Method for dynamic load simulation by means of parallel kinematics

Abstract

The invention relates to a method for dynamic load simulation, wherein loads are specified by target signals and applied to a test object by a parallel kinematic excitation unit via an end effector, including the following operations: measuring loads at a contact point (200), comparing the measured loads with the target signals (300), and determining target pressures (400) for individual actuators of the parallel kinematic excitation unit for applying the target signals by use of a control algorithm (F.sub.q,ref). This provides a method for dynamic load simulation that reduces the time and cost expenditure compared to previously known methods and at the same time enables hardware-in-the-loop simulations to be used.

Claims

1. A method for dynamic load simulation comprising the steps of: applying a target signal (300) to a test object using a parallel kinematic excitation unit with an end effector wherein the parallel kinematic excitation unit comprises individual actuators; specifying a load by use of the target signal; measuring the load at a contact point (200) with a force measuring wheel; comparing the measured load to the applied target signal (300) with a control unit; determining target pressures (400) for the individual actuators of the parallel kinematic excitation unit by use of a control algorithm (F.sub.q,ref); applying the target signals (300) to the end effector by means of a control of the target pressures (400) for the actuators determined by the control algorithm
F.sub.q,ref=J.sup.T(z).Math.[M(z).Math.z″+C(z,z′).Math.z′+g(z)+u.sub.fl,F], wherein u.sub.fl,F is a new system input for force control, J.sup.T (z) is a transposed Jacobian matrix, M (z) is a mass matrix, z is a position vector, C (z, z′).Math.z′ is a vector of generalized centrifugal and Coriolis forces and g (z) is a vector of generalized weight forces; and applying the determined target pressures (400) to the target signal (300).

2. The method according to claim 1, wherein a new system input (u.sub.fl,F) for force control is formed as follows:
u.sub.fl,F=τ+R.sub.F(τ.sub.ref−τ)+R.sub.F,D(τ′.sub.ref−τ′), wherein τ, τ′, τ.sub.ref and τ′.sub.ref are load vectors that act between the end effector and the test object and R.sub.F and R.sub.F,D are control parameters formed as matrices.

3. The method according to claim 2, wherein the control parameters R.sub.F and R.sub.F,D are determined such that a control error differential equation converges to zero.

4. A method for dynamic load simulation, comprising the steps of: applying a target signal (300) to a test object using a parallel kinematic excitation unit with an end effector wherein the parallel kinematic excitation unit comprises individual actuators; specifying a load by use of the target signal; measuring the load at a contact point (200) with a force measuring wheel; comparing the measured load to the applied target signal (300) with a control unit; determining target pressures (400) for the individual actuators of the parallel kinematic excitation unit by use of a control algorithm (F.sub.q,ref); applying the target signals (300) to the end effector by means of a control of the target pressures (400) for the actuators determined by the control algorithm (F.sub.q,ref); wherein a direct force control is achieved by the following control algorithm (F.sub.q,ref):
F.sub.q,ref=F.sub.q+J.sup.T(z).Math.[R.sub.F(τ.sub.ref−τ)+R.sub.F,D(τ′.sub.ref−τ′)], wherein F.sub.q are the forces applied to the end effector by the cylinders of the parallel kinematic excitation unit, J.sup.T (z) is a transposed Jacobian matrix, τ, τ′, τ.sub.ref and τ′.sub.ref are the load vectors that act between the end effector and the test object, and R.sub.F and R.sub.F,D are control parameters designed as matrices.

5. A method for dynamic load simulation comprising the steps of: applying a target signal (300) to a test object using a parallel kinematic excitation unit with an end effector wherein the parallel kinematic excitation unit comprises individual actuators; specifying a load by use of the target signal; measuring the load at a contact point (200) with a force measuring wheel; comparing the measured load to the applied target signal (300) with a control unit; determining target pressures (400) for the individual actuators of the parallel kinematic excitation unit by use of a control algorithm (F.sub.q,ref); applying the target signals (300) to the end effector by means of a control of the target pressures (400) for the actuators determined by the control algorithm (F.sub.q,ref); wherein the control algorithm (F.sub.q,ref) is carried out according to the following equation:
F.sub.q,ref=J.sup.T(z).Math.[C(z,z′).Math.z′+g(z)+(1−S).Math.(M(z).Math.u.sub.fl,P+τ)+S.Math.(M(z).Math.z″+u.sub.fl,F)], wherein J.sup.T (z) is a transposed Jacobian matrix, C (z, z′).Math.z′ is a vector of generalized centrifugal and Coriolis forces, z is a position vector, g (z) is a vector of generalized weight forces, S is a selection matrix, M (z) is a mass matrix, τ is a load vector between the end effector and the test object, and u.sub.fl,P and u.sub.fl,F are the new system inputs for position and force control.

