Abstract:
An apparatus and method for controlling an electric steering assist system, which system provides assist in response to a steering control signal, the apparatus comprising: torque sensing means ( 20 ) operatively connected to a vehicle hand wheel ( 12 ) for providing a torque signal (Ts) indicative of applied steering torque, blending filter means connected to the torque sensing means ( 20 ) for providing a blended filtered torque signal having a first functional characteristic at torque frequencies less than a blending frequency and a second functional characteristic at torque frequencies greater than the blending frequency, the blending filter means including a low pass filter ( 70 ) which passes all frequencies below the blending frequency and a high pass filter ( 71 ) which passes all frequencies above the blending frequency, steering assist means for providing steering assist in response to a control signal, control means operatively connected to the blending filter means for providing said control signal to the steering assist means in response to the blended filtered torque signal, and means ( 166 ) whereby high frequency gain of the steering assist system is arranged to be low for on-center operation of the hand wheel and relatively higher for off-center operation.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of International Application No. PCT/GB00/03166 filed Aug. 17, 2000, which claims priority to Great Britain Patent Application No. 9919277.5 filed Aug. 17, 1999. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention is concerned with a method and apparatus for controlling an electric power assisted steering system in a motor vehicle and of the type which uses an adaptive blending torque filter to improve steering feel. 
     Electric assist steering systems are well known in the art. Electric power assist steering systems that utilize a rack and pinion gear set provide power assist by using an electric motor to either (1) apply rotary force to a steering shaft connected to a pinion gear, or (2) apply linear force to a steering member having the rack teeth thereon. The electric motor in such systems is typically controlled in response to (1) a driver&#39;s applied torque to the vehicle steering wheel, and (2) sensed vehicle speed. 
     Known electric assist steering systems have a dynamic performance characteristic, known as the system bandwidth, that varies as a function of vehicle speed. As the vehicle operator applies steering torque and rotates the steering wheel back and forth, e.g. left-to-right-to-left, the electric assist motor is energized to provide steering assist commensurate with the steering inputs. How the steering system responds to a particular frequency of back-and-forth steering wheel movement is indicative of the system&#39;s dynamic performance. 
     The amount of local change at the electric assist motor divided by the amount of local change in steering torque applied by the driver is the steering system gain. A time delay occurs from the time steering torque is applied to the steering wheel to the time the assist motor responds. This time delay is a friction of the frequency at which the input command is applied. This is referred to as the system response time. The system gain is set to a predetermined value so as to have a short system response time while still maintaining overall system stability. The system response time and system gain determine the system bandwidth. 
     The bandwidth in known steering systems varies as a function of vehicle speed. If dynamic steering frequency or the “frequency” of a transient response exceeds the system bandwidth at a particular vehicle speed, the steering feel becomes “sluggish” (felt as a “hesitation”when the steering wheel direction is changed) since the steering assist motor does not respond quick enough. Typically, steering system gain as well as system bandwidth decreases as the vehicle speed increases so that system hesitation or sluggishness becomes more noticeable as vehicle speed increases. 
     According to our earlier U.S. Pat. No. 5,504,403, which is incorporated by reference herein, it is known for the power assist apparatus to comprise torque sensing means operatively connected to a vehicle hand wheel for providing a torque signal indicative of applied steering torque. Blending filter means are connected to the torque sensing means for providing a blended filtered torque signal having a first functional characteristic at torque frequencies less than a blending frequency and a second functional characteristic at torque frequencies greater than the blending frequency. The apparatus further includes steering assist means for providing steering assist in response to a control signal, and control means operatively connected to the blending filter means for providing said control signal to the steering assist means in response to the blended filtered torque signal. The blending filtering means filters the torque signal so as to maintain a selectable system bandwidth during system operation. 
     Similarly, according to a later U.S. Pat. No. 5,704,446, which is incorporated by reference herein, a blending filter is provided for splitting the driver torque signal into a low frequency component and a high frequency component. However a further feature is provided where the low frequency component sets the high frequency gain. This is so that the gain for the high frequency component signal mirrors the effective gain of the low frequency component signal, whereby the high frequency signal is close to but always slightly higher than the low frequency signal. As this makes the high frequency gain a function of the amplitude of the low frequency torque signal component, a phase lag is introduced into the high frequency component above the blending frequency which itself could induce instability within the system. 
     It is an object of the present invention to provide blended filtering of the high and low frequency torques present within the steering system that ensures stability and improved driver feel under all operating conditions. 
     It is a feature of the present invention to seek to further optimize the torque blending operation in the aforegoing systems. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, there is provided an apparatus for controlling an electric steering assist system, which system provides assist in response to a steering control signal, the apparatus comprising: torque sensing means operatively connected to a vehicle hand wheel for providing a torque signal indicative of applied steering torque, blending filter means connected to the torque sensing means for providing a blended filtered torque signal having a first functional characteristic at torque frequencies less than a blending frequency and a second functional characteristic at torque frequencies greater than the blending frequency, the blending filter means includes a low pass filter which passes all frequencies below the blending frequency and a high pass filter which passes all frequencies above the blending frequency, steering assist means for providing steering assist in response to a control signal, control means operatively connected to the blending filter means for providing said control signal to the steering assist means in response to the blended filtered torque signal, and means whereby high frequency gain of the steering assist system is arranged to be low for on-centre operation of the hand wheel and relatively higher for off-centre operation. 
     By “on-centre” operation, we mean operation of the steering wheel in operating regions within a few degrees, typically 5-10°, deviation from the straight ahead position and where the driver input torques are relatively small, eg. 1 or 2 Nm (see FIG.  14 ). “Off-centre” operation means operation of the steering wheel for larger angles and larger driver input torques, for example, 3 to 4 Nm. 
     In one embodiment, this operation is achieved in that said means enable the gain of the high frequency path via the high pass filter to be adjusted in accordance with the sensed level of applied steering torque so as to be low for on-centre operation of the steering wheel and relatively higher for off-centre operation. 
     In another embodiment, an additional frequency dependent transfer function is provided in the blending filter means by which the steering system gain is made to vary as a function of the lower frequency filtered component 
     Advantageously, the additional frequency dependent transfer function element comprises a proportional plus differential filter. 
     In some embodiments, the proportional plus differential filter is positioned after an assist curve means which provides a desired steering torque assist signal having a value functionally related to the low pass applied steering torque and sensed vehicle speed. In other embodiments, the proportional plus differential filter may be positioned in front of the assist curve means. The preferred implementation includes the PD filter in front of the assist curve by using a single gain to couple some of the high frequency output from the blending filters into the low frequency path. 
     The proportional plus differential filter can be realized by a combination of the low frequency and high frequency components (T SL  and T SH  wherein the input to the assist curve means is given by          T     S                 L       +         ω   b       ω   z            T     S                 H                                
     where T SL =The low passed signal 
     T SH the high passed signal 
     ω b =blending filter frequency          ω   z     =           ω   b          G   b            |     off   -   centre             G   ∞          |     off   -   centre            -     G   ∞            |     on   -   centre                                  
     G ∞ =high frequency gain 
     G b =assist curve (low frequency) gain 
     Advantageously, the transfer function K(s) of the proportional plus differential filter is of the form:          K        (   s   )       =     1   +       1     ω   z       ·   s                 w                 h                 e                 r                 e                   ω   z       =           ω   b          G   b            |     off   -   centre             G   ∞          |     off   -   centre            -     G   ∞            |     on   -   centre                                  
     with | on-centre and | off-centre representing preferred “ideal” values and with ω Z ω b G b  and G ∞ as defined hereinafter. 
     In the present blending filter design, both the low frequency component and the high frequency component set the high frequency gain. This ensures that the high frequency on-centre, and the high frequency off-centre gains can be set uniquely and independently. As the high frequency gain is a function of the low frequency gain, no phase lag is necessarily introduced above the blending frequency and therefore the system stability and driver feel can be appropriately maintained over the whole of the vehicles operating conditions such as with vehicle speed where the high frequency gain can also be arranged to be a function of vehicle velocity. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic block diagram illustrating a known power assist steering system of a type to which the present invention is applicable; 
     FIG. 2 is a schematic representation of the control loop system of the known steering system of FIG. 1; 
     FIG. 3 is a simplified block diagram of a known torque compensator used in the system of FIG. 1; 
     FIGS. 4 a  and  4   b  show frequency response characteristics for optimized on-centre and off-centre behaviour; 
     FIG. 5 is a simplified block diagram of a modified torque compensator in accordance with the present invention; 
     FIGS. 6 a  and  6   b  show frequency response characteristics for a system embodying a P+D filter in accordance with an embodiment of the present invention; 
     FIG. 7 shows a typical assist curve; 
     FIG. 8 shows an example of the response of the P+D and assist curve to a ramp input; 
     FIG. 9 shows an arrangement in accordance with the present invention, with a P+D element disposed after the assist curve; 
     FIG. 10 shows an arrangement in accordance with the present invention, with a P+D element disposed in front of the assist curve; 
     FIG. 11 shows a means of realizing the arrangement of FIG. 10; 
     FIGS. 12 a  and  12   b  illustrate respectively gain v frequency characteristics for the known blending structure and a structure in accordance with the present invention, where ω z  (as defined hereinafter)=∞; and the linear assist centre gain G b  (as defined hereinafter is varied); 
     FIGS. 13 a  and  13   b  illustrate respectively gain v frequency characteristics for the known blending structure and a structure in accordance with the present invention, where          ω   z     =         ω   b     s                   a                 n                 d                            
     FIG. 14 illustrates “on-centre” and “off-centre” operation of the system. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, the illustrated power assist steering system  10  includes a steering wheel  12  operatively connected to a pinion gear  14 . Specifically, the vehicle steering wheel  12  is connected to an input shaft  16  and the pinion gear  14  is connected to an output shaft  18 . The input shaft  16  is operatively coupled to the output shaft  18  through a torque sensor  20 . 
     The pinion gear  14  has helical teeth which-are meshingly engaged with straight cut teeth on a rack or linear steering member  22 . The pinion gear  14  in combination with the straight cut gear teeth on the rack member  22  form a rack and pinion gear set. The rack is steerably coupled to the vehicle&#39;s steerable wheels  24 ,  26  with steering linkage in a known manner. When the steering wheel  12  is turned, the rack and pinion gear set converts the rotary motion of the steering wheel  12  into linear motion of the rack  22 . When the rack moves linearly, the steerable wheels  24 ,  26  pivot about their associated steering axes and the vehicle is steered. 
     An electric assist motor is operatively coupled to a member of the steering mechanism at some appropriate point. Examples include rack drive (U.S. Pat. No. 5,257,828), column drive or pinion drive. When the electric motor  28  is energized, it provides power assist steering so as to aid in the rotation of the vehicle steering wheels  12  by the vehicle operator. 
     The electric assist motor  28  is energized by a motor controller that includes a means of varying the current flowing through the motor windings or the voltage applied to the windings so as to control the level of assistance that is applied to the steering mechanism. The electric motor may be a brushless permanent magnet type in which the motor controller modulates the motor winding current in accordance with the position of the motor in a manner that is well known in the art 
     The torque sensor  20  is operatively connected between the input shaft  16  and output shaft  18  to provide an electrical signal T S  that is indicative of the applied steering torque. One means for measuring the torque is by the use of a torsion bar which twists in response to applied steering torque thereby permitting relative rotation between the input shaft  16  and the output shaft  18 . Stops, not shown, limit the amount of such relative rotation between the input and output shafts in a manner known in the art. The torsion bar has a spring constant referred to herein as K i . The amount of relative rotation between the input shaft  16  and the output shaft  18  in response to applied steering torque is functionally related to the spring constant of the torsion bar. A position sensor is operatively connected across the input shaft  16  and the output shaft  18  and provides an electrical signal having a value indicative of the relative rotational position or relative angular orientation between the input shaft  16  and the output shaft  18 . The position sensor in combination with the torsion bar forms the torque sensor  20 . The steering wheel  12  is rotated by the driver during a steering maneuver through an angle Θ HW . The relative angle between the input shaft  16  and the output shaft  18  as a result of applied input torque is referred to herein as Θ p . Taking the spring constant K, of the torsion bar into account, the electrical signal from the sensor  20  is also indicative of the applied steering torque referred to herein as T S . 
     The output of the torque sensor  20  is connected to a torque signal processing circuit  50 . The processing circuit  50  monitors the angle Θ P  and, “knowing” the spring constant K 1  of the torsion bar provides an electric signal indicative of the applied steering torque T S . 
     The torque sensor signal is passed through a pair of “blending” filters. The two blending filters are constructed such that the first is a low pass filter  70  and the second is a high pass filter  71 . The filters are designed such that summation of the two filters is identically one for all frequencies. The low pass filter  70  allows all of the signal T S  with frequency content below some blending frequency ω pass through while rejecting all high frequency data. The high pass filter allows all of the signal T S  with frequency content above some blending frequency ω b  to pass through while rejecting all low frequency data. The blending filter frequency ω b  may be accomplished using an actual calculation in accordance with a desired control function. The low pass torque sensor output signal T sL  is connected to an assist curve circuit  54 . 
     The assist curve circuit  54  may be a look-up table or an analytical function as described in EP 0947413 that provides a desired torque assist signal T assist  having a value functionally related to the low pass applied steering torque T SL  and sensed vehicle speed. A vehicle speed sensor  56  is also operatively connected to the assist curve circuit  54  The assist curve function may be accomplished using a look-up table in a microcomputer or may be accomplished using an actual calculation in accordance with a desired control function. 
     As is well known in the art, the amount of power assist desired for a vehicle steering system decreases as vehicle speed increases. Therefore, to maintain a proper or desirable feel to steering maneuvers, it is desirable to decrease the amount of steering power assist as the vehicle speed increases. This is referred to in the art as speed proportional steering. Hence, the gain of the assist curve “circuit”  54  will normally reduce as the vehicle speed increases. 
     The high passed torque sensor signal T sH  is connected to a high frequency assist gain circuit  72 . The high frequency assist gain circuit  72  multiplies the high passed torque sensor signal T sH  by a predetermined gain G that is a fiction related to vehicle speed. The determination of G ∞ may be accomplished using a look-up table in a microcomputer or may be accomplished using an actual calculation in accordance with a desired control function. 
     The outputs of the assist curve circuit  54  and the high frequency assist gain circuit  72  are summed in a summing circuit  79 . The output of the summing circuit  79  is referred to as T ba  and is connected to an adaptive filter circuit  80 . The two signals are combined to determine the input T ba  to the adaptive filter circuit. 
     The adaptive filter circuit  80  filters the input blended assist torque signal T ba  The filter is adaptive in that its poles and zeros are allowed to change as the vehicle speed changes so as to provide an optimal control system. The combination of this filtering is referred to as adaptive blending filtering and results in a filtered torque signal T m , which is referred to as the torque demand signal. The torque demand signal is connected to a motor controller  90 . The motor controller  90  controls energization of the motor  28  in response to the torque demand signal T m . The motor controller  90  controls steering damping in response to sensed speed of the steering mechanism. Other inputs  94  are connected to the motor controller  90 , including an ECU temperature sensor, soft-start circuitry, etc. 
     The output of the motor controller  90  is connected to a drive control circuit  96 . The drive control circuit is controllably connected to a plurality of power switches  100  to control the application of electrical energy to the electric assist motor  28 . 
     Referring to FIG. 2, the closed loop control system of the known system of FIG. 1 is shown again. 
     A torque applied to the handwheel gives the torque signal T S  that is connected to the low pass/high pass filter circuits. 
     The torque signal T S  is passed through the low pass filter  70  resulting in the low passed assist torque T sL.  The high passed assist torque T sH  is determined by subtracting the low frequency assist torque from the torque signal T S . The reason that T sH  can be determined in this way is discussed below. 
     The continuous domain blending filters are chosen such that the sum of the low pass filter G L (s) and the high pass filter G L (s) is always equal to one: 
     
