·88· 智能系统学报 第6卷 x=M(0)0+V(0,0)+G(0). The more complete dynamic model becomes: Where M is a 3 x3 mass matrix,V is a 3 x 1 vector for r=M(0)0+V0,0)+G(0)+F(0,0). Corilois/Centrifugal forces and G is a 3 x1 gravity vec- 4)Modeling of encoders. tor.The equations for the mass matrix and vectors are Encoders are normally attached to the joints to re- listed below. cord their motions (i.e.how many degrees the joint rm(1,1) 0 m(1,3)1 has rotated).However,they are limited by their reso- M(0)= 0m(2,2)m(2,3) lutions to interpret the motion of joints.As the encoder m(3,1)m(3,2)m(3,3) output is discrete,there will be errors caused by reso- Wher lution limitation.In the presented study,quantiser m(1,1）-250+25m（1+10cos64）+ blocks using Simulink are incorporated to simulate the discrete nature and errors resulting from the limited 625m3cos203, resolutions of encoders. m1,3》=m(3,1)=ia,(5m+10%,+ Assuming all the position encoders consisting of the 2 4 and 3(luff and slew)joints have 4 096 bits 50m3c0s03), per revolution,the long travel encoder is directly cou- m(2,2)=625m3, pled to a non-drive bogie wheel axel with a wheel circ- m(2,3)=m(3,2)=-25m3sin03cos02, umference about 2 m.Thus,the resolution is 360 (de- m(3,3)=m1+m2+m3, grees)/4096=0.087 89 degrees,which is equivalent r(1,1)7 to 0.001 533 4 radians.The quantization intervals for V(0,0)= (2,1) the three encoders are therefore set at 0.001 533 4 for LV(3,1) the presented study. Where, 5)Modeling of disturbances. V(1,1)=-25m30203sin03(1+5cos03）, In order to model more realistically,a vector with V(2,1)=125m35sin03(1+5cos03), a random disturbance force/torque was applied at all V(3,1）=-2.5m25cos02-5m3cos02- three joints,Ta,which have the random values be- 25m305co802cos03+50m30203sin028in03- tween 100 and -100(kg for prismatic joint and kg-m 25m33c0802c0s03, for revolute joints)with a mean value of zero while act- 0 ing to disturb the system is introduced into the control G(0)= 25magcos 03 system.This external noise is introduced to partially 0 cover the combined influences of modelling inaccura- 3)Modeling of friction forces. cies caused by factors such as simplifying the dynam- The dynamic equations derived above do not cover ics,un-modelled bucket wheels,and scooped materi- all the forces acting on the BWR,including friction.In als in the bucket wheels. order to create a simulation environment that can reflect the imperfect knowledge of the system,it is important 2 Fuzzy logic to model friction forces such as disturbances and errors It is always difficult for an expert to represent the coming from encoders as the parts of the system that required knowledge to solve an engineering problem u- are unknown to the controller.There are two friction sing vague and ambiguous computer terms until certain forces to be modelled,viscous friction and Coulomb artificial techniques such as fuzzy logic are available. friction.Nevertheless,in this study,a vector of fric- From an engineer's perspective,using engineering tion coefficients for three joints is set as the gain, common sense in vague and ambiguous terms to solve [0.05,0.05,0.05]which is multiplied by the joint engineering problems is intuitive and even preferred in velocities to generate friction forces similar to viscous many cases.For example,to prevent a motor from run- friction forces.These gains can later be changed for ning too hot,it is much easier to describe the control more accurate results or even replaced by the combina- actions required in vague and ambiguous terms,such tion of Coulomb and viscous friction forces. as"if the motor is overheating,you must slow it down