METHOD FOR CONTROLLING A HYDROSTATIC DRIVE

Abstract

A method for controlling a hydrostatic drive, which has a driving engine, a hydraulic pump coupled to the driving engine and a hydraulic motor coupled to the hydraulic pump by way of a pressurized hydraulic work line, includes calculating a manipulated variable vector comprising at least one manipulated variable for the hydrostatic drive based on (i) an output torque setpoint value for a torque on a secondary shaft driven by the hydraulic motor, (ii) a rotational speed and torque of the driving engine emerging from a predetermined operating point characteristic for the driving engine, and (iii) volumetric and mechanical losses of at least one adjuster unit comprising the hydraulic pump and the hydraulic motor. The manipulated variable vector is used to control the hydrostatic drive.

Claims

1. A method for controlling a hydrostatic drive, which has a driving engine, a hydraulic pump coupled to the driving engine, and a hydraulic motor coupled to the hydraulic pump by way of a pressurized hydraulic work line, the method comprising: calculating a manipulated variable vector comprising at least one manipulated variable for the hydrostatic drive based on (i) an output torque setpoint value for a torque on a secondary shaft driven by the hydraulic motor, the secondary shaft rotating at a secondary shaft rotational speed, (ii) a rotational speed and torque of the driving engine emerging from a predetermined operating point characteristic for the driving engine, and (iii) volumetric and mechanical losses of at least one adjuster unit comprising the hydraulic pump and the hydraulic motor; and using the calculated manipulated variable vector to control the hydrostatic drive.

2. The method according to claim 1, further comprising: calculating the manipulated variable vector based further on at least one manipulated variable constraint of the at least one manipulated variable.

3. The method according to claim 1, further comprising: determining a static feedforward control component of the calculated manipulated variable vector by solving an optimization problem for minimizing a stationary power loss as a consequence of the volumetric and mechanical losses of the at least one adjuster unit while maintaining the rotational speed and torque of the driving engine emerging from the predetermined operating point characteristic for the driving engine.

4. The method according to claim 3, further comprising: determining a characteristic map by solving the optimization problem depending on the output torque setpoint value and on the secondary shaft rotational speed, wherein the characteristic map has a number of work points.

5. The method according to claim 1, further comprising: determining a dynamic feedforward control component of the calculated manipulated variable vector depending on a temporal change of a setpoint state based on a pressure in the pressurized hydraulic work line and/or the secondary shaft rotational speed of the secondary shaft.

6. The method according to claim 5, wherein the manipulated variable vector has a regulator component, which compensates system deviations between the setpoint state and an actual state that is based on the pressure in the pressurized hydraulic work line and/or the secondary shaft rotational speed of the secondary shaft.

7. The method according to claim 6, further comprising: determining the regulator component based on a specification of a desired error dynamics with suitable regulator parameters.

8. The method according to claim 1, wherein the predetermined operating point characteristic is predetermined based on a line of optimal efficiencies and/or depending on a full-load curve.

9. The method according to claim 1, wherein the at least one manipulated variable for the hydrostatic drive comprises a manipulated variable that influences a transmission ratio between the hydraulic pump and the hydraulic motor and/or the torque of the driving engine.

10. The method according to claim 9, wherein the at least one manipulated variable influencing the transmission ratio between the hydraulic pump and the hydraulic motor comprises an adjustable volume of the at least one adjuster unit.

11. The method according to claim 1, further comprising: ascertaining the volumetric and the mechanical losses of the at least one adjuster unit based on stationary measurements in the form of polynomial ansatz functions depending on a pressure in the pressurized hydraulic work line, an adjustment degree, and a rotational angle speed of the at least one adjuster unit.

12. The method according to claim 1, wherein the hydrostatic drive has a power-split transmission with a mechanical power branch and/or a travel drive.

13. The method according to claim 1, wherein a computational unit carries out the method.

14. The method according to claim 13, wherein a computer program prompts the computational unit to carry out the method when the computer program is executed on the computational unit.

15. The method according to claim 14, wherein a machine-readable storage medium has the computer program stored thereon.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] FIG. 1 schematically shows a model of a power split drivetrain with a combustion engine, planetary transmission and hydraulic adjuster units.

[0019] FIG. 2 shows the basic structure of a control loop according to a preferred embodiment of the disclosure.

[0020] FIG. 3 shows a typical torque map of a combustion engine.

[0021] FIG. 4 shows manipulated variables arising according to a preferred embodiment of the disclosure, as a function of the travel speed.

[0022] FIG. 5 shows graphs illustrating an acceleration process of a drivetrain actuated according to a preferred embodiment of the disclosure.

DETAILED DESCRIPTION

[0023] FIG. 1 schematically shows a model of a power split drivetrain 100, as may underlie the disclosure. By way of example, the drivetrain 100 is a traveling drivetrain and has a driving engine embodied as a combustion engine 110, for example, which is followed by a power split transmission that is embodied here as a planetary transmission 120. The power split transmission has a secondary shaft 121 for a hydrostatic power branch and a secondary shaft 122 for a mechanical power branch.

[0024] The secondary shaft 122 is connected to one or more wheels 151 by way of a transmission and a secondary shaft 150.

[0025] The secondary shaft 121 is connected via a transmission to a hydraulic pump 130 that is embodied as an adjuster unit with an adjustable capacity V.sub.1. The hydraulic pump 130 is connected to the hydraulic motor 140 that is embodied as an adjuster unit with adjustable displacement volume V.sub.2 via a high-pressure line 132 (secured by means of a pressure release valve 131) and via a low-pressure line (with a low-pressure reservoir or tank 133). By way of a transmission, the hydraulic motor 140 is likewise connected to the secondary shaft 150.

[0026] Overall, a drive torque M.sub.w emerges at the secondary shaft 150 by specifying the drive torque M.sub.m of the driving engine 110 and the adjustable volumes V.sub.1, V.sub.2 of the pump 130 and of the motor 140, respectively.

[0027] For the purposes of actuating the hydrostatic drive by specifying the manipulated variables, use can be made of a control loop scheme 200, in particular a computer implemented control loop scheme, according to a preferred embodiment of the disclosure, as illustrated schematically in FIG. 2. The control loop scheme has a control member 210 and the controlled system 220.

[0028] A driver desired torque M.sub.w.sup.d, which is supplied to the control member 210, serves as a setpoint variable. The control member is configured to calculate and output a manipulated variable vector u.sup.d comprising setpoint values for the adjustment degrees and the driving engine torque u.sup.d=[.sub.1.sup.d,.sub.2.sup.d,M.sub.m.sup.d] from the driver desired torque M.sub.w.sup.d and the secondary shaft rotational speed co, fed back from the controlled system 220.

[0029] Essentially, this is based on a quasi-static feedforward control by a feedforward control member 201, which is configured to calculate and output a manipulated variable vector of the quasi-static feedforward control u*=[.sub.1*,.sub.2*,M.sub.m*(W.sub.m*)]T from the driver desired torque M.sub.w.sup.d and the secondary shaft rotational speed .sub.w.

[0030] According to a preferred embodiment of the disclosure, the feedforward control member 201 is furthermore configured to calculate and output a manipulated variable vector u.sup. of a dynamic feedforward control from the driver desired torque M.sub.w.sup.d and the secondary shaft rotational speed (b said manipulated variable vector forming the manipulated variable vector u.sup.ff of the feedforward control together with the manipulated variable vector u* of the quasi-static feedforward control. As a result of additionally taking account of a dynamic feedforward control, the response to setpoint changes, i.e. the reaction of the feedback control to a change in the setpoint value, is improved, while the quasi-static component contributes the necessary manipulated variable for the stationary case.

[0031] According to a further preferred embodiment of the disclosure, the control member 210 also has a regulating member 202 which is configured to calculate and output a manipulated variable vector u.sup.fb of the feedback control from a system deviation between a setpoint state z* and an actual state z comprising high-pressure p.sub.h and drive rotational speed .sub.m. The manipulated variable vector u.sup.fb of the feedback control forms the manipulated variable vector u.sup.d=u.sup.ff+u.sup.fb together with the manipulated variable vector u.sup.ff of the feedforward control. This improves the disturbance behavior, i.e. the reaction of the feedback control to disturbances.

[0032] A preferred embodiment of a corresponding method is described below with reference to the figures.