       
           G   L ( s )+ G   H ( s )=1  
       
     
     where F(s) is the Laplace transform of f(t). 
     The low pass filter is preferably chosen to be a first order filter with a pole at ω b .The low pass filter pole ω b  may be computed as a function of vehicle speed by using circuit  83 . 
     The high pass filter is uniquely defined by the above constraint that the sum of the two filters must equal 1. Therefore, the transfer functions of the low and high pass filters are given by:            G   L          (   s   )       =       ω   b       s   +     ω   b                     G   H          (   s   )       =     s     s   +     ω   b                                
     When realizing a set of blending filters in a digital computer, those skilled in the art will appreciate that it is not necessary to construct separate high and low pass filter stages. Rather, the input to the blending filters T S  is passed through the low pass filter resulting in the signal T sL . The high passed signal is the original input torque minus the low passed portion: 
     
       
         
           T 
           sH 
           =T 
           s 
           −T 
           SL  
         
       
     
     This can be thought of equivalently as determining the low frequency portion of the signal and simply subtracting it out of the original signal. The result is a signal with only high frequency information. Alternatively, one can use higher order blending filters. However, the complexity of the filter computations increases with filter order in a digital computer. The use of first order filters is preferred. 
     The low passed torque signal T SL  is connected to assist curve circuit  54 . Referring again to FIG. 2, the linearized control system includes an assist curve circuit  54  designated as G b (v). 
     In the steering system, the low passed torque T SL  is passed through the assist curve to determine T assist . The low passed assist value T assist  is summed with the high passed assist value. The high passed assist value is determined by multiplying the high passed torque sensor signal T sH  times the high frequency assist gain G 28 . The blended assist is: 
     
       
         
           T 
           ba 
           =T 
           assist 
           +G 
           28 
           T 
           SH  
         
       
     
     The pole of the blending filter cob and the high frequency assist gain G are computed as functions of speed in circuits  83  and  74  respectively. The determination of (ω b  and G 28  may be accomplished using a look-up table in a microcomputer or may be accomplished using actual calculations. The circuits  83  and  74  in the control system of FIG. 2 form the blending filter determination circuit  68  of FIG.  1 . The blended assist is connected to the adaptive torque filter G f  which allows the vehicle steering system to adapt to changes in the dynamics of the system that occur as the vehicle speed changes. 
     The output from the adaptive torque filter  80  is a torque demand signal T m . The motor provides a torque assist which is summed with the manual assist transmitted through the pinion shaft producing a total force on the rack. 
     The system described thus far is known from our earlier U.S. Pat. No. 5,504,403. As described above, in the known system, the high frequency assist gain G 28  established at block  72  in FIGS. 1 and 2 is essentially a constant value for a given vehicle speed. However, it has been determined experimentally that different high frequency assist gains are required to get good performance when driving with the steering wheel on-centre and when driving with the steering wheel off-centre, respectively. 
     FIG. 3 shows a linearized version of the compensation circuit of FIGS. 1 and 2 which comprises a frequency filter  150 ,  152  that separates the measured column torque T S  into high frequency and low frequency parts, the boost curve  154  that is applied to the low frequency content and a gain (G ∞ )  156  that is applied to the high frequency content. The low and high frequency paths are then added at  158  and passed through an adaptive torque filter  160 . This filter provides phase advance to stabilize the loop. In the linearized version, none of the functions are vehicle speed related. Typically, the frequency filter is implemented using a single low pass filter. 
     Thus,            G   L          (   s   )       =       ω   b       s   +     ω   b                                
     The gain G b  is the local derivative of the assist function with respect to the input torque evaluated at some low passed input torque and speed.          G   b     =       δ                   T     a                 s                 s                 i                 s                 t           δ                   T     S                 L                                  
     The gain G b  represents how much incremental T assist  is provided for an incremental change in low passed input torque T SL  about some nod low passed input torque and vehicle speed. 
     The torque filter transfer function is G ∞ (s). 
     In practical high speed tuning tests, it has been established that good on-centre feel can be obtained with a relatively low value of G (e.g. 6) and a frequency split at 4 Hz. When on-centre, the assist curve gain is locally zero. However, with this setting of G ∞ , the off-centre feel is poor and has a pronounced lag in the response. On the other hand, good off-centre feel can be obtained with a higher value of G ∞ (eg. 20) and a frequency split at 4 Hz. Changing the split frequency does not provide any significant benefit in these circumstances. Typically the local gain of the assist curve in the centre is around 10. 
     Frequency responses of the linearized centered system for the aforegoing two settings are shown by way of example in FIGS. 4 a  and  4   b.    
     It is apparent from these responses that a good on-centre response requires a relatively inactive steering system to allow the driver to feel the centre but, in contrast, a good off-centre response needs more gain to avoid a sluggish feeling. 
     It is therefore required for the compensator structure to be altered to allow the best on-centre and off-centre settings to be achieved simultaneously. 
     A presently preferred option for achieving this operation is to insert an additional frequency dependent block within the low frequency path, the effect of which is to provide an additional high frequency component derived from the low frequency gain which increases the overall high frequency gain of the steering assist system. This component will depend inherently on the assist curve gain which, in turn will vary with the low frequency torque level. An example of how this additional frequency dependent block can be established is now described. 
     The following nomenclature is used in the description which follows: 
     
       
         
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 G L (s): transfer function of low-pass filter 
               
               
                   
                 G H (s): transfer function of high-pass filter 
               
               
                   
                 (= 1 − G L (s)) 
               
               
                   
                 H t (s): overall transfer function of compensator 
               
               
                   
                 (excluding torque filter) 
               
               
                   
                 K(s): additional component in low-frequency path 
               
               
                   
                 ω b : blending filter frequency 
               
               
                   
                 ω z  frequency of additional zero in K(s) 
               
               
                   
                 G b : assist curve (local low-frequency) gain 
               
               
                   
                 G∞: the high-frequency gain 
               
               
                   
                   
               
             
          
         
       
     
     The transfer functions of the low and high pass filters are:            G   H          (   s   )       =       1   -     G   L       =     s     s   +     ω   b                                  
     The table below shows the desired parameters and the consequent transfer functions, based on the abovementioned example 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                   
               
               
                   
                 Desired on-centre 
                 Desired off-centre 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 G b   
                 0 
                 10 
               
               
                 ω b   
                 2π × 4 
                 2π × 4 
               
               
                 G ∞   
                 6 
                 20 
               
               
                 H t (s) 
                 6 H H (s) 
                 10 H L (s) + 20 H H (s) 
               
               
                   
               
             
          
         
       
     
     The modified compensator structure is shown in FIG.  5 . The additional transfer function, K(s), is added to the low-frequency path as shown by block  162 . It is assumed that is will have a vehicle-speed dependent gain. 
     The K(s) that is needed to achieve both the on-centre and off-centre transfer functions can be calculated as follows: Assume that the high-frequency path is unchanged and the assist curve gain is zero when on-centre; thus G ∞ must take on the value needed to get the desired on-centre characteristic (i.e. G ∞ 6). The blending filter frequency is the same for both desired characteristics. The desired off-centre response has G b  of 10 and ideal G ∞ of 20 is:                  H                     t        (   s   )         off                 centre         =                  10          G   L          (   s   )            K        (   s   )         +     6          G   H          (   s   )                         ⇒     K        (   s   )         =                    10          G   L          (   s   )         +     1.4          G   H          (   s   )             10          G   L          (   s   )                       =                1   +       1.4          G   H          (   s   )             G   L          (   s   )                       =                1   +     1.4        (       s     (     s   +     ω   b       )           ω                 b       (     s   +     ω   b       )         )                     =                1   +       1.4      s       ω   b                                           
     Thus K(s) takes the form of a proportional+differential (P+D) filter. In general, let K(s) be:          K        (   s   )       =     1   +     s     ω   z                                
     with a proportional gain of 1 and a derivative gain of          1     ω   z                            where   :     ω   z       =             ω   b          G   b              off   -   centre                   G   ∞            off   -   centre       -     G   ∞              on   -     ce                 ntre                                  
     with | on-centre  and.| off-centre  indicating the “ideal” values given in the table above. With the particular values tabled above, the derivative gain (1/ω z , is 1.4/(2×π×4)=0.557≈1/18, i.e. ω z =2.86 Hz. 
     To restore the existing characteristic at low vehicle speeds, the derivative gain of K(s) must be zero when the vehicle is stationary. 
     The effect of the P+D filter can be considered in frequency terms. The filter will only affect the off-centre response. FIGS. 6 a  and  6   b  show how the off-centre frequency response varies with the derivative gain (=1/ω z ). The on-centre response is also shown. 
     Although the analysis has been carried out in the continuous time domain, those skilled in the art will appreciate that all of the continuous time functions can be implemented in a sampled data system provided that the sampling frequency is sufficiently high. The mapping from continuous time to digital filters is well known and can be performed for example by a pole-zero mapping in which continuous time poles P and zeros Z are mapped to discrete time poles P and zeros Z via 
     
       
           P =exp( P   Δt ), Z =exp( Z   66 t )  
       
     
     where  Δ t is the sampling period. 
     The P+D element can be located before or after the assist curve. The location will affect the filter response because the assist curve is a nonlinear component. 
     Referring again to FIG. 2, the low pass filter G L , high pass filter G H  and filter G F  are given by:            G   L          (   s   )       =       ω   b       s   +     ω   b                     G   H          (   s   )       =     s     s   +     ω   b                                
     G F (s) is a notch filter, for example            G   F          (   s   )       =         (     s   +   40     )     2         (     s   +   4     )          (     s   +   400     )                                
     Note that the notch filter G F (s) can be arranged to have complex zeros and/or poles. 
     FIG. 9 shows one possible realization of the controller and the PD element  166  and with the high frequency component of the torque sensor input T SH  being calculated in the same manner as FIG. 2, ie. by subtracting the low frequency components T SL  from the input T S  using the subbing element  171 . For clarity, the effect of vehicle speed is omitted from FIG. 9 but as with the technique shown in FIG. 2, the following elements can be altered with vehicle speed: ω b  the assist curve, G ∞  G F (S) and the new derivative term ω z . 
     FIG. 10 shows the arrangement of FIG. 2 with the added improvement of a P+D element in accordance with one embodiment of the present invention disposed in front of the assist curve  154 . 
     FIG. 8 shows an example with a ramp input to the boost curve and the P+D element (D gain=1/18). The figure shows that there is only a very slight difference in the overall response in this particular case. 
     A benefit of placing the P+D element in the signal flow before the assist curve is that a simplification can be made. In FIG. 10 the low pass path to point  180  go is given by:                  (     1   +     s     ω   z         )            G   L          (   s   )         =       (     1   +     s     ω   z         )          (       ω   b       s   +     ω   b         )                     (     =     (       ω   b       s   +     ω   b         )       )     +       (     (       ω   b       ω   z       )     )          (     (     s     s   +     ω   b         )     )                   =         G   L          (   s   )       +       (       ω   b       ω   z       )            G   H          (   s   )                                        
     Thus the P+D element can be realized by using a combination of the low frequency and high frequency components T SL  and T SH . This can be realized as shown in FIG. 11 in which the P+D element has been replaced by a gain block  172  and a summation element  174 . 
     In operation, the high frequency component will be present in the blending filter output T ba  two paths. The first, as shown in FIG. 2 onwards is via the gain element G ∞ . The second is shown in FIGS. 5,  9 ,  10  and  11  and is via the gain element        (       ω   b       ω   z       )                          
     and the local gain of the assist curve G b . The local gain of the assist curve will depend on the low frequency component T sL  and will vary continuously between on-centre and off-centre operation. 
     Finally, FIGS. 12 a  and  12   b  illustrate respectively gain and phase v. frequency characteristics for the known blending structure and a structure in accordance with ω z =∞ and the linearized assist centre gain G b  is varied. FIGS. 13 a  and  13   b  illustrate respectively gain and phase v. frequency characteristics for the known blending structure and a structure in accordance with one embodiment of the present invention, wherein          ω   z     =       ω   b     s                            
     and the locally increased assist curve gain is varied. It can be seen from these figures that the high frequency gain is constant in the known structure and varies with G b  in the new structure. The amount of variation is controlled by the parameter ω z . 
     In accordance with the provisions of the patent statutes, the principle and mode of operation of this invention have been explained and illustrated in its preferred embodiment. However, it must be understood that this invention may be practiced otherwise than as specifically explained and illustrated without departing from its spirit or scope.