Four wheel steering system with closed-loop feedback and open-loop feedforward
This invention relates to motor vehicle four wheel steering systems, and more particularly to a closed-loop rear steering control in combination with an open-loop feedforward feature. 
     BACKGROUND OF THE INVENTION 
     In most four-wheel steer vehicles, the front wheels are steered together in direct and usually linear relation to the steering input of the driver, as in a two-wheel steer vehicle. The rear wheels are steered together as a function of the front wheel steering angle and/or the vehicle speed, to provide desired ride or handling characteristics. The desired ride or handling characteristics are electrically or mechanically simulated to define a reference model, and the rear steering angle required to achieve the desired characteristics is carried out by the rear wheel steering mechanism. 
     An early mechanization of a four-wheel steer control, as generally set forth above, was described in detail in a paper presented by K. J. McKenna at the Joint Automatic Control Conference held at University of Texas in June, 1974, entitled &#34;A Variable Response Vehicle--Description and Applications&#34;. The control described in the paper incorporated a reference steer mode in which a reference model supplied the desired yaw rate and lateral velocity, and a closed-loop control developed the steering commands in relation to a comparison between the desired and actual (measured) Parameters. 
     SUMMARY OF THE PRESENT INVENTION 
     The present invention is directed to an improved rear steering control system employing separate closed-loop feedback controller and open-loop feedforward control paths. The closed-loop feedback path may be optimized to enhance directional stability, to compensate for changes in the vehicle or road condition, and to shape the steady-state response of the system. The separate open-loop feedforward control path may be optimized to shape both the transient and the steady-state response of the system. 
     By separating the open-loop and closed-loop control paths, the authority and/or delay properties of the two paths may be independently varied for the optimum response. In a mechanization of the present invention, it has been demonstrated that the advantages of both open-loop and closed-loop control may be achieved in a single system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is schematic diagram of a four-wheel steer vehicle including a computer-based control unit for carrying out the control of this invention. 
     FIG. 2 is a system block diagram depicting the control of this invention. 
     FIG. 3 graphically depicts the open-loop control function of FIG. 2. 
     FIGS. 4 and 5 graphically depict the filter function of FIG. 2. 
     FIGS. 6 and 7 graphically depict the closed-loop control function of FIG. 2. 
     FIGS. 8-9 graphically depict the transient and steady-state response of the control of this invention. 
     FIG. 10 is a flow diagram representative of computer program instructions executed by the computer-based control unit of FIG. 1 in carrying out the control of this invention. 
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS 
     Referring now particularly to FIG. 1, the reference numeral 10 generally designates a motor vehicle having four steerable wheels. The front wheels 12, 14 are steered together in response to rotation of an operator manipulated handwheel 16. The handwheel 16 is mechanically connected via steering column 18 to a pinion gear 20, which is maintained in meshing engagement with teeth formed on a front rack 22. The front rack 22, in turn, is connected to front wheel tie rods (not shown), completing the mechanical linkage connecting the front wheels 12, 14 to the handwheel 16. 
     An electric motor 24 drives a second pinion gear 26, also maintained in meshing engagement with the front rack teeth. The motor 24 is adapted to be energized in relation to the operator exerted steering torque for generating a power steering assist torque which aids the driver exerted torque. To this end, a torque sensor 28 is disposed in relation to the steering column 18 for generating an electrical signal in accordance with the operator exerted steering torque. Such signal is applied as an input to a computer-based control unit 30, which among other things, controls the energization of electric motor 24 via line 32 for generating the proper magnitude and direction of steering assist. A signal indicative of the vehicle speed V x  is applied as an input to the control unit 30 via line 34, which signal may also be used as a parameter for steering control. Control apparatus and methods for suitably energizing the motor 24 are disclosed in U.S. Pat. No. 4,509,611 to Kade et al. issued Apr. 9, 1985, and assigned to the assignee of the present invention. 