Modeling

[0033] A model of the drivetrain that captures the substantially dynamic processes in the system forms the basis of the regulator design. Modeling of the power split drivetrain according to FIG. 1 is considered in an exemplary manner below. The two hydraulic adjuster units 130 and 140 are embodied as axial piston machines of swash plate type construction and are denoted as AKM1 and AKM2, respectively in the following. Their high-pressure-side coupling is modeled as a constant hydraulic volume V.sub.h. Hence, the dynamics of the high-pressure emerges as

[00001]$\begin{array}{cc}\frac{d}{\mathrm{dt}}.Math.p_h=\frac{}{V_h}.Math.\left(q_1+q_2\right),& \left(1\right)\end{array}$

where is the bulk modulus of the hydraulic liquid and q.sub.1 and q.sub.2 are the volumetric flows of AKM1 and AKM2.

[0034] The low-pressure dynamics can be neglected on account of the large volume of the low-pressure reservoir 133. Hence, {dot over (p)}.sub.n0 applies and p.sub.n=0 can be set without loss of generality.

[0035] AKM1 and AKM2 are advantageously modeled with losses, as a result of which the volumetric flows q.sub.i in (1) and the torques M.sub.i are given in the form

q.sub.i=V.sub.i.sub.i.sub.iq.sub.i,v(.sub.i,p.sub.h,.sub.i),(2a)

M.sub.i=V.sub.ip.sub.h.sub.iM.sub.i,v(.sub.i,p.sub.h,.sub.i),(2b)

where i=1, 2 and V.sub.i is the maximum adjustment volume per radian achieved for the adjustment degree .sub.i=1.

[0036] The volumetric losses q.sub.i,v and the hydromechanical losses M.sub.i,v of the adjuster units are approximated on the basis of stationary measurements in the form of suitable polynomial ansatz functions of the operating variables adjustment degree .sub.i, pressure p.sub.h and rotational angle speed .sub.i.

[0037] The kinematics of the drivetrain are modeled in correspondence with the mechanical equivalent circuit diagram according to FIG. 1. The planetary transmission 120 has three connection shafts, wherein the input shaft (left, rotational angle speed .sub.m) is coupled directly to the driving engine 110. The output shafts 121, 122 (right) are coupled by constant transmission ratios i.sub.1 and i.sub.w to AKM1 (rotational angle speed .sub.1) and the secondary shaft (rotational angle speed .sub.w), respectively. The kinematic constraint (Willis equation)

i.sub.1.sub.1=i.sub.0i.sub.w.sub.w+(1i.sub.0).sub.m(3)

describes the coupling between the three connection shafts of the planetary transmission, wherein i.sub.0 denotes the gear ratio between the two output shafts 121, 122 when the input shaft is at rest (.sub.m=0).

[0038] If use is made of the two independent rotational angle speeds .sub.m and .sub.w, it is possible to use (3) to specify the rotational angle speeds of AKM1 and AKM2:

.sub.1=i.sub.1.sub.w+i.sub.1m.sub.m(4a)

.sub.2=i.sub.2.sub.w,(4b)

with i.sub.1w=i.sub.0iw/i.sub.1, i.sub.1m=(1i.sub.0)/i.sub.1 and the transmission ratio 1.sub.2 between AKM2 and secondary shaft 150.

[0039] In order to derive the equations of motion, the assumption is made that all rotational inertia of the drivetrain (gear wheels, shafts, drive wheels, etc.) can be reduced into the three moments of inertia J.sub.m, J.sub.1 and J.sub.w of FIG. 1. The kinetic energy of this system is T=(m.sub.vv.sub.v.sup.2+J.sub.m.sub.m.sup.2+J.sub.1.sub.1.sup.2+J.sub.w.sub.w.sup.2), where m.sub.v is the vehicle mass and v.sub.v=.sub.wr.sub.w (wheel radius r.sub.w) is the vehicle speed.

[0040] If (4) is taken into account, the equations of motion emerge as

[00002]$\begin{array}{cc}\left[\begin{array}{cc}{I}_m& I_{\mathrm{mw}}\\ I_{\mathrm{mw}}& I_w\end{array}\right].Math.\frac{d}{\mathrm{dt}}\left[\frac{{}_m}{{}_w}\right]=\left[\begin{array}{c}{i}_{1.Math..Math.m}.Math.M_1+M_m\\ i_{1.Math..Math.w}.Math.M_1+i_2.Math.M_2-M_e\end{array}\right],& \left(5\right)\end{array}$

wherein the positive definite mass matrix on the left-hand side of (5) has the constant entries I.sub.m=i.sub.1m.sup.2J.sub.1+J.sub.m, I.sub.mw=i.sub.1mi.sub.1wJ.sub.1 and I.sub.w+i.sub.1w.sup.2J.sub.1+J.sub.w+m.sub.vr.sub.w.sup.2. The generalized forces on the right-hand side of (5) contain the torques M.sub.1 and M.sub.2 of AKM1 and AKM2 according to (2b) and the torque M.sub.m of the driving engine 110.

[0041] An external force F.sub.e that acts on the vehicle center of mass in the longitudinal direction (e.g., air resistance and rolling resistance, downgrade force) is modeled as an external torque M.sub.e=r.sub.wF.sub.e.

[0042] The system variable to be regulated is given by the drive torque M.sub.w, the setpoint value of which is predetermined by the driver by way of the position of the accelerator pedal (driver desired torque M.sub.w.sup.d). In order to calculate M.sub.w, {dot over ()}.sub.m is eliminated from (5) and the following is obtained:

I.sub.e{dot over ()}.sub.w=M.sub.wM.sub.e,(6)

where I.sub.e=I.sub.wI.sub.mw.sup.2/I.sub.m is the equivalent moment of inertia, and the drive torque is given by

[00003]$\begin{array}{cc}{M}_w=i_{1.Math..Math.w}.Math.M_1+i_2.Math.M_2-\frac{I_{\mathrm{mw}}}{I_m}.Math.\left(i_{1.Math..Math.m}.Math.M_1+M_m\right).& \left(7\right)\end{array}$

[0043] Taking account of (2) and (4), differential equations (1) and (5) are written in the state space representation

{dot over (x)}=f(x,u),(8)

with the state x=[p.sub.h,.sub.m,.sub.w].sup.T, the input u=[.sub.1,.sub.2,M.sub.m].sup.T and the output y=M.sub.w according to (7) to be regulated.

[0044] In the considered system, subordinate regulators are preferably used for the adjustment degree and the drive torque of the motor, which update the input u of (8) according to the desired input u.sup.d=[.sub.1.sup.d,.sub.2.sup.d,M.sub.m.sup.d]. Here, the desired input u.sup.d forms the manipulated variable for the regulation strategy developed below.

[0045] By way of example, the dynamics of the subordinate control loops can be approximated by linear models in the time or frequency domain. The manipulated variable limits

u.sup.u.sup.du.sup.+(9)

take account of the limit in the adjustment degrees |.sub.i|1, i=1, 2 and the torque limit 0M.sub.mM.sub.m.sup.+(.sub.m) of the driving engine 110. Here, the maximum torque of the driving engine 110 is given by the full-load curve M.sub.m.sup.+(.sub.m) thereof; see FIG. 3.

Generating Ideal Work Points

[0046] For a driver desired torque M.sub.w.sup.d specified at a rotational angle speed co, of the drive shaft 150, the following three nonlinear equations are obtained from the stationary condition 0=f(x,u) of (8) and from taking account of M.sub.e=M.sub.w=M.sub.w.sup.d according to (6):

0=i.sub.1m(V.sub.1.sub.1p.sub.h+M.sub.1,v)+M.sub.m

0=i.sub.1w(V.sub.1.sub.1p.sub.hM.sub.1,v)+i.sub.2(V.sub.2.sub.2p.sub.hM.sub.2,v)M.sub.w.sup.d

0=V.sub.1.sub.1.sub.1+q.sub.1,v+V.sub.2.sub.2.sub.2+q.sub.2,v.(10)

[0047] Hence, for specified pairs (M.sub.w.sup.d,.sub.w), two degrees of freedom are available for determining the five unknown variables .sub.1, .sub.2, M.sub.m, .sub.m and p.sub.h.

[0048] The first of these two degrees of freedom is set by the requirement of operating the driving engine 110 in a stationary fashion on the predetermined operating point characteristic (operation line). Here, the predetermined operating point characteristic is approximated in the form of a functional relationship M.sub.m=M.sub.m*(.sub.m) in the rotational speed torque map; see FIG. 3.

[0049] The remaining degree of freedom is set by virtue of the fact that stationary power loss P.sub.v=M.sub.m.sub.mM.sub.w.sup.d.sub.w, in the hydraulic adjuster units 130, 140 as a consequence of volumetric and mechanical losses is minimized. To this end, the vector w=[p.sub.h, .sub.m, .sub.1, .sub.2].sup.T of the optimization variables is defined and the following optimization problem is solved:

min.sub.wP.sub.v=M.sub.m.sub.mM.sub.w.sup.d.sub.w(11a)

with the constraint of (10) and M.sub.m=M.sub.m*(.sub.m)(11b)

w.sup.ww.sup.+(11c)

[0050] The optimal solution w* of the static optimization problem (11) defines a map of ideal work points for predetermined pairs (M.sub.w.sup.d,.sub.w); see FIG. 4.

[0051] The ideal work points are characterized in that the stationary power loss P, of the hydraulic adjuster units is minimized and the driving engine 110 is operated along the operation line M.sub.m=M.sub.m*(.sub.m). With the inequality constraints (11c), the admissible operating ranges of the optimization variables are taken into account.

Multivariable Feedback Control

[0052] For the purposes of realizing time-varying torque prescriptions M.sub.w.sup.d(t), use is preferably made of a MIMO (multiple input multiple output) feedback control strategy according to FIG. 2.

[0053] Here, the map

*:(M.sub.w.sup.d,.sub.w).fwdarw.(u*,z*)(12)

determined from the solution of (11) forms the quasi-static feedforward control u*=[.sub.1*,.sub.2*,M.sub.m*(.sub.m*)].sup.T and the setpoint trajectory z*=[p.sub.h*,.sub.m*].sup.T for pressure and rotational speed.

[0054] An improvement to the response to setpoint changes is obtained by the control law

u.sup.d=u*u.sup.+u.sup.fb,(13)

by means of which the quasi-static feedforward control u* is extended by the component u.sup. of a dynamic feedforward control and the component u.sup.fb of a stabilizing regulator.

[0055] For the regulator design, the dynamics of the subordinate regulators are neglected, as result of which u=u.sup.d applies. Moreover, the term I.sub.mw{dot over ()}.sub.w<<1 in the first line of (5) is neglected and the reduced model

=S(z)u(z,u),(14)

for the regulator design is obtained, with the state z=[p.sub.h, .sub.m].sup.T, the input u=[.sub.1, .sub.2, M.sub.m].sup.T, the vector

[00004]$\begin{array}{cc}\left(z,u\right)=\left[\frac{}{V_h}.Math.\left(q_{1,v}+q_{2,v}\right),\frac{i_{1.Math..Math.m}}{I_m}.Math.M_{1,v}\right],& \left(15\right)\end{array}$

and the matrix

[00005]$\begin{array}{cc}S\left(z\right)=\left[\begin{array}{ccc}-\frac{}{V_h}.Math.V_1.Math.{}_1& -\frac{}{V_h}.Math.V_2.Math.{}_2& 0\\ \frac{i_{1.Math..Math.m}}{I_m}.Math.V_1.Math.p_h& 0& \frac{1}{I_m}\end{array}\right],& \left(16\right)\end{array}$

[0056] With .sub.i, i=1, 2 according to (4).

[0057] The output rotational speed .sub.w is considered to be an externally predetermined (measurable) variable and, in terms of its dynamics, is not considered in the regulator design.

Dynamic Feedforward Control

[0058] If u=u*+u.sup. is inserted into (14),

*=S(z*)(u*+u.sup.)(z*,u*+u.sup.),(17)

is obtained for the dynamic feedforward control u.sup..

[0059] With the stationary condition

0=S(z*)u*(z*,u*),(18)

and the simplification (z*,u*+u.sup.)(z*,u*), the underdetermined linear system of equations

S(z*)u.sup.=*,(19)

is obtained for calculating u.sup..

[0060] The degree of freedom in the selection of u.sup. is set on the basis of the solution to the following optimization problem:

[00006]$\begin{array}{cc}\underset{u^{}}{\min }.Math.\frac{1}{2}.Math.{\left(u^{}-c\right)}^T.Math.W\left(u^{}-c\right)& \left(20.Math.a\right)\\ \mathrm{with}.Math..Math.\mathrm{the}.Math..Math.\mathrm{constraint}.Math..Math.\mathrm{of}.Math..Math.S\left(z^{*}\right).Math.u^{}={\stackrel{.}{z}}^{*}.& \left(20.Math.b\right)\end{array}$

[0061] Which manipulated variables should preferably be used for the dynamic feedforward control can be influenced in a targeted manner by way of the positive definite weighting matrix W in the cost function (20a). Furthermore, c denotes a desired offset of u.sup..

[0062] The conditions (19) are taken into account in the form of the linear equation secondary conditions (20b) in the optimization problem. The optimization problem (20) has the optimal solution

[00007]$\begin{array}{cc}{u}^{}=c+\underset{\underset{S^{\#}}{}}{W^{-1}.Math.{S^T\left({\mathrm{SW}}^{-1}.Math.S^T\right)}^{-1}}.Math.\left({\stackrel{.}{z}}^{*}-\mathrm{Sc}\right),& \left(21\right)\end{array}$

with the weighted pseudoinverse S.sup.#=W.sup.1S.sup.T(SW.sup.1S.sup.T).sup.1 of S=S(z*).

[0063] For highly dynamic torque requirements, it may be the case that the optimal solution according to (21) contravenes the constraints

.sup.u.sup..sup.+(22)

as a consequence of the manipulated variable limits (9), where .sup.=u.sup.u* and .sup.+=u.sup.+u*.

[0064] In order to take account of (22) when calculating u.sup., use can be made of e.g. an algorithm that can be found in the literature under the term redistributed pseudoinverse; see, e.g., W. S. Levine. The Control Handbook, Second Edition: Control System Applications. CRC Press, Boca Raton, Fla., 2010.

[0065] Here, (21) with c=0 is used if none of the constraints (22) is contravened. Otherwise, i.e., if u.sub.i.sup.<.sub.i.sup. or u.sub.i.sup.>.sub.i.sup.+ for i{1,2,3}, the offset c.sub.i=max{min{u.sub.i.sup.,.sub.i.sup.+},.sub.i.sup.} is introduced for c, by means of which the respective manipulated variable is set to its limit. The limited dynamic feedforward control is finally obtained from

u.sup.=c+W.sup.1S.sub.i.sup.T(S.sub.iW.sup.1S.sub.i.sup.T).sup.1(*Sc),(23)

where S.sub.i denotes a matrix that arises from the i-th column in S being replaced by a zero vector. The weighting matrix is predetermined in diagonal form; i.e., W=diag(W.sub.1.sup.d,W.sub.2.sup.d,W.sub.3.sup.d), with W.sub.1.sup.=W.sub.2.sup.=1 and W.sub.3.sup.<<1.

Stabilizing Regulator

[0066] With u=u*+u.sup.+u.sup.fb according to (13), the following error system

=S(z*+e)u(z*+e,u)*(24)

is obtained for the error e=zz*. Under the assumption of (z*+e,u)(z*,u*) and if (18) and (19) are taken into account, the error system (24) simplifies as

=Aeu.sub.1.sup.ff+S(z*+e)u.sup.fb,(25)

with the matrix

[00008]$\begin{array}{cc}A=\left[\begin{array}{cc}0& -\frac{}{V_h}.Math.i_{1.Math..Math.m}.Math.V_1\\ \frac{1}{I_m}.Math.i_{1.Math..Math.m}.Math.V_1& 0\end{array}\right].& \left(26\right)\end{array}$

[0067] Here, the relationship

S(z*e)u=S(z*)u+Aeu.sub.1(27)

for S according to (16) is taken into account.

[0068] On account of the comparatively slow dynamics of the subordinate regulators, a decoupling regulator is not suitable for stabilizing the error system (25). Instead, the stationary relationship e=1/u.sub.1A.sup.1S(z*)u.sup.fb between e and e is considered, which is obtained from (25) for =0 and taking account of (27). If e=v is required, the relationship

S(z*v)u.sup.fb=Avu.sub.1.sup.ff(28)

is obtained for determining the regulator component u.sup.fb.

[0069] Stationary decoupling of the error system is obtained by the prescription v=K.sub.iedtK.sub.pe, with the diagonal matrices K.sub.i and K.sub.p. The entries of these matrices are determined experimentally on the basis of simulation scenarios. In order to ensure sufficient damping of the error system over the entire operating range (see FIG. 4), the weighting of the matrix K.sub.p is increased for .sub.1*.fwdarw.0. In order to fix the degree of freedom when determining u.sup.fb from (28), the same algorithm is used as when determining the feedforward control component. The inequality limits to be taken into account are

u.sup.u*u.sup.u.sup.fbu.sup.+u*u.sup.(29)

on account of (9) and (13) in this case.

[0070] In contrast to the feedforward control, a weighting matrix in diagonal form with the entries W.sub.1.sup.fb=W.sub.2.sup.fb=1 and W.sub.3.sup.fb>>1 is suitable.

[0071] FIG. 3 shows a typical torque map, in the form of a rotational speed-torque map, of a combustion engine. The maximum torque is given by the measured data points (x in the figure) of the full-load curve 301. By way of example, the maximum torque M.sup.+(.sub.m) can be presented analytically by way of cubic splines. Moreover, FIG. 3 shows the typical curve of the operation line 302 of a driving engine 110. The operation line connects work points (o in the figure) in the rotational speed-torque map of the driving engine 110 at which the efficiency for a desired mechanical power M.sub.i.sub.m (power hyperbolas) is maximized. An approximate representation M.sub.m*(.sub.m) of the operation line in analytic form can be effectuated, for example by M.sub.m*(.sub.m)=k.sub.0+k.sub.1 tan h(k.sub.2.sub.mk.sub.3), with suitable parameters k.sub.i, i=0, . . . , 3.

[0072] FIG. 4 shows maps of the work points defined by the optimal solution of the optimization problem (11) in the case of a normalized representation of pressure p.sub.h and torque (legend) as a function of the vehicle speed v.sub.v=.sub.vr.sub.w along the abscissa. The dependence on the driver desired torque M.sub.w.sup.d is expressed in the different graphs. The limits of the optimization variables illustrated by dashed lines denote the admissible operating ranges of pressure p.sub.h, rotational speed .sub.m and the two adjustment degrees .sub.1, .sub.2. Here, an actuation reserve for the regulator is provided in the shown example by restricting the adjustment degrees to |.sub.i|0.9.

[0073] FIG. 5 shows simulated graphs for illustrating an acceleration process of a drivetrain actuated according to a preferred embodiment of the disclosure, with a normalized illustration of pressure p.sub.h, drive torque M.sub.w and torque M.sub.m of the driving engine 110.

[0074] In detail, FIG. 5a shows the curve of the rotational speed .sub.m of the driving engine, FIG. 5b shows adjustment degrees .sub.1 (bottom, smaller than zero) and .sub.2 (top, greater than zero), FIG. 5b shows the normalized high pressure p.sub.h, FIG. 5d shows the torque M.sub.m of the driving engine 110, FIG. 5e shows the drive torque M.sub.w and FIG. 5f shows the driving speed v.sub.v.

[0075] Here, FIGS. 5a, 5c and 5e plot setpoint values (thick line) and simulated (actual) values (thin line), in each case over time t. FIG. 5f only shows simulated (actual) values since no setpoint values exist for the driving speed. In FIGS. 5b and 5d, setpoint values emerging from the purely quasi-static feedforward control u* are denoted by thick lines and setpoint values emerging overall (u.sup.d) from the feedforward control and the regulation are denoted by thin lines. Limits that are present are denoted by dashed lines.

[0076] In order to examine a realistic scenario, sensors for the rotational speeds and the pressure in the simulation had noise applied thereto. In order to exhibit the robustness of the feedback control strategy, the losses of the adjuster units are simulated with deviations from the nominal value of up to 30%. Taking account of the manipulated variable constraints in the dynamic feedforward control guarantees very good stabilization of the pressure at the setpoint value, even in the case of high accelerations of the driving engine 110, in which the maximum torque is typically demanded.

[0077] It is clear from FIG. 5a that the rotational speed .sub.n, of the driving engine directly follows the setpoint value in the simulation.

[0078] The observed control error in the output torque M.sub.w in FIG. 5e is mainly due to the system and cannot, as a matter of principle, be compensated by the feedback control. On the one hand, an abrupt increase in the output torque requires such a strong acceleration of the driving machine 110 that, briefly, a considerable part of the power fed in is applied to accelerate the driving machine 110, thus having a slump in the output torque as a consequence. On the other hand, the power of the driving machine 110 is restricted by the maximum admissible rotational speed (e.g., 6000 min.sup.1 in FIG. 5a). If the demanded power exceeds the maximum power, the output torque deviates from the setpoint value, even in the case of a constant curve of the driver desired torque.