WO2005091091A2

WO2005091091A2 - A method and system for controlling semiactive suspensions, for example for vehicles, and corresponding structure and computer-program product

Info

Publication number: WO2005091091A2
Application number: PCT/IB2005/000622
Authority: WO
Inventors: Massimo Canale; Mario Milanese; Carlo Novara
Original assignee: Modelway S.R.L.
Priority date: 2004-03-16
Filing date: 2005-03-08
Publication date: 2005-09-29
Also published as: WO2005091091A8; ITTO20040173A1; WO2005091091A3

Abstract

A system for controlling a semiactive suspension for vehicles (10), or vibrating structures in general, controls (U) a force of reaction exerted by the suspension (A) as a function of a set (P) of input variables. The system comprises at least one electronic control unit (14, 16) configured for controlling (U) the force of reaction as a function of the set (P) of input variables with a control law of a predictive type. In a preferred way, the system is configured for installation on board a structure (10). provided with said suspension and is configured for implementing an approximation (ƒ) of the control law (ƒ) generated, once and for all, in a remote position with respect to the structure (10). The system is thus configurable for controlling (U) the suspension in real time using the aforesaid approximation (f) of the control law (f). without any significant constraints in terms. of processing capacity and speed, but fully preserving the advantages of the predictive control law.

Description

^λA method and system for controlling semiactive suspensions, for example for vehicles, and corresponding structure and computer-program product"

Field of the invention The present invention relates to techniques for controlling suspensions. The invention has been developed with particular attention paid to its possible use for controlling semiactive suspensions of vehicles, such as for example motor vehicles. Reference to this particular sector of application is not, however, to be understood as in any way limiting the invention, which is in itself applicable also to suspensions of a semiactive type used in other sectors, such as, for example, the engineering of civil structures (suspensions for buildings, bridges and various structures which may be subject to variable loads . Description of the related art In a motor vehicle, suspensions serve several conflicting purposes, such as, in particular, ensuring road-holding, vehicle-handling and passenger comfort. Broadly speaking, three basic categories of suspensions may be identified: passive suspensions, active suspensions, and semiactive suspensions. Passive suspensions are made up of springs and dampers with pre-set functional parameters. They present limitations due to the fact that they are only able to store or dissipate energy and that the parameters must be designed, making a choice that will provide a balancing between the conflicting needs of road-holding, vehicle-handling and passenger comfort, in the presence of a wide variability in the road conditions and the kind of routes along which the vehicle is required to travel . Active suspensions are not only able to store or dissipate energy, but also to introduce energy into the system. Active suspensions are hence able to ensure optimal balancing between the conflicting requirements and consequently to achieve excellent levels of performance. The main drawback of active suspensions regards the high costs of the device and the high levels of energy consumption involved, said costs and said consumption levels being linked, for example, to the use of a dynamo-electric machine as active element of the suspension. Semiactive suspensions are provided with dampers capable of modulating the capacity for dissipating energy by varying the damping coefficient in a controllable way. For motor vehicles, they represent the best compromise between the performance that can be achieved and the costs and consumption levels of the device. For this reason, they are already available on various recently designed cars. For a more detailed examination of the problem addressed herein, the quarter-car scheme of Figure 1(a) is to be considered (i.e., the scheme corresponding to the suspension associated, for example, to one of the four wheels of a motor vehicle - not represented as a whole in the figure) . In the scheme, m_c is the sprung mass (one quarter of the weight of chassis, engine and passengers) , m is the unsprung mass (wheel, tyre, axle, etc.), z^c , z^w , z^r are the vertical positions of the sprung mass, the unsprung mass, and the road profile, respectively, k and β are the stiffness and damping coefficients of the tyre, k is the stiffness coefficient of the spring of the suspension, and u is the force exerted by the damper. R represents, instead, the road profile. In the semiactive-suspension systems, the force exerted by the damper is u = β\z^w - z^cJ , where the damping coefficient β is rendered variable as a function of a control variable t(t) . The most widely used method for achieving this consists in controlling, by means of valves, the flow of the fluid with which damping is obtained in a traditional hydraulic damper. In particular, this is achieved using a servomechanism driven by a current i(t) . If the required force u(t) is assumed to be determined at a given instant t, determination of the current i(t) can be obtained using the 'force-current' map M=M,-(V_WC), which yields the dependence of the force u(t) upon the current i(t) and the relative velocity between the sprung mass and the unsprung mass