     The control unit 30 also controls the energization of an electric motor 36 as indicated by the line 38 to control the steering of rear wheels 40, 42. The motor 36 rotatably drives a pinion gear 44 which is maintained in meshing engagement with teeth formed on a rear rack 46. The rack 46, in turn, is mechanically connected to the rear wheel tie rods (not shown) so that the rear wheels 40, 42 steer together. In mechanizing such control, electrical signals indicative of the lateral and yaw velocities V y , r and the front steering angle D f  are supplied as inputs to the control unit 30 via lines 48-52. The lateral and yaw velocity inputs are obtained with conventional accelerometers (not shown), and the front steering angle D f  is obtained with a rotary potentiometer 54 responsive to the rotary position of handwheel 16. 
     The system diagram of FIG. 2 illustrates the control of this invention in a closed-loop reference model steering system having an open-loop feedforward feature, such open-loop feedforward feature being the subject of co-pending patent application U.S. Ser. No. 211,731, filed June 27, 1988, assigned to the assignee of the present invention. 
     Neglecting compliance in the steering column 18, the operator (DRIVER) of the vehicle 10 directly controls the steering angle D f  of the front wheels 12, 14. As indicated in FIG. 1, the rear steering angle D r  is controlled via motor 36, designed in FIG. 2 as ACTUATOR. In addition, the DRIVER manipulates an accelerator pedal or like control (not shown) to effectively command a desired longitudinal acceleration d(V x )/dt for the vehicle 10. The vehicle, in turn, is propelled at a longitudinal velocity V x , and experiences given yaw and lateral velocities r, V y  which are provided as feedback to the DRIVER. 
     The control unit 30 performs the functions of the FILTER 60, the REFERENCE MODEL MAP 62, the OPEN-LOOP CONTROLLER 64, the CLOSED-LOOP CONTROLLER 66, and the summing junction 68. The OPEN-LOOP CONTROLLER 64, described below in reference to FIG. 3, develops an open-loop feedforward command D r  (OL) for the rear steer ACTUATOR as a function of the front steering angle D f  and the longitudinal velocity V x . The FILTER 60, described below in reference to FIGS. 4 and 5, generates a filtered front steering angle output D f  &#39; as a function of the front steering angle D f  and the longitudinal vehicle velocity V x . The filtered front steering angle D f  &#39;, in turn, is applied as an input to the REFERENCE MODEL MAP 62 along with the longitudinal velocity indication V x . The REFERENCE MODEL MAP 62 defines a desired vehicle response in terms of the desired yaw velocity r(des) and the desired lateral or slip velocity V y  (des). The CLOSED-LOOP CONTROLLER 64, described below in reference to FIGS. 6 and 7, develops a closed-loop steering command D r  (CL) for the ACTUATOR for bringing the actual yaw and lateral velocities r, V y  into correspondence with the desired yaw and lateral velocities r(des), V y  (des). The closed-loop control is also a function of the longitudinal velocity V x  as indicated. Finally, the summing junction 68 develops a steering command D r  (CMD) for the ACTUATOR according to the difference of the closed-loop command D r  (CL) and the open-loop feedforward command D r  (OL). 
     FIG. 3 graphically depicts the gain ratio OLGR for OPEN-LOOP CONTROLLER 64 of FIG. 2. The gain ratio OLGR defines the magnitude and direction of the open-loop feedforward command D r  (OL) per unit change in front steering angle D f  as a function of the longitudinal velocity V x . When V x  is relatively low--less than V x  (1). in FIG. 3--the ratio OLGR is negative for producing rear steering out-of-phase with the front steering. The ratio OLGR decreases as V x  approaches V x  (1), where the rear wheels 40, 42 are commanded to the straight position. When V x  is greater than V x  (1), the ratio OLGR is positive for producing rear steering in-phase with the front steering. 
     The FILTER 60 is disclosed herein as a nonlinear first-order lag filter, digitally implemented using the expression: 
     
         D.sub.f &#39;(new)=D.sub.f &#39;(old)+(D.sub.f -D.sub.f &#39;(old)) * GF 
    
     where D f  &#39;(new) is the updated output value of FILTER 60, D f  &#39;(old) is the past output value of FILTER 60, and GF is a filter (integrator) gain factor. The gain factor GF, in turn, is given by the expression: 
     
         GF=lesser of 1 and [F1+|F2 * (D.sub.f -D.sub.f &#39;(old))|] 
    
     where F1 and F2 are coefficients which vary as a function of the longitudinal velocity V x . When the coefficients F1 and F2 are scheduled substantially as depicted in FIG. 4, the gain factor GF varies substantially as depicted in FIG. 5, where V x  (1), V x  (2) and V x  (3) represent successively increasing values of longitudinal velocity V x , and the expression |(D f  -D f  &#39;(old))| represents the change in the driver steering input. For any velocity V x , it will be recognized that the corresponding gain factor slope is given by the coefficient F2, and the minimum gain factor value is given by the coefficient F1. 
     The output D f  &#39; of the above-described filter thus tracks the front steering angle D f  at a delay or lag which varies as a function of the longitudinal velocity V x  and the change in the driver generated steering input. The delay varies in inverse relation to the gain factor GF, and thus increases with increasing longitudinal velocity V x  and decreases with increasing change in driver steering input. 
     Since the filtered signal D f  &#39; controls the closed-loop response to driver generated steering inputs, such response will be (1) relatively fast at low vehicle speed, becoming progressively slower as the vehicle speed increases, and (2) relatively slow for small changes in driver steering input, becoming progressively faster as the change in driver steering input increases. Item (1) ensures a stable control system response to driver generated steering inputs at progressively higher vehicle speeds, and item (2) reduces the control system sensitivity to low amplitude noise in the front steering angle signal D f . Meanwhile, the control system response to externally generated steering inputs--wind gusts, for example--remains relatively fast and is unaffected by the operation of FILTER 60. 
     The REFERENCE MODEL MAP 62 is based on a cornering model of the vehicle 10 and generates a static or steady-state reference point (V y  (des), r(des)) for the CLOSED-LOOP CONTROLLER 66 to follow. The static model is mathematically represented by the matrix expression: ##EQU1## The A and B matrix terms are defined in terms of the front and rear cornering stiffnesses C f , C r , the front steering angle D f , the open-loop feedforward rear steering angle D r  (OL), the yaw moment of inertia I z , the longitudinal velocity V x , the vehicle mass m, the distance 1 1  between the front wheel axis and the vehicle center of gravity, and the distance 1 2  between the rear wheel axis and the center of gravity as follows: ##EQU2## 
     In order to conveniently implement the above described reference model with a real-time controller, such as the control unit 30, the A and B matrix terms may be combined into four term a, b, c, d, and computed off-line as a function of the longitudinal velocity V x . Thereafter, the computed values a, b, c, d, or a simplified mathematical representation of the same, may be stored in the control unit 30 to effect relatively fast real-time computation of the yaw and lateral velocity terms r(des) and V y  (des). 
     In a mechanization of the present invention, the computed values a, b, c, d were characterized by the second-order polynomial expressions: 
     
         a=a.sub.1 V.sub.x +a.sub.2 V.sub.x.sup.2 
    
     
         b=b.sub.1 V.sub.x +b.sub.2 V.sub.x.sup.2 
    
     
         c=c.sub.1 V.sub.x +c.sub.2 V.sub.x.sup.2 
    
     
         d=d.sub.1 V.sub.x +d.sub.2 V.sub.x.sup.2 
    
     where a 1 , a 2 , b 1 , b 2 , c 1 , c 2 , d 1  and d 2  are constants. This yields the algebraic expressions: 
     