6. The method according to any one of the preceding claims, wherein a compensation controller, a general transmission element, a PID controller, or a PD controller with an additional sliding mode component is used for force and/or position control.

7. The method according to any one of claims 5 to 6, wherein a means for compensating disturbance variables and/or for adding disturbance variables is used, which is designed such that a disturbance behavior of the control of the target pressures is reduced, wherein disturbance variables to be compensated can be measured or determined directly before the disturbance variables are compensated.

8. The method according to any one of claims 5 to 7, wherein a measured non-linear kinematics and/or dynamics of the test object is determined and used as a precontrol.

9. The method according to any one of the preceding claims, wherein a phase and/or amplitude drop in a band-limited force control loop is compensated by a phase and amplitude correction.

10. The method according to any one of the preceding claims, wherein the control algorithm (F.sub.q,ref) is selected such that a model-based compensation of the non-linearities takes place according to the following equation:
F.sub.q,ref=J.sup.T(z).Math.[M(z).Math.u.sub.fl,P+C(z,z′).Math.z′+g(z)+τ], wherein J.sup.T (z) is a transposed Jacobian matrix, M (z) is a mass matrix, u.sub.fl,P is a new system input for force control, z is a position vector, C (z, z′).Math.z′ is a vector of generalized centrifugal and Coriolis forces, g (z) is a vector of generalized weight forces and τ is a load vector between the end effector and the test object.

11. The method according to any one of the preceding claims, wherein the control algorithm (F.sub.q,ref) is selected such that the target loads by the actuators are used as the variable (τ.sub.q,ref) to be iterated:
F.sub.q,ref=J.sup.T(z).Math.τ.sub.q,ref, wherein τ.sub.q,ref are the target loads between the end effector and the test object and J.sup.T (z) is a transposed Jacobian matrix.

12. The method according to any one of the preceding claims, wherein the parallel kinematic excitation unit is a hexapod.

13. The method according to any one of the preceding claims, wherein the measuring of loads at the contact point is carried out by a force measuring wheel.

14. The method according to any one of the preceding claims, wherein the test object is a vehicle axle.

15. The method according to any one of the preceding claims, characterized by defining target signals (100) for loads to be applied to the contact point between the end effector and the test object, wherein this is implemented prior to the step of measuring loads at the contact point (200).

16. The method according to any one of the preceding claims, characterized by applying the target signals (500) to the end effector by means of a control of the target pressures for the actuators determined by the control algorithm (F.sub.q,ref), wherein this is implemented subsequently to the step of determining the target pressures (400) for individual actuators of the parallel kinematic excitation unit.

17. System for dynamic load simulation between a parallel kinematic excitation unit and a test object, comprising components suitable for carrying out method steps according to at least one of the preceding claims.

Description

(1) In the Drawing:

(2) FIG. 1 shows a flow chart of a method according to the prior art;

(3) FIG. 2 shows a flow chart of a first embodiment of the invention;

(4) FIG. 3 shows a flow chart of a second embodiment of the invention;

(5) FIG. 4 shows a flow chart of a third embodiment of the invention; and

(6) FIG. 5 schematically shows a perspective view of a parallel kinematic excitation unit designed as a hexapod.

(7) FIG. 1 shows a flow chart according to the prior art for the simulation of target signals from previously known test rigs. As a rule, one or more linear actuators, such as hydraulic cylinders, are used for each degree of freedom to be activated. The high bandwidth and quality required for simulating the target signals is achieved in such test rigs with the help of an iterative learning process. With the help of the learning process, the control inputs of the excitation units, so-called drive signals, are systematically changed until the target signals are simulated sufficiently well. In this process, the parameters of the control are usually not changed.

(8) Initially, according to FIG. 1, target signals (100) are set by recording load data. The next step is a system identification (110). This means that an iteration takes place until a sufficiently good, linear model is provided. This is followed by a target simulation (120). This corresponds to an iteration until the test loads achieved reflect the target signals sufficiently well. Finally, the drive signals (130) are obtained as control signals for the actuators.

(9) So far, the high bandwidths required have only been achieved for the axle test by use of the previously known procedure. The tedious learning process must be carried out again for other target signals. The reasons for this approach are, among others, the structural design and the narrow control bandwidth of the actuators used. In addition, there are the strongly non-linear characteristics of the test object, in particular the vehicle axle, and mostly also the actuators used with regard to kinematics and dynamics. As a result of aging and wear of the vehicle axle mentioned as an example, the iterated drive signals no longer lead to a satisfactory imaging quality of the target signals in the case of frequently repeated, constant test maneuvers. As a result, the control must be learned again.

(10) In contrast, FIG. 2 shows a flow chart according to a first embodiment as a control method for dynamic load simulation. Here, a load (target signal) is applied to a test object by a parallel kinematic excitation unit (1) with an end effector, including the following operations: Defining target signals (100) for loads to be applied to a contact point between the end effector and the test object, measuring loads at the contact point (200), comparing the measured loads with the target signals (300), determining target pressures (400) for individual actuators of the parallel kinematic excitation unit (1) for applying the target signals by use of a control algorithm (F.sub.q,ref), and applying the target signals (500) to the end effector by means of a control of the target pressures for the actuators determined by the control algorithm (F.sub.q,ref).

(11) In general, the dynamic behavior of the end effector, in particular with a parallel kinematic excitation unit designed as a hexapod, can be described by the following equation of motion: M (z).Math.z″+C (z, z′).Math.z′+g (z)=J.sup.−T (z).Math.F.sub.q−τ (equation [I]). Here, M (z) is a mass matrix, C (z, z′).Math.z′ is a vector of generalized centrifugal and Coriolis forces, g (z) is a vector of generalized weight forces, J.sup.−T(z) is a negatively transposed Jacobian matrix, z is a position vector, F.sub.q are the forces applied to the end effector by the cylinders of the parallel kinematic excitation unit and ti is a load vector between the end effector and the test object.

(12) For position control, based on the equation of motion, the following approach is initially used to compensate for non-linearities:

(13) F.sub.q,ref=J.sup.T (z).Math.[M (z).Math.u.sub.fl,P+C (z, z′).Math.z′+g (z)+τ] (equation [II]). With an ideal model and ideal measurement and observation, the overall system thus behaves like a double integrator in every spatial direction with regard to the new system input u.sub.fl,P. The individual displacements and rotations are decoupled. Based on this compensation approach, the position control is achieved based on the formula

(14) u.sub.fl,P=z″.sub.ref+R.sub.D (z′.sub.ref−z′)+R.sub.P (z.sub.ref−z) (equation [III]), wherein modifications thereof are possible. By inserting the equation for position control (F.sub.q,ref) into the equation of motion and u.sub.fl,P into the resulting equation:

(15) z″=z″.sub.ref+R.sub.D (z′.sub.ref−z′)+R.sub.D (z.sub.ref−z) (equation [IV]) and from this the error differential equation Δz″+R.sub.D Δz′+R.sub.P Δz=0 (equation [V]) is obtained by rearranging. With a sufficiently precise model and a suitable choice of the controller gains R.sub.D and R.sub.P, a globally asymptotically stable position control loop results.

(16) Step (400) shown in FIG. 2 with respect to the use of the control algorithm (F.sub.q,ref) comprises at least one directionally decoupled variable (u.sub.fl,P, u.sub.fl,F). In particular, a directionally decoupled variable is a new system input.

(17) The new system input (u.sub.fl,F) is preferably formed as follows:
u.sub.fl,F=τ+R.sub.F(τ.sub.ref−τ)+R.sub.F,D(τ′.sub.ref−τ′)  (equation [VII]),

(18) wherein τ, τ′, τ.sub.ref and τ′.sub.ref are load vectors that act between the end effector and the test object and R.sub.F and R.sub.F,D are control parameters formed as matrices. Here, the control parameters R.sub.F and R.sub.F,D are determined in particular in such a way that they converge to zero as a first order error differential equation. This preferably means that the first order error differential equation converges to zero as follows:
R.sub.F,DΔτ′+R.sub.FΔτ=0  (equation [VIII]).

(19) The following control algorithm (F.sub.q,ref) is preferably used for step (400):
F.sub.q,ref=J.sup.T(z).Math.[M(z).Math.z″+C(z,z′).Math.z′+g(z)+u.sub.fl,F]  (equation [VI]),

(20) wherein u.sub.fl,F is a new system input for force control, J.sup.T (z) is a transposed Jacobian matrix, M (z) is a mass matrix, z is a position vector, C (z, z′).Math.z′ is a vector of generalized centrifugal and Coriolis forces and g (z) is a vector of generalized weight forces.

(21) This equation is chosen to control the forces and moments between the end effector and the test object, wherein, moreover, a new system input u.sub.fl,F is chosen. u.sub.fl,F can be interpreted as a force and moment vector between the end effector and the environment. Based on this, the aforementioned force control u.sub.fl,F=τ+R.sub.F (τ.sub.ref−τ)+R.sub.F,D(τ′.sub.ref−τ′) (equation [VII]) can be formulated. Modifications of this force control are possible. By inserting the control algorithm (F.sub.q,ref) into the aforementioned equation of motion M (z).Math.z″+C (z, z′).Math.z′+g (z)=J.sup.−T (z).Math.F.sub.q−τ (Equation [I]) and by inserting the force control u.sub.fl,F=τ+R.sub.F (τ.sub.ref−τ)+R.sub.F,D (τ′.sub.ref−τ′) (equation [VII]) in the equation just developed by use of the control algorithm (F.sub.q,ref) and the equation of motion the aforementioned differential error equation R.sub.F,D Δτ′+R.sub.F Δτ=0 (equation [VIII]) is obtained. With a suitable choice of the matrices R.sub.F,D and R.sub.F, the first order error differential equation converges to zero. As a result, the actual forces or moments converge against the target forces or moments.

(22) Alternatively, a force control in step (400′) according to FIG. 3 can also be realized by the following control rule: F.sub.q,ref=F.sub.q+J.sup.T (z).Math.[R.sub.F (τ.sub.ref−τ)+R.sub.F,D (τ′.sub.ref−τ′)](equation [IX]). Here, F.sub.q are the forces applied to the end effector by the cylinders of the parallel kinematic excitation unit, J.sup.T (z) is a transposed Jacobian matrix, τ, τ′, τ.sub.ref and τ′.sub.ref are load vectors that act between the end effector and the test object, and R.sub.F and R.sub.F,D are control parameters designed as matrices. In this way, a direct force control is achieved.

(23) Another alternative of steps (400) and (400′) to step (400″) is appreciated in FIG. 4, wherein a choice has to be made between force and position control for each degree of freedom. This is achieved by appropriately adding a selection matrix S=diag(s.sub.i). With s.sub.i=1 for force-controlled degrees of freedom and s.sub.i=0 for position-controlled degrees of freedom, the hybrid force/position control approach results, for example, from equations [II], [III], [VI] and [VIII]:

(24) F.sub.q,ref=J.sup.T (z).Math.[C (z, z′).Math.z′+g (z)+(1−S).Math.(M (z).Math.u.sub.fl,P+τ)+S.Math.(M (z).Math.z″+u.sub.fl,F)] (equation [X]), wherein J.sup.T (z) is a transposed Jacobian matrix, C (z, z′).Math.z′ is a vector of generalized centrifugal and Coriolis forces, z is a position vector, g (z) is a vector of generalized weight forces, S is a selection matrix, M (z) is a mass matrix, τ is a load vector between the end effector and the test object and u.sub.fl,P and u.sub.fl,F are new system inputs for the position and force control.

(25) By using parallel kinematics and the possible model-based compensation of the non-linearities according to equation [III], the decoupled variables can be used directly as optimization variables for the iteration, that is, as drive signals. The negative effects of the non-linearities of the excitation unit (1) and the mutual coupling of the individual actuators are thereby greatly reduced.

(26) Alternatively, it can be provided that the control algorithm (F.sub.q,ref) is selected in such a way that the target loads by the actuators are used as the variable (τ.sub.q,ref) to be iterated: F.sub.q,ref=J.sup.T (z).Math.τ.sub.q,ref (equation [XI]), wherein J.sup.T (z) is a transposed Jacobian matrix. Here, τ.sub.q,ref are the target loads between the end effector and the test object and J.sup.T (z) is the transposed Jacobian matrix.

(27) As shown by way of example in FIG. 5, the parallel kinematic excitation unit (1) is a hexapod. It is preferred, but not recognizable in FIG. 5, that the measurement of loads at the contact point is carried out by a force measuring wheel. It is also preferred that the test object is a vehicle axle. Thus, FIG. 5 discloses at least partially a system for dynamic load simulation between a parallel kinematic excitation unit and a test object, at least comprising components according to the preceding description.

LIST OF REFERENCE SYMBOLS

(28) 1 parallel kinematic excitation unit 100 setting target signals 110 system identification according to the state of the art 120 target simulation according to the state of the art 130 drive signals according to the state of the art 200 measuring loads at the contact point 300 comparing the measured loads with the target signals 400 determining target pressures by use of a first control algorithm 400′ determining target pressures by use of an alternative control algorithm 400″ determining target pressures by use of a further alternative control algorithm 500 applying target signals 555 individual actuators