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TECHNICAL FIELD 
     This invention relates to an electronic traction control system for an articulated work machine and, more specifically, to an electronic control system which brakes each wheel independently and at least partially bases the brake control on the rate of articulation of the work machine. 
     BACKGROUND 
     Work machines used at construction sites and other off-road locations are often four wheel drive articulated machines. An articulated machine includes front and rear frames hinged together by an articulation joint for relative pivotal movement. When one of the frames is moved relative to the other, the machine turns. The articulation joint also moves back and forth in a known manner perpendicular to a centerline of the machine as the machine articulates, imparting an additional component of motion to the machine&#39;s turning dynamics. 
     Sometimes such work machines experience a loss of traction, often due to poor underfoot conditions or a change in the weight distribution of the machine. Traction loss events may also occur when one wheel of the machine spins at a very different speed than the other wheels, because that wheel is stuck in one position (therefore not spinning) or is spinning uncontrollably because the tread of the wheel cannot grip the ground. This slipping and subsequent loss of traction is undesirable in that the machine works less efficiently when slipping, and the ground surface under the machine can become rutted and damaged. The tire or wheel of the machine can also suffer physical damage or thermal wear if the wheel slips or skids. 
     Various mechanical traction solutions have been developed and placed in commercial use. For example, one method to prevent front or rear wheel slip involves locking the differential on the slipping axle. However, since the differential operation is then restrained and not controlled responsive to some sensed factor, the wheels are held to the same speed and articulation may be adversely effected. Some difference in left/right wheel speed is needed for the front and rear frames to articulate in an optimal manner to turn the machine. 
     Articulated work machines are often provided with a separately actuable brake for each wheel. These brakes can be actuated manually or automatically as needed to bring a free-spinning wheel under control, much as the automobile driver taps the brake pedal to restore traction, albeit with much more precise control. 
     An automatic traction control system used to actuate brakes individually is disclosed in U.S. Pat. No. 5,535,124, issued Jul. 9, 1996 to Javad Hosseini et al. (hereafter referenced as &#39;124). The traction control system of &#39;124 detects the difference in rotational velocity between the two wheels of the front or rear frame, detects the articulation angle of the machine (an articulation angle of zero means that the machine is not being turned), and then responsively produces a braking control signal to slow the faster rotating wheel. The &#39;124 braking control signal takes into account the fact that one of the wheels may need to rotate more quickly if it is the outer wheel and weights the braking control signal accordingly. 
     The &#39;124 traction control system, however, calculates the braking control signal using a desired speed ratio between each set of inner and outer wheels. The ratio can falsely indicate that the wheels are not slipping when there actually is a loss of traction. Missed traction events often occur if, for example, both inner and outer wheels are slipping slightly, or only the inner wheel is slipping, since the controller only checks to see if the ratio of the faster wheel speed to the slower wheel speed is greater than expected, thus ignoring the absolute wheel speeds. Also, the &#39;124 system does not take into account the effect of the back-and-forth, or lateral, movement of the articulation joint during articulation. The portion of the wheel speed attributed to the articulation rate and the lateral movement of the articulation joint is not insignificant and can mask small losses of traction, leading the &#39;124 traction control system to miss the wheel slipping events. Finally, the &#39;124 system does not consider the effect of the load carried by the machine and how that load causes one or more wheels of the machine to be slightly more or less likely to slip. 
     The present invention is directed to overcoming one or more of the problems as set forth above. 
     SUMMARY OF THE INVENTION 
     In a preferred embodiment of the present invention, an electronic traction control system for a work machine is disclosed. The work machine has a front frame, a rear frame, and an articulation joint connecting the front and rear frames. The system includes an articulation sensor, at least two wheels, a brake associated with the work machine, and an electronic control module. The articulation sensor is adapted to provide an articulation angle signal. Each wheel is adapted to provide a wheel speed signal. The electronic control module is adapted to receive the articulation angle and wheel speed signals; calculate an articulation rate responsive to the articulation angle signal; determine a desired wheel speed having at least one of: an articulation-caused linear velocity component calculated responsive to the articulation rate, articulation angle, and wheel speed signals, and a transient articulation-caused velocity component calculated responsive to the articulation rate, articulation angle, and wheel speed signals; and responsively produce a brake signal to control the brake. 