         V.sub.y (des)=a * D.sub.f &#39;+b * D.sub.r (OL), and 
    
     
         r(des)=c * D.sub.f &#39;+d * D.sub.r (OL) 
    
     It will be noted in that in the above described embodiment, the open-loop feedforward term D r  (OL) is used as an input to the reference model. In such case, the open-loop term D r  (OL) is not affected by the FILTER 60 and the control system response thereto is substantially immediate. However, if a slower open-loop response is desired, the open-loop feedforward term D r  (OL) can be replaced with the product (D f  &#39;* OLGR). 
     The CLOSED-LOOP CONTROLLER 66 compares the reference yaw and lateral velocity terms V y  (des) and r(des) with the measured yaw and lateral velocity V y  and r to develop a closed-loop error term E(CL) according to the expression: 
     
         E(CL)=(r(des)-r) * F3+(V.sub.y (des)-V.sub.y) * F4 
    
     The coefficients F3 and F4 are scheduled as a function of the longitudinal velocity V x  substantially as depicted in FIG. 7, resulting in a similar speed-dependent variation in the error term E(CL). This ensures that the closed-loop response rate decreases with increasing vehicle speed. 
     The closed-loop steering command D r  (CL), in turn, is determined by applying the closed-loop error term E(CL) to a saturation function as graphically depicted in FIG. 7. The saturation (limiting) point is scheduled as a function of the longitudinal velocity V x  as indicated by the successively increasing velocity values V x  (1), V x  (2) and V x  (3). This has the effect of reducing the closed-loop steering command D r  (CL) per unit closed-loop error with increasing vehicle speed, again contributing to high speed stability of the vehicle. 
     The closed-loop steering command D r  (CL) and the open-loop feedforward command D r  (OL) are differenced as indicated by the summing junction 68 to form a rear steering command D r  (CMD). The command D r  (CMD) is applied to the ACTUATOR which, in turn, positions the rear wheels 40, 42 accordingly. 
     Separation of the open-loop feedforward and closed-loop feedback control paths according to this invention permits the delay and authority properties of the paths to the separately controlled for optimum response. The result is a single system which achieves the benefits of both open-loop and closed-loop control. FIG. 8 illustrates the benefit of providing differential delay properties for the open-loop and closed-loop control paths; FIG. 9 illustrates the benefit of providing differential control authority for the open-loop and closed-loop control paths. 
     The solid trace in Graph B of FIG. 8 depicts the lateral velocity V y  response of the steering system of this invention to the generally sinusoidal driver steering input shown in Graph A. The control objective of the reference model is to maintain zero lateral velocity V y . In the closed-loop feedback control path, filtering of the driver steering input is desired for noise rejection; see co-pending application U.S. Ser. No. 211,731. However, such filtering in the open-loop feedforward control path would result in undesired lateral velocity excursions and phase lag, as indicated by the broken trace in Graph B. 
     In the control of this invention, however, the driver steering input is separately filtered as desired for the open-loop feedforward and the closed-loop feedback control paths. Substantial filtering of the steering input is provided (FILTER 60) in the closed-loop control path as above to yield the desired noise rejection characteristic. However, little or no filtering is provided (FILTER 61) in the open-loop control path; this minimizes the lateral velocity excursions and phase-lag, as indicted by the solid trace in Graph B. In such case, a minimal open-loop filter (FILTER 61) would approximate the response of a mechanical linkage between the front and rear steering. Thus, the noise rejection characteristic of closed-loop control and the lateral velocity response characteristic of open-loop control are both achieved in a single system. 
     The graphs of FIG. 9 show that the closed-loop authority may be scheduled independent of the open-loop control path while still achieving the desired open-loop response characteristics. The trace 70 of Graph B depicts a yaw velocity disturbance, due to a wind gust for example. The trace 72 of Graph A represents a typical driver steering response to the disturbance. The traces 74 and 75 of Graphs B and C represent the yaw and lateral velocity responses of a system having a relatively low authority closed-loop control path; the traces 76 and 77 represent the yaw and lateral velocity responses of a system having a relatively high authority closed-loop control path. In each case, the substantially unfiltered open-loop control path results in a relatively low excursion, in-phase lateral velocity response, as indicated by the traces 75 and 77. This is consistent with the solid trace example of FIG. 8. 
     In the system having a relatively low authority closed-loop control path, a relatively lengthy period of time is required to correct the yaw disturbance, as indicated by the trace 74 in Graph B. By increasing the closed-loop authority, the yaw disturbance is corrected much more quickly, as indicated by the trace 76 in Graph B. Due to the separation of the open-loop and closed-loop control paths, the relatively low excursion, in-phase lateral velocity response is retained substantially intact, as indicated by the traces 75 and 77. In the illustrated embodiment, the closed-loop authority is scheduled relatively high to achieve the performance of trace 76, but is decreased with increasing longitudinal velocity of the vehicle, as seen in FIG. 7. 
     The flow diagram of FIG. 10 represents computer program instructions executed by the computer based control unit 30 in carrying out the control of this invention. The INITIALIZATION block 80 represents a series of instructions executed at the initiation of each period of vehicle operation for initializing the various registers, input counters and flags used in connection with the control of this invention. Thereafter, the instruction blocks 82-92 are repeatedly and sequentially executed as indicated by the flow lines and the return line 94. 
     The instruction block 82 serves to read and condition the various input signals including the longitudinal velocity V x , the front wheel steering angle D f , the actual yaw velocity r, and the actual lateral or slip velocity V y . As indicated in FIG. 1, such signals are supplied to the control unit 30 via lines 34, 52, 50 and 48. 
     The instruction block 84 pertains to the open-loop feedforward function designated by the OPEN-LOOP CONTROLLER 66 in FIG. 2. The performance of such function comprises the steps of determining the open-loop gain ratio OLGR as a function of the longitudinal velocity V x , and computing the open-loop feedforward command D r  (CMD) as a product of the measured front steering angle D f  and the term OLGR. 
     The instruction block 86 pertains to the front steering angle filter function designated by the FILTER 60 in FIG. 2. This involves the determination of coefficients F1 and F2, the computation of the gain factor GF, and the updating of the filter output D f  &#39; according to the product of the steering angle change and the computed gain factor GF. On initialization of the control, the instructions designated by the block 80 initially set the filtered front steering value D f  &#39; to zero. 
     The instruction block 88 pertains to the reference model function designated by the REFERENCE MODEL MAP 62 in FIG. 2. The reference model inputs include the filtered front steering angle D f  &#39;, the vehicle longitudinal velocity V x , and the open-loop feedforward steering command D r  (OL). Based on such inputs, the reference model maps the reference (desired) yaw and lateral velocity values r(des), V y  (des). 
     The instruction block 90 pertains to the closed-loop control function designated by the CLOSED-LOOP CONTROLLER block 66 of FIG. 2. As indicated at block 90, this involves the determination of the coefficients F3 and F4, and the computation of the closed-loop error term E(CL) and steering command D r  (CL). 
     The instruction block 92 performs the function of summing junction 68 of FIG. 2. It computes a rear steer command D r  (CMD) according to the difference between the closed-loop steering command D r  (CL) and the open-loop feedforward steering command D r  (OL), and outputs the command D r  (CMD) to motor 36 as represented by the ACTUATOR in FIG. 2. 
     While this invention has been illustrated in reference to the illustrated embodiment, it will be understood that the scope of the present invention is not limited thereto. The use of the driver steering angle filter 60, for example, is unnecessary to a mechanization of the present invention. Moreover, various modifications to the illustrated embodiment may occur to those skilled in the art, and it should be understood that systems incorporating such modifications may also fall within the scope of this invention, which is defined by the appended claims.