. 6 Simlification of the system transfer function Fig. 6 shows, the ulse transfer function of the system of generalized object:
362 Manufacturing Automation echnology and System s s 1 e e G0 ( z) GhG( z) z[ * ] s ( s 1)( s 0.5) 1.814( z 0.103) z( z 0.368)( z 0.606) he closed-loo transfer function: D( z) G ( z) 1 ( ) ( ) 0 () z D z G 0 z he outut of the system: D( z) G ( z) C z z R z R z 1 D( z) G ( z) 0 ( ) ( ) ( ) ( ) System inut unit ste, hat is r( t) 1( t ), So Rz () 0 z. z 1 (14) (15) (16) he digital PD controller with roortional control he controller transfer function is: D() s K P, hat is D() z K P, When K P = 0.1, 0.2, 0.3, unit order system ste resonse curve, as shown in Fig. 7. Fig. 7 When the roortional control, the system ste resonse curve As seen from Fig. 7, when the roortion coefficient increases, the resonse seed of the system seed, steady error is reduced, and the overshoot of the system increases, the number of oscillations increases, system to achieve stable rocess variable length of time; while increasing the scale coefficient, the steady-state error is smaller, but the system always has static difference. herefore, in ractical control systems, can be aroriate to increase the roortion of the size factor, to imrove the resonse seed of the system, reduce steady-state error; but the ratio cannot be too large, otherwise it will cause the system to oscillate or unstable. Digital PD controller uses a roortional integral control 1 he controller transfer function is: D( s) K( P 1 ) s, hat is, When 1 z D( z) KP(1 ), z1 are resectively 0, 10, 20, unit order system ste resonse curve, as shown in Fig. 8.
Key Engineering Materials Vol. 621 363 Fig. 8 When the roortional integral control, the system ste resonse curve As you can see in Fig. 8, based on ure roortional control, increase the integral, the steady-state error of the system is greatly reduced, almost 0 times, the overshoot and oscillation increased, system achieve steady increase in transition time. Reduce the integral constant, integral effect becomes strong, overshoot, oscillation frequency of the system and the transition time increased, the steady-state error is smaller. herefore, in actual control system, through the roortion integral, allowing the system to achieve zero steady-state error. n addition, the integral coefficient cannot be too small, otherwise it will cause system oscillation and divergence. Digital PD controller with a roortional integral differential control he controller transfer function is: 1 D( s) K( P 1 D s), hat is, s 1 z z1 D( z) KP(1 D ), z 1 z When K P 0.25, 10, D are resectively 0, 0.05, 0.35, unit order system ste resonse curve, as shown in Fig. 9. Fig. 9 When the roortional integral differential control, the system ste resonse curve As you can see in Fig. 9, based on the roortional, integral, joined the differential element, system has fast resonse seed, overshoot is decreased, but not obviously, this may and differential constant selection is not suitable for. he general theory is that, select the aroriate differential constant, dynamic erformance, the system can imrove the effective Jian Xiaochao, accelerate the resonse seed, the transition time decreases system. Differential constant is too small, not to the differential redictive role. Differential constant too large, it will cause the system to divergence.
364 Manufacturing Automation echnology and System Conclusion he simulation of PD control algorithm, and focuses on the study and analysis of the digital PD control algorithm, the marine gear lube oil temerature control system model, the three arameters of digital PD: roortional coefficient, integral constant, differential constant on the control system erformance was also analyzed. References [1] Z. Zheng, G.Q. Lu and H.D. Du: System modern measurement and laboratory management control rocess of crude oil dynamic measurement, Vol. 12 (2004) No.6,. 12-15. [2] D.W. John and W. Pedro: Flow Measurement and nstrumentation. Vol. 8 (2000) No.5,. 24-26. [3].. Yeh: Proceedings of the ASME Heat ransfer/fluids Engineering Summer Conference, Vol. 1 (2004) No.6,. 524-533. [4] F.B. Robert: nstitute of Physical Publishing, Vol. 12 (2003) No.3,. 58-62. [5] J. Chen: Precision manufacturing and automation, Vol. 9 (2004) No.4,. 79-83. [6] F. Li: Alication rosect of embedded PLC in the automation of Chinese wealth of science and technology, Vol. 5 (2011) No.14,. 37-39.
Manufacturing Automation echnology and System 10.4028/www.scientific.net/KEM.621 Oil emerature Control System PD Controller Algorithm Analysis Research on Sliding Gear Reducer 10.4028/www.scientific.net/KEM.621.357