     In a preferred embodiment of the present invention, an electronic traction control system for a work machine is disclosed. The work machine has front and rear frames connected by an articulation joint for relative pivotal movement. Each frame has at least one driven wheel. The electronic traction control system includes an articulation sensor associated with the articulation joint and adapted to produce an articulation angle signal, a wheel speed sensor associated with each wheel and adapted to produce a wheel speed signal, and an electronic control module. The electronic control module is adapted to receive the articulation angle signal and the wheel speed signals, determine a measured wheel velocity value responsive to each wheel speed signal, determine an articulation rate value responsive to the articulation angle signal, calculate an articulation-caused linear velocity value for each wheel responsive to the articulation angle, articulation rate, and wheel speed signals and a transient articulation-caused velocity value for each wheel responsive to the articulation angle, articulation rate, and wheel speed signals, calculate a desired wheel velocity value for each wheel responsive to the articulation-caused linear velocity value and the transient articulation-caused velocity value, calculate an error value responsive to the measured wheel velocity value and the desired wheel velocity value, and produce a brake signal for each wheel responsive to the error value. The electronic control system also includes a brake associated with each wheel, adapted to receive the brake signal and actuate responsively thereto. 
     In a preferred embodiment of the present invention, a method of controlling wheel slip of an articulated work machine is disclosed. The method includes the steps of: comparing the relative positioning of a front frame and a rear frame of the work machine and responsively producing an articulation angle signal; sensing a speed of at least one wheel associated with at least one of the front and rear frames and responsively producing a wheel speed signal; receiving the articulation angle signal and each wheel speed signal; producing a wheel speed value responsive to each wheel speed signal; and determining a rate of change of the articulation angle signal and responsively producing an articulation rate value. The method also includes: producing an articulation-caused linear velocity value responsive to the articulation angle signal, the articulation rate value, and each wheel speed signal; producing a transient articulation-caused velocity value responsive to the articulation angle signal, the articulation rate value, and each wheel speed signal; and producing a desired wheel speed value based on the articulation-caused linear and transient articulation-caused velocity values. Additionally, the method includes: comparing the wheel speed value to the desired wheel speed value; producing a brake signal responsive to the difference between the actual wheel speed value and the desired wheel speed value; and controlling a brake associated with each wheel responsive to the brake signal. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a work machine including an electronic traction control system of an embodiment of the present invention; 
     FIG. 2 is a top-level flowchart of one embodiment of an electronic traction control system-of an embodiment of the present invention; 
     FIG. 3 is a second level flowchart of an embodiment of the present invention; 
     FIG. 4 is a third level flowchart of an embodiment of the present invention; 
     FIG. 5 is a block diagram of the work machine illustrating certain machine nomenclature and characteristics; 
     FIG. 6 is a third level flowchart of an embodiment of the present invention; 
     FIG. 7 is a third level flowchart of an embodiment of the present invention; and 
     FIG. 8 is a second level flowchart of an embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION 
     Referring first to FIG. 1, an electronic traction control system  100  embodying certain principles of the present invention is illustrated. Shown is a partial schematic representation of a work machine having an articulated chassis made up of a front frame  1168  and a rear frame  1170  interconnected by an articulation joint  1116  having a vertical axis about which the work machine is steered by a power steering arrangement. Wheels  102 , 104 , 106 , 108  are driven through differentials  110 , 112  of the drive axles  114 , 116  and hydraulically applied and spring released service brakes  118 , 120 , 122 , 124  are operatively associated with the wheels  102 , 104 , 106 , 108 , respectively, to control their rotation. 
     A pair of electrically controlled proportional service valves  126 , 128  are connected in fluid delivery relation to the service brakes  118 , 120 , respectively, by fluid conduits  130 , 132  and a pair of electrically controlled proportional service valves  134 , 136  are connected in pressure fluid delivery relation to the service brakes  122 , 124  by fluid conduits  138 , 140 . The service valves  126 , 128 , 134 , 136  have control elements  142 , 144 , 146 , 148 , respectively, having fluid delivery and closed positions of adjustment. Pressure fluid delivery to the service valves  126 , 128  is by way of an electrically controlled proportional safety valve  150  and a fluid service conduit  152  having branches connected in parallel to the service valves  126 , 128 . In a similar manner an electrically controlled proportional safety valve  154  is connected by a fluid service conduit  156  to the service valves  134 , 136 . The safety valves  150 , 154  have fluid flow control elements  158 , 160 , each of which have fluid delivery and closed positions of adjustment. The flow control elements  142 , 144 , 146 , 148 , 158 , 160  of all the service and safety valves  126 , 128 , 134 , 136 , 150 , 154  are normally in their closed positions of adjustment and are proportionally opened depending on the amount of electric current delivered to those valves. 
     The work machine includes a source of pressure fluid including an engine driven pump  162  drawing fluid from a reservoir  164  and delivering pressurized fluid to two accumulators  166 , 168  by way of a double check valve  170  and fluid conduits  172 , 174 . The accumulator  166  is connected in pressure fluid delivery relation to the safety valve  150  by a fluid conduit  176  and the accumulator  168  is connected in pressure fluid delivery relation to the safety valve  154  by a fluid conduit  178 . 
     Each of the differentials  110 , 112  has a fluid pressure applied and spring released lock-up mechanism (not shown). The lock up mechanisms of the differentials  110 , 112  are connected in pressure fluid receiving relation to an electrically controlled proportional lock valve  180  by a fluid conduit  182  and branch conduits  184 , 186  and the lock valve  180  is connected in pressure fluid receiving relation to the fluid conduit  178  by a fluid conduit  188 . The differential lock-up mechanism may be a positive lock type or it may be a slip type differential lock wherein the amount of slip depends on the pressure of the fluid delivered to the lock-up mechanism. The fluid pressure delivered to the differential lock up mechanism can be varied because the lock valve  180  is a proportional valve. 
     The work machine is also provided with a fluid control for its spring applied and fluid pressure released parking brake  190 . The parking brake  190  is connected in pressure fluid receiving relation to the accumulators  166 , 168  via electrically controlled parking valves  192 , 194  and a shuttle valve  195 . The parking valves  192 , 194  are connected in pressure fluid receiving relation to the fluid conduits  176 , 178  by fluid conduits  196 , 198 , respectively, for redundancy reasons. However, only one parking valve  192 , 194  and associated fluid conduits may be provided in some situations. A pair of inlet ports of the shuttle valve  195  are connected in pressure fluid receiving relation to the parking valves  192 , 194  by a pair of fluid conduits  1100 , 1102  and a fluid conduit  1104  connects an outlet port of the shuttle valve  195  to the parking brake  190 . 
     Individual wheel speed sensors  1106 , 1108 , 1110 , 1112  are operatively associated with the wheels  102 , 104 , 106 , 108 , respectively, and a steer angle or articulation angle sensor  1114  is operatively associated with the articulation joint  1116 . The wheel speed sensors  1106 , 1108 , 1110 , 1112  will be described in greater detail below. 
     An electric control is provided for operating the parking valves  192 , 194 , the service valves  126 , 128 , 134 , 136 , the safety valves  150 , 154  and the differential lock valve  180 , which includes an electronic control module  1118  and an optional back-up electronic control module  1120 , which may be integral with the electronic control module  1118  or a physically separate controller. Electronic control modules  1118 , 1120  are well-known in the art, and any suitable electronic control module  1118 , 1120  which acts to receive the desired inputs and calculate the desired outputs may be employed. The wheel speed sensors  1106 , 1108 , 1110 , 1112  and the steer angle sensor  1114  are connected in signal delivery relation to inputs of the electronic control module  1118 , 1120 . The service valves  126 , 128 , 134 , 136 , the safety valves  150 , 154 , the parking valves  192 , 194  and the differential lock valve  180  are individually connected to outputs of the electronic control module  1118  by electric lines  1122 , 1124 , 1126 , 1128 , 1130 , 1132 , 1134 , respectively. The service valves  134 , 136  and the safety valve  154  associated with the service brakes  122 , 124  of the rear axle  116  and the parking valve  194  may be individually connected to outputs of the back-up electronic control module  1120  by electric lines  1136 , 1138 , 1140 , 1142 , respectively; again, if this is done, it is for redundancy reasons unrelated to the present invention and may be connected in another manner without effecting the operation of the electronic traction control system  100 . 
     The electronic control modules  1118 , 1120  are connected to two power sources, namely, an engine driven generator  1144  and a battery  1146 . The generator  1144  and the battery  1146  are jointly connected in power delivery relation to, a pair of relays  1148 , 1150  which are in turn connected in power delivery relation to the electric control modules  1118 , 1120 , respectively, by a pair of electric lines  1152 , 1154 . The relays  1148 , 1150  are operated by a manually operated ignition type power switch  1156  which is preferably located in the cab of the work machine or another operator-accessible position (such as on a remote control device) and is connected to the relays  1148 , 1150  by a pair of electric lines  1158 , 115 . 
     If the differentials  110 , 112  are equipped with positive locking mechanisms, the electronic control modules  1118 , 1120  can be programmed to apply current to the proportional differential lock valve  180  commensurate with the sensed vehicle speed, thus automatically applying only the necessary force to engage the positive lock-up mechanisms. The greater the vehicle speed the smaller the force required to engage the differential lock-up mechanism, since the machine is not capable of generating as much torque to resist the differential at higher vehicle speeds. The electronic control modules  1118 , 1120  can be programmed to supply current to the proportional lock valve  180  corresponding to the sensed slippage of a wheel, whereby a corresponding fluid pressure is delivered to the friction clutches in the differential locking mechanisms. This mode of traction control can serve as a back-up type traction control in the event the traction control using the service brakes should become inoperative or is undesirable. The differential lock traction control algorithm will be discussed below. 
     In addition to the power switch  1156 , the various manually operated controls may include a brake actuating mechanism, shown here as a brake pedal  1162 , a differential lock switch  1164 , and an electronic traction control switch  1166 , each of which are adapted to provide input to at least one of the electronic control modules  1118 , 1120  in a known manner. 
     FIGS. 2,  3 ,  4 ,  6 ,  7 , and  8  depict flowcharts collectively illustrating a computer software program for implementing a preferred embodiment of the present invention. Here, it should be noted that the wheels  102 , 104 , 106 , 108  are controlled independent from each other. Thus, the figures represent the control of one wheel  102 , 104 , 106 , 108 —the other wheels  102 , 104 , 106 , 108  will have substantially identical flow charts. For the purposes of the following discussion, the term “inner wheel” represents the inside turning wheel and “outer wheel” represents the outside turning wheel. If the machine is not turning, then the inner wheel represents the left wheel, while the outer wheel represents the right wheel. 
     Electronic Traction Control System Mode Selection 
     FIG. 2 depicts a flowchart of a preliminary decision process which controls the mode of the electronic traction control system  100 . Please note that the electronic traction control system  100  may operate continuously as the machine is running, or may be controlled by an automatic (such as a sensor input or a transmission state) or manual (such as an operator-manipulated input) command. The electronic traction control system  100  will be discussed herein as having discrete and distinct start and end points. One skilled in the art could easily devise an operation scheme in which the electronic traction control system constantly monitors the wheels and produces a brake signal when needed; such an embodiment would fall under the claims of the present invention. 
     Control begins in FIG. 2, at the START block  2 , and proceeds to first decision block  200 , where the state of the operator&#39;s brake pedal  1162  is determined. If the brake pedal  1162  is depressed, control proceeds to first control block  202  and enters the service brake state without activating the traction control system of the present invention. If the brake pedal  1162  is not depressed, control proceeds to second decision block  204 , where the ground speed of the work machine is preferably compared to an optional predetermined maximum traction control speed (TCS_limit). If the ground speed is less than or equal to the maximum traction control speed or if no maximum traction control speed is provided, control proceeds to third decision block  206 , where the state of the differential lock mechanism (diff lock) is assessed. If the ground speed is greater than the maximum traction control speed, control proceeds to second control block  208  (END). At third decision block  206 , if the differential lock mechanism is engaged, control proceeds to third control block  210 , at which point control enters the differential lock traction control state, to be described in more detail below. 
     Back to the other fork from third decision block  206 : if the differential lock  113 , 115  is not engaged, control passes to fourth control block  212 . From fourth control block  212 , control next enters the traction control system starting at block  300  of FIG.  3 . 
     Traction Control State 
     First control block  300  of FIG. 3 is where the individual wheel speeds (V ACTRR , V ACTRF , V ACTLR , V ACTLF ) and machine articulation angle (θ) are sampled. As apparent from the flowchart, the wheel speeds and machine articulation angle are sampled on each control loop. As described below, the control is continually adjusting the braking forces in response to the changing machine parameters. After the machine parameters have been sampled, the control preferably passes to first decision block  302  to determine if the machine speed is beyond an optional upper limit established for the wheel-slip control. The upper limit is exceeded if the machine is traveling at greater than a predetermined maximum velocity value, 10 km/hr, for example. The upper limit represents a machine quality such as the maximum machine speed in second gear. If the upper limit is present and is exceeded, then control proceeds to second control block  304  where the inner and outer brakes are released. 
     Before the desired wheel speed is calculated, several machine parameters must be determined and/or calculated. From first decision block  302 , control passes to block  400  in FIG.  4 . For the discussion to follow, reference should be made to FIG. 5 which shows graphically many of the machine parameters referenced in the other figures and in the equations. 
     Referring now to block  400  of FIG. 4, the machine turning radius, TR, is calculated according the following relationship: 
       TR =1/2 WHEEL BASE/tan (θ ART /2) 
     where θ ART =Articulation angle of machine 
     Next, at second control block  402 , the steady state angular velocity of the machine, ω SS  is calculated according to the following relationship: 
     
       
         ω SS   =VM/TR   
       
     
     where, VM=((V ACTRR +V ACTRF +V ACTLR +V ACTLF )/4)*(rolling radius of the wheels) 
     Once ω SS  is calculated, control then passes to third control block  404  where the articulation rate of the machine, ω ART , is calculated according to: 
     
       
         ω ART   =dθ   ART   /dt   
       
     
     The control then proceeds back to third control block  306  and where the desired wheel velocity of each wheel, V DES , is calculated using equations laid out below. Please note that throughout the equations, RR is the right rear wheel, RF the right front, LR the left rear, and LF the left front. When a variable is described using a chosen one of the wheel position designations RR, RF, LR, or LF, the variable for the other, nonchosen, wheel positions is determined similarly but by replacing the chosen wheel position designation with the corresponding nonchosen wheel position designation. For instance, V SSRF  represents a property corresponding to the right front wheel, and V SSLF  is the same property, but corresponding to the left front wheel instead. 
     First, the wheel velocity due to a steady state articulation condition, V SS , is calculated according to: 
     For the left front wheel, 
     
       
           V   SSLF   =VM −(ω SS *TREAD WIDTH/2) 
       
     
     For the left rear wheel, 
     
       
         
           V 
           SSLR 
           =V 
           SSLF 
         
       
     
     For the right front wheel, 
     
       
           V   SSRF   =VM +(ω SS *TREAD WIDTH/2) 
       
     
     For the right rear wheel, 
     
       
         
           V 
           SSRR 
           =V 
           SSRF 
         
       
     
     Where: 
     V SSRF =Articulation-caused linear velocity of right front wheel, assuming inner differential (that is, front axle speed=rear axle speed), 
     Second, the wheel velocities due to a transient articulation condition (i.e., that provided by the time-varying relative motion of the front and rear frames about the articulation joint), V ART , are calculated according to: 
     For the right front wheel, 
     
       
           V   RF =(ω ART /2)*((TREAD WIDTH/2)−(WHEEL BASE/2)*tan(θ ART /2)) 
       
     
       V   ARTRF =(sign of  V   RF )*( F   MIN *min( f   ABS ( V   RF ),  f   ABS ( V   LF   ))+   F   MAX *max( f   ABS ( V   RF ),  f   ABS ( V   LF ))) 
     For the left front wheel, 
     
       
           V   LF =−(ω ART /2)*((TREAD WIDTH/2)+(WHEEL BASE/2)*tan(θ ART /2)) 
       
     
     
       
           V   ARTLF =(sign of  V   LF )*( F   MIN *min( f   ABS ( V   RF ),  f   ABS ( V   LF ))+ F   MAX *max( f   ABS ( V   RF ),  f   ABS ( V   LF ))) 
       
     
     For the right rear wheel, 
     
       
         
           V 
           RR 
           =−V 
           RF 
         
       
     
     
       
           V   ARTRR =(sign of  V   RR   )*(   F   MIN *min( f   ABS ( V   RR ),  f   ABS ( V   LR ))+ F   MAX *max( f   ABS ( V   RR ),  f   ABS ( V   LR ))) 
       
     
     For the left rear wheel, 
     
       
         
           V 
           LR 
           =−V 
           LF 
         
       
     
     
       
           V   ARTLR =(sign of  V   LR )*( F   MIN *min( f   ABS ( V   RR ),  f   ABS ( V   LR ))+ F   MAX *max( f   ABS ( V   RR ),  f   ABS ( V   LR ))) 
       
     
     where 
     (sign of V RF )=+1 or −1, depending upon the positive/negative value of V RF , V RF =articulation rate-caused wheel speed of right front wheel with inter-axle differential (front axle speed ≠rear axle speed), 
     f ABS =floating point absolute, 
     V ARTRF =articulation rate-caused linear velocity of right front wheel, no inter-axle differential (front axle speed=rear axle speed), 
     F MIN =A predetermined load-based factor for minimum speed wheel (the likelihood that the faster wheel will slip when articulating), and 
     F MAX =A predetermined load-based factor for maximum speed wheel (=1−F MIN ), the likelihood that the slower wheel will slip when articulating. 
     The values of F MIN  and F MAX  range from 0 to 1, are taken from a predetermined lookup table, formula, or equation, and are based on individual machine parameters and a sensed value for the variable load carried by the work machine. F MIN  and F MAX  bias the wheel velocity to account for the variable load causing a variable weight distribution to the wheels; the exact values of F MIN  and F MAX  are not essential to the present invention and may be easily determined by those skilled in the art. 
     Finally, the desired wheel speeds are calculated according to the following relationship: 
     For the left front wheel, 
     
       
         
           V 
           DESLF 
           =V 
           SSLF 
           +V 
           ARTLF 
         
       
     
     For the right front wheel, 
     
       
         
           V 
           DESRF 
           =V 
           SSRF 
           +VARTRF 
         
       
     
     For the left rear wheel, 
     
       
         
           V 
           DESLR 
           =V 
           SSLR 
           +V 
           ARTLR 
         
       
     
     For the right rear wheel, 
     
       
         
           V 
           DESRR 
           =V 
           SSRR 
           +V 
           ARTRR 
         
       
     
     Once the machine parameters and the desired wheel speeds are calculated, the control transfers to first control block  600  of FIG. 6, where the machine parameters are compared to the working range of the wheel slip control. 
     Referring to first control block  600  of FIG. 6, the steady state wheel velocity, V SSS , is determined as the minimum of all desired wheel speeds. Once the steady state wheel velocity, V SSS , is determined, the control proceeds to first decision block  602  where V SSS  is compared to the lower limit velocity value, S limit. S limit represents a predetermined value of a threshold for effective electronic traction control system  100  operation and may have a value of 1.5 km/h, for example. If V SSS  is found to be less than S limit, then the assumption is that the wheel speeds are too low for the traction control system to function properly and the electronic traction control system  100  takes no action, control returning to eighth decision block  208  of FIG. 2 for an end to the program logic. Otherwise, the machine parameters are said to be within the working range of the electronic traction control system  100 . 
     After performing the logic in FIG.  6  and achieving a “no” result in first decision block  602 , the control returns to fourth control block  308  shown in FIG.  3 . At fourth control block  308 , a predetermined reference value, A, is determined from a preset list of values dependent upon any number of system characteristics or, preferably and for better accuracy, calculated using the following: 
     
       
           A=|ω   ART |/2*WHEEL BASE/2*|tan(θ ART /2)|+ K   DB   
       
     
     where K DB =constant value representing lower sensing limit of wheel speed sensors (˜0.5 rpm or else as provided for a specific sensor type). A symbolizes the maximum possible error between the desired and measured wheel speeds without loss of traction. Such an error may exist due to factors such as sensor measurement error, machine dynamics, and differences between the actual and assumed wheel speed biases during transient articulation. 
     Control then passes to fifth control block  310 , where an error value, E, is produced. E represents the difference between the actual wheel speed and the desired wheel speed: 
     
       
           E=|V   ACT   −V   DES |  (for each wheel) 
       
     
     At second decision block  312 , the error value, E, is compared to the predetermined reference value, A. If the E is greater than A, control continues to sixth control block  314 . Otherwise the control proceeds to third decision block  316 . 
     At sixth control block  314 , braking forces for the faster rotating or slipping wheel are adjusted using a Proportional-Integral-Derivative (“PID”) technique. PID is commonly used to modulate and smooth the response of an electronic control system. In the current invention, PID acts to transform the wheel speed error (E) value into a brake command signal (V). 
     FIG. 7 depicts a sample of a block diagram of a PID control loop which could be performed at sixth control block  314 . The desired wheel speed, V DES , is input at first control block  700 . At the summing junction  702 , the desired wheel speed and actual wheel speed are read and the E and A values are calculated. Control then enters the PID block, shown generally at  706 , where V P , V I , and V d  are calculated using PID, preferably by the equations: 
     
       
         
           V 
           p 
           =K 
           p 
           X 
         
       
     
       V   i   =K   i   ∫Xdt   
     
       
         
           V 
           d 
           =K 
           d 
           dX/dt 
         
       
     
     where X=E−A, or by any other suitable PID format. 
     The values of the constants K p , K i , and K d  are determined from simulation and analysis of empirical data in response to under footing conditions, machine dynamics, type of work performed by the machine, etc. For example, the values of the constants K p , K i , and K d  may be on the order of 1.0, 0.5, and 1.0, respectively. It will be readily apparent to those skilled in the art that the PID constant values may be any of a wide range of numerical values depending on the desired gain of the feedback system and may be readily determined experimentally for a given traction control system. 
     At first decision block  706 ( a ), E and A are compared. If E is larger than A, then control passes to second decision block  706 ( b ), where the proportional section, V p , of the PID is calculated. If E is equal to or smaller than A, control passes to third control block  706 ( c ), and V p  is set to zero. This zeroing out assists in fine-tuning the response of the system by avoiding a deceptive V p  component in cases where the error is approaching a physical limit of the system. 
     At or about the same time as control enters the proportional aspect of the PID loop at first decision block  706 ( a ), the integral portion V i  is calculated at fourth control block  706 ( d ), and control enters a derivative portion of the PID loop at second decision block  706 ( e ). At second decision block  706 ( e ), the previous state of the control is evaluated. If the previous state of the control is not traction control system activated, the derivative portion of the PID is skipped and the previous state is set to traction control system on at fifth control block  706 ( f ). This portion of the PID loop is intended to prevent artificially large values in the derivative portion due to the sudden initiation of the logic of third or fourth control blocks  210 , 212 . Optionally, the PID loop may be run for several cycles without running the derivative portion of the control. Only one cycle is shown by the “previous state” logic of FIG. 7 but it is well-known to skip a portion of a loop for several cycles through the use of an incremented variable. If the previous state is that the traction control system was activated, control proceeds to sixth control block  706 ( g ) and the derivative portion of the PID is activated. 
     The PID block  706  sends outputs V p , V i , and V d  to seventh control block  708  and V, the brake signal, is calculated. V can be represented by the equation, V=V p +V i +V d . From seventh control block  708 , control passes to eighth control block  710  and the final V value is sent back to the main program. It should be noted that the logic of FIG. 7 takes place within sixth control block  314  of FIG.  3 . After generating the brake command signal and sending it back to the main program of FIG. 3 at eighth control block  710 , control then passes to ninth control block  712 , where the wheel speed is read once more from the wheel speed sensors  1106 , 1108 , 1110 , 1112  and the actual wheel speed is sent to the summing junction  702  to re-start the PID loop. 
     The closed loop of FIG. 7 illustrates that in response to the error value, E, the PID control calculates the braking forces necessary to reduce the error value, E, to the first predetermined reference value, A. V is calculated by the FIG. 7 loop and sent to sixth control block  314  in FIG. 3 until E becomes equal to or less than A. At that point, traction will be considered to have been regained and the electronic traction control system  100  will not be needed until the next slipping event. 
     With reference to the seventh control block  318  shown in FIG. 3, the braking system is supplied a sufficient amount of hydraulic fluid to build the pressure before the service brakes  118 , 120 , 122 , 124  are applied, an operation known as “pre-fill”. This is accomplished by energizing the safety and service valves  150 , 154 , 126 , 128 , 134 , 136  to fill the braking system with pressurized fluid. Pre-filling the service brakes  118 , 120 , 122 , 124  substantially removes any time lag between the moment that the braking control signal is issued and the moment in which the brake  118 , 120 , 122 , 124  is applied. For example, the safety and service valves  150 , 154 , 126 , 128 , 134 , 136  may be energized for a time period of 100 ms or for such time as to achieve a desirable fluid pressure. It should be apparent that once braking has initiated there is no ongoing need to pre-fill the braking system and seventh control block  318  may include an instruction to skip the prefill step if the brake pressure is adequate. Control then proceeds to eighth control block  320  and the brake signal V is sent to the brakes. 
     Returning to second decision block  312  in FIG. 3, if E is not greater than A—that is, if the slipping wheel(s)  102 , 104 , 106 , 108  are no longer considered to be slipping—control proceeds to third decision block  316 , where the engaged/disengaged state of the brakes  118 , 120 , 122 , 124  is evaluated. If the brakes  118 , 120 , 122 , 124  are disengaged, control returns to first command block  300  and starts over. If the brakes  118 , 120 , 122 , 124  are engaged at third decision block  316 , control proceeds to ninth control block  322 . At ninth control block  322 , the braking is reduced by sending a new brake command signal with a value of either less than the previous brake command signal or zero and control then returns to first command block  300  and starts over. The purpose of the third decision block  316 -ninth control block  322  loop is to disengage the brakes  118 , 120 , 122 , 124  when the electronic traction control system is no longer needed. From second, eighth, or ninth control blocks  304 , 320 , 322  or from third decision block  320 , control returns to the END block, element  208  of FIG.  2 . 
     Differential Lock Traction Control System 
     If the third decision block  206  of FIG. 2 indicates that the ground speed of the machine is less than the TCS limit, control proceeds to third control block  210 , and the machine enters the differential lock traction control system state. The differential lock traction control system is simply a version of the electronic traction control system  100  which operates in conjunction with the differential lock  110 , 112 . 
     At first control block  800  of FIG. 8, the desired wheel speeds are set such that a ratio of the desired wheel speeds of the two wheels  102 , 104 , 106 , 108  which share an axle  114 , 116  is equal to 1. Control then proceeds to first decision block  802  and checks the wheel speed against a desired wheel speed. If the wheel speed is as desired, control returns to the END block  208  in FIG.  2 . If the wheel speed is not at the desired wheel speed, control proceeds from first decision block  802  to second decision block  804 , where the engagement of the differential lock (“diff lock”)  110 , 112  is investigated. If the differential lock  110 , 112  is not at maximum engagement, the wheel slip torque has presumably overcome and partially disengaged the differential lock  110 , 112 . In that case, the differential lock  110 , 112  is engaged, usually through hydraulic pressure, at second control block  806 . Control then proceeds to third decision block  808 , where the wheel speeds are again compared to the desired wheel speeds. If the wheel speeds are not at the desired values, control repeats the logic of second decision block  804 . Otherwise, the wheel speed must have been brought under control by the differential lock  110 , 112  at second control block  806 , and control proceeds to the END block  208  in FIG.  2 . 
     If the differential lock  110 , 112  is already at maximum engagement in second decision block  804 , control proceeds to third control block  810 . At third control block  810 , the service brakes  118 , 120 , 122 , 124  are activated to slow the overspeeding wheel(s)  102 , 104 , 106 , 108  to the desired wheel speed. Control then proceeds to fourth decision block  812 , at which the wheel speed is once more compared to the desired wheel speed. If the two are equal, control ends the differential lock traction control system at the END block  208  of FIG.  2 . If the two speeds are different, control returns to third control block  810  and continues to slow the overspeeding wheel until the wheels sharing an axle have a speed ratio of 1. 
     General Operation and Actuation 
     It should be remembered that the electronic traction control system  100  may be activated in a number of different ways. For instance, the electronic control module  1118 , 1120  could operate automatically to detect and eliminate a slipping condition of the wheels at all times, the operator could manually actuate the electronic traction control system  100  under certain work conditions, or the like. The exact method of actuation of the electronic traction control system  100  is not crucial to the present invention. 
     From the foregoing it is apparent that the electronic traction control system  100  operates to detect a slipping wheel  102 , 104 , 106 , 108 , apply braking force to the slipping wheel  102 , 104 , 106 , 108 , and periodically and incrementally modulate the braking force in accordance with the degree of slip which is detected by the electronic traction control system  100 . 
     It will be evident to those skilled in the art to delay certain portions of the control within the various control algorithms disclosed with respect to the present invention. For example, a delay may filter out short term wheel slip aberrations. However, this is not critical to the present invention. 
     It is noted that values described herein are for exemplary purposes only. It will be apparent to those skilled in the art that any of the illustrated values may be modified depending upon the desired effects. 
     Industrial Applicability 
     The present invention is well suited toward regulating the wheel-slip of an articulated machine such as a wheel loader. It will however, be apparent to those skilled in the art that the present invention is not limited to a wheel loader, as the present invention is well suited to many other types of articulated machines. 
     As set forth above, the wheel-slip control of the present invention senses the individual wheel speeds and calculates a desired wheel speed value. Based on feedback control, an error value is determined. In response to the magnitude of the error value, the control determines the proper braking forces needed to eliminate wheel slip and commands the brakes to apply those forces. The brake forces are incrementally modulated with each loop of the control for smooth transitions from the initial braking force to the final braking force. 
     It should be appreciated by one skilled in the art that using PID feedback control provides a more desirable braking control. The V p  term of the PID control leads to a proportional gain which provides for a fast response. The V i  term of the PID control cancels any offset in error introduced by the V p  term. The V d  term dampens the response, providing for control stability. Thus, the result provides for a wheel-slip control which eliminates wheel-slip quickly and without the undesirable effects of brake “pulsing”. Thus, the PID control accurately determines the magnitude and the rate at which the braking force is to be applied. 
     As shown, the present invention is particularly suited to machines that are articulated and have two sets of axles for driving at least two wheels for each axle set. Moreover, the present invention measures the articulation angle of the machine, calculates the articulation rate, and adjusts the slip signal value to account for the normal wheel speed differential associated with each axle set during cornering, as well as compensating for movement of the articulation joint during articulation and for the variable load carried by the machine. Further, the electronic traction control system independently monitors wheel-slip, providing for efficient machine operation. 
     Other aspects, objects and advantages of the present invention can be obtained from a study of the drawings, the disclosure and the appended claims.

Summary:
An articulated work machine has a front frame and a rear frame connected for pivotal movement therebetween for steering the machine by an articulation joint. Each of the front and rear frames has two driven wheels, spaced laterally, each having a brake associated therewith. As the machine articulates during steering, one or more of the wheels may lose traction and slip. An electronic traction control system receives measured wheel speed signals and an articulation angle signal, calculates a desired wheel speed responsive to the wheel speed and articulation angle signals, and selectively applies the brakes until the measured wheel speed is equal to the desired wheel speed.