Figure 2 shows a typical force-current map for commercially available dampers. For reasons of simplicity, only the values of the extreme curves ^u,_mJ^v _Wc ) ^{and u}imax(^vwc ) ^are 9^iveι1- ^τhe hatched region represents the values of forces that can be exerted by the semiactive damper. Consequently, the strategy of control of semiactive suspensions must calculate the force u(t) for optimizing the level of performance of the suspension, taking, however, into account the passivity constraint of the damper: ^uimin

— ^u — ^uimax ^yvwc ) If the force-current map is taken into account, said constraint can be written in a more detailed form as: ( 1 )

Currently, two strategies are used for generating laws of control of the force u(t) which are able to take into account this passivity constraint: the On-Off Skyhook strategy and the Clipped strategy. The On-Off Skyhook strategy seeks to emulate the behaviour of an ideal damping system in which the sprung mass is "hooked" to the sky via a passive damper. This leads to the control law:

The Clipped strategy consists in determining first of all a control u * without taking into account the passivity constraint. This can be done using one of the available control techniques without saturation constraints (LQ, H_∞, etc.). The control u(t) effectively provided at each instant t is the value that is as similar as possible to w *(t) . This leads to the control l w:

As may be noted, both strategies seek to optimize the suspension performance, taking, however, into account instant by instant the passivity constraint. In this way, the dynamic evolution of the suspension- vehicle system, in which the effects of inertia are considerable, is not taken into account. This can cause significant limitations in the performance that can be achieved as compared to the strategy forming the subject of the present invention, which is able to optimize the performance of the suspension, taking into account the passivity constraints and the dynamic evolution of the different variables involved (accelerations, velocities, positions) . Object and summary of the invention The object of the present invention is to overcome the limitations inherent in the solutions according to the known art examined previously. According to the present invention, the above purpose is achieved by means of a method having the characteristics recalled in the ensuing claims. The present invention relates also to a corresponding system, to a vehicle equipped with such a system, as well as to a computer-program product which can be loaded into the memory of at least one computer (for example, at the level of a control card or a so-called "electronic control unit") comprising portions of software code for implementing the aforesaid method. As used herein, the reference to such a computer-program product is to be deemed equivalent to the reference to a medium which can be read by a computer and contains instructions for controlling a computer system for the purpose of co-ordinating development of the method according to the invention. Reference to "at least one computer" is aimed at highlighting the possibility that the present invention is implemented even in a distributed, i.e., modular, way. Brief description of the annexed drawings The invention will now be described, purely by way of non-limiting example, with reference to the figures of the annexed plate of drawings, in which: - Figures 1 and 2 have already been described previously; Figure 3 is a schematic illustration of a vehicle equipped with a suspension-control system of the type described herein; Figure 4 is a functional block diagram corresponding to part of the suspension-control system of the type described herein; and - Figures 5 to 13 are diagrams representing the performance of the system described herein, viewed possibly in a comparative way with the performance of known systems. Detailed description of exemplary embodiments of the invention In Figure 3, the reference number 10 designates as a whole a vehicle, such as a motor vehicle equipped with a suspension-control system of a semiactive type. The vehicle 10 hence represents, in general, any structure which can be equipped with a suspension- control system of the type described herein. Vehicles of this type are known also in the form of currently manufactured motor vehicles. Likewise known, in general terms, is the architecture of the control system in question. Associated to the suspension of each (or of at least some) of the wheels 12 of the vehicle 10 is a control module 14, and the various control modules 14 come under a central processing unit 16 (of the type usually referred to as "electronic control unit") . Of course, there may also be hypothesized embodiments in which the same function is achieved in a distributed way, hence without envisaging the presence of a central processing unit. As exemplified in Figure 4, each of the modules 14 receives at input the signals produced by a set of sensors that detect various parameters representing the conditions of operation of the suspension system. The sensors and signals in question are designated as a whole by 18 and P, respectively. With the exception of what is said expressly in what follows, the characteristics of the aforesaid sensors and signals are to be deemed in themselves known. Starting from the signals P, processed according to the modalities described in greater detail in what follows, the system performs a function of suspension control. In what follows, said function (designated as a whole by U in Figure 4) will be assumed as being carried out chiefly through the control of the force of reaction exerted by the damper A of the suspension. This can occur (also in this case according to criteria in themselves known) by driving, for example via a current signal, an actuator which regulates selectively the net section of the ports for passage (seepage) of the damping fluid between the different chambers of the damper, or else by resorting to solutions that exploit effects of a magnetorheological type: in any case, the specific constructional details of the controlled semiactive suspension are not in themselves of determining importance for the solution described herein. In this connection, the dynamics of the quarter- car model represented in Figure 1 is described by the following

These equations can be rewritten in the form of state equations as: A_cx + B_cu where x = [z^c z^w z^c i^w]e R⁴. The control methodology adopted by the solution described herein uses a model in discrete-time state equations. Hence, choosing a sampling interval T , a discrete-time model can be obtained as: x_t+l = Ax_t + Bu_t (2 ) where x_t and u_t are the discrete-time state and the discrete-time input variable and: A = e^λ<τ

The solution described herein sets itself the task of finding a control law w, that optimizes the performance of the vehicle as regards comfort and road- holding and at the same time satisfies the passivity constraint (1) and the dynamic equations (2) . The performance criteria to be optimized include sprung-mass acceleration z^c , suspension deflection z^c - z^w) , and wheel acceleration z^w . These performance criteria can be included in an objective function J . If we define the prediction horizon N , the control horizon N c < N p„ and the positive-definite matrices

Q = Q^T x and R = R^T >- 0 (the performance weights), the objective function can be expressed by a quadratic function: J[U, x_l{, , N_p,N_c)= ∑ x _+k[l Qx_t+kll + ∑ «,₊*_!/ Rw,₊*„ where x_{t+k t} is the state predicted by the model (2) , given the input sequence u_lf ,...,u_t+k_ _f and the "initial" state x_lf = x_t , and U = [w_r|,, u_t+Vt, —, i_l+N ^f is the control sequence to be optimized. If N_c < N_p , the following choice is made: u_{l+k l} = u_l+Nc__{]l , k = N_C,N_C + l,...,N_p -1. The passivity constraints can be written as linear inequalities on the control force u and on the state variables x . In particular, the relative velocity v_r = x^w -x^c between the sprung mass and the unsprung mass can be written as the product Cx , where C = [θO-ll]. Hence, for each control instant t + k \ t such that k = 0,1,...,N_C -1 , the control action u_t+kf must be calculated taking into account the following constraints:

if Cx_t+kll ≥ 0

On the basis of the above premises, it is possible to identify a control law of a predictive type, for example, of an MPC (Model Predictive Control) type. This result can be obtained, for example, by applying the following receding-horizon strategy: 1. At instant t , measure x_t . 2. Solve the quadratic problem:

subject to the conditions expressed by the relation (3) given previously. 3. Apply the first element of the solution sequence U to the optimization problem as the actual control action: u_t =κ._|, . 4. Repeat the entire procedure at the instant t +1 . The passivity constraints are defined in a different way according to the sign of the predicted relative velocity v_{r l+k]l} = Cx_t+k]k of the suspension. Consequently, the sign of v_r(+i|( introduces, within the interval between the instant t and the prediction horizon, the need to change the constraints to be satisfied. This situation can be formulated as a predictive control scheme with logic constraints, the solutions of which can be calculated via mixed techniques of integer programming . However attractive it may be from the standpoint of performance, the procedure described proves to be, at least thus far, hard to implement in real time at the level of an electronic control unit, such as the processing unit 16, designed to be installed on board a currently manufactured motor vehicle (or any other structure equipped with a semiactive suspension) . In fact, the procedure in question calls for the solution of the optimization problem (4) at each sampling instant, a task that is difficult to perform on line at the sampling times (which are in the region of 0.001-0.005 s) that electronic control units of a motor-vehicle type require, said control units having been developed and configured to accomplish processing tasks which are usually much more modest. The above difficulty can be overcome as described in what follows. The MPC control u, is a non-linear function of the state x, , i.e.:

The function / is not known explicitly, but a certain number of values of f ^χ) ^an be known via an off-line MPC procedure, starting from the initial conditions x_k, k = \,...,M . We thus have : ** = /(**). k = \,...,M From these values x_k,ii_k k = l,-..,M , an approximation / of / is obtained. This can be achieved using techniques of function approximation, starting from a certain finite number of correspondences. Said processing can be carried out in different ways (in themselves known) , for example with the use of neural networks . In a possible example of embodiment, the procedure is as follows. The following functions are defined:

/„ (*, Y)( ^min (ύ_k + γ \\x -%J)

The following is calculated: γ^* = γ:f_u(x_k ,γi)>nύf_k, k=\,...,M γ

The estimate of / is hence given by:

Assume, for reasons of simplicity, that the points x_k are chosen on a uniform grid of a rectangular region

N e R⁴ within which the state x = z z^w z^c z^w \ can evolve. We hence have : lim M→∞ f{x)-f{^χ) ^~ 0, Vx e

Furthermore, for any given M , the estimation error f (x)-f(x) is limited as follows: f⁽*⁾-π ^≤ [fΛ^χSH{^χS)^~_ Vx e N This makes it possible to verify whether yields a sufficient approximation of / or else whether a higher value of M is necessary. The MPC can thus be implemented on line, envisaging that the electronic control unit 16 will calculate, on the basis of the signals received from the periphery of the system, the function f(x,) at each sampling instant: In other words, by operating in this way, it is possible to calculate the aforesaid approximation by solving M optimization problems, as expressed by Equation (4) , off line, hence without being subjected to any particular constraints either in terms of processing power available or in terms of processing times . The approximation thus calculated can hence be provided on board the vehicle 10, in practice, for example, storing in a memory associated to the electronic control unit 16 the approximation of the control law / , an approximation that has been generated, once and for all, in a remote position with respect to the vehicle 10. The electronic control unit 16 may hence control in real time, on board the vehicle, the force of reaction of the dampers A of the suspensions using the approximation instead of the control law f proper. Persons skilled in the sector will understand that said processing task can be conveniently fulfilled, within the electronic control unit 16, by a dedicated processor (of any known type) , as well as with a processor of a general-purpose type programmed

(according to criteria in themselves known) with a corresponding computer-program product. The operating method described requires the knowledge of the state x = z^c z^w z^c z^wΛ at each sampling instant. The most common configuration of sensors for semiactive suspensions consists in accelerometers that measure z^c and z^w , since the measurement of z^c,z^w,z^c,z^w calls for excessively costly sensors. What follows hence shows how to estimate the state x , starting from the measurements supplied by the accelerometers. The standard method consists in using an observer (Kalman filter) which employs the equations of the system (2) for estimating the state using the measurements of the accelerometers. However, in this way the accuracy can be seriously impaired by the nonexact knowledge of the physical parameters m_c,m_w,k , etc . A method for obtaining a robust estimate of the state x the accuracy of which does not depend upon the values of said parameters is described in what follows. Let α = z^cz^M'] and y = [z'^'z^,,'J . The kinematic relations between positions, velocities and accelerations are described by the following dynamic equations, which are independent of the physical parameters: x = A x + B„a + B_jd , (5) y = C_ax + D_dd where :

0 0 1 0 0 0 0 1 A. 0 0 0 0 0 0 0 0

1 0 0 0 0 1 0 0

In equation (5), rfeR⁴ is a vector that represents the uncertainties on the values of the accelerations a and positions . The estimate x of x is obtained by means of the observer H_∞ of equation: x = [A_a-QC_a ^τ]x + B_aa ₊ QC_a ^τy (6) where Q is the solution of the equation:

Qξ + A_aQ + B_dB_d ^T -Q(c C_a-y-²l)Q = 0

and γeR is the minimum value for which A-Q C_a ^τC_a-γ-²l)Q = Q is Hurwitz. If no position measurements are available, in equation (6) a given reference value is used, for example v=0. The observer (a filter of an H_∞ type) in question can be conveniently implemented, according to criteria in themselves known, at the level of the electronic control unit 16 (or, possibly, even at the level of the peripheral unit 14) . Presented in what follows are the simulation results obtained by applying the solution described herein. The design method has been applied to the quarter-car suspension model illustrated in Figure 1(b) with the following values of the parameters : m_c = 396.25 kg; m_w = 40 kg; k =17200 Nlm; k_w =190000 Nlm; β_w =10000 Nslm.

The passivity constraint has been considered using the following parameters: β ~ β₄ = β_mn ~ 1500 Ns/m β = β₂ = β₅ = β_max = 5000 Ns/m a_t =0, ι = l,...,5. The problem of optimization involved was formulated taking into account the prediction and control horizons N_p = N_c = 10 and the following weight matrices in the quadratic cost functional J:

1000 0 0 0 0 10000 0 0 Q 0 0 1 0 0 0 0 1 R = 0.00001

The tests were conducted using "standard" profiles usually adopted in industrial tests. In particular, in order to verify the behaviour in different road and driving conditions, the profiles listed below were considered. - Random profile: this is a road with random profile driven along at a speed of 60 km/h. English-track profile: this is a road with irregularly spaced holes and bumps driven along at a speed of 60 km/h. - Motorway profile: this is a road with a smooth surface driven along at a speed of 140 km/h. The tests were conducted using a sampling time T = 1/512 s and a simulation time of 14 s for each road profile considered. The performance obtained with the MPC semiactive control strategy proposed herein was compared with that achieved by the On-Off Skyhook technique and by a Clipped technique. In particular, the Clipped technique considered was based upon an LQ controller, which uses the same quadratic cost functional J employed in the MPC design. In order to highlight the performance in terms of comfort that can be achieved by the design procedure proposed, the behaviour of the acceleration ϊ^c of the sprung mass was considered. Figures 5, 6 and 7 show the typical plots of the different accelerations of the sprung mass ϊ^c obtained using the MPC technique, the Skyhook control and the LQ-clipped strategy for the random profile, the English-track profile, and the motorway profile, respectively. From Figures 5, 6 and 7 there may readily be noted the significant reductions in the peak amplitudes that may be obtained with the proposed technique as compared to the Skyhook and LQ-Clipped techniques. Said reductions are particularly evident in the case of irregular road profiles, as in the cases of the random profile and the English-track profile. Furthermore, Figures 8, 9 and 10 show the typical behaviours of the accelerations of the unsprung mass. From an analysis of these figures, it may be noted that the plot of the acceleration jj^w is very similar for all three strategies considered (MPC, Skyhook and LQ- Clipped) . Finally, Figures 11, 12 and 13 show the typical plots obtained from the deflection of the suspension z^c -z^w , where it is possible to note a slight increase in the deflection obtained with the MPC technique as compared to the Skyhook and LQ-Clipped strategies. Tables 1, 2 and 3 compare the extreme peak values of the variables z^c , z^w , \ z^c -z^w \ and \ z^w -z^r \ obtained with the three design techniques used for each of the road profiles considered, namely, random profile, English-track profile, and motorway profile, respectively. Analysis of the results presented in the figures and in the tables highlights how the predictive

'technique described herein reduces significantly the peak values of the acceleration of the sprung mass, thus leading to an improvement in the characteristics of comfort of the suspension. In particular, it may readily be noted that for the random profile and for the English-track profile the extreme values of the acceleration peaks of the sprung mass have been reduced by approximately 50% and 60%, respectively. As regards the behaviour of the acceleration of the unsprung mass z " , it may be concluded that the three design techniques lead to levels of performance that are altogether similar. As regards the behaviour of the deflection of the suspension \ z^c -z^w \ , it may be noted that the MPC technique introduces a slight increase (less than 10%) in the peak values of deflection.

However, said increase is balanced by a decrease (higher than 10%) in the distance between the wheel (unsprung mass) and the ground \ z^w -z^r \ . Table 1 - Extreme peak values detected for the random profile

Table 2 - Extreme peak values detected for the English- track profile

Table 3 - Extreme peak values detected for the motorway profile

Consequently, without prejudice to the principle of the invention, the details of implementation and the embodiments may vary, even significantly, with respect to what is described and illustrated herein purely by way of non-limiting example, without thereby departing from the scope of the invention, as defined by the ensuing claims.

Claims

1 CLAIMS

1. A method for controlling a semiactive suspension by controlling (TJ) a force of reaction exerted by the suspension (A) as a function of a set

(P) of input variables, characterized in that it comprises the operation of controlling (U) said force of reaction as a function of said set (P) of input variables with a control law of a predictive type.

2. The method according to Claim 1, characterized in that it comprises the operation of using a control model in discrete-time state equations.

3. The method according to Claim 1 or Claim 2, characterized in that it comprises the operation of using a control model of an MPC type.

4. The method according to any one of the preceding claims, characterized in that it comprises the operation of defining an objective function of the control ( J ) , which includes at least one quantity chosen in the set consisting of: acceleration of the sprung mass ( z^c ) , deflection of the suspension z^c - z^w) , and acceleration of the unsprung mass (z^'w) .

5. The method according to any one of the preceding claims, characterized in that it comprises the operation of defining an objective function of the control ( J ) expressed by a quadratic function.

6. The method according to any one of the preceding claims, characterized in that it comprises the operation of imposing, in said suspension-control law, the passivity constraints as linear inequalities on said force of reaction («) and on at least one of the state variables of the system ( x ) .

1 . The method according to any one of the preceding claims, characterized in that it comprises the operation of imposing, in said suspension-control law, the passivity constraints in a different way according to the sign of the predicted relative velocity ( v_{r t+k}^_t = Cx_l+kϊk ) of the suspension.

8. The method according to any one of the preceding claims, characterized in that it comprises the operations of: - determining said control law ( u_t = (,)) as a state function (x, ) of the suspension; - generating an approximation ( f ) of said control law (/) starting from a set of points ( x_k ) chosen on a grid of a region in which said state ( x_t ) may evolve; and - controlling (U) said force of reaction as a function of said set (P) of input variables using said approximation ( ) of said control law (/).

9. The method according to Claim 8, characterized in that it comprises the operations of: making available on board a structure (10) provided with said suspension said approximation ( ) of said control law ( ), said approximation ( ) being generated in a remote position with respect to the structure (10) ; and controlling (U) in real time, on board the structure (10) , said force of reaction as a function of said set (P) of input variables using said approximation ( ) of said control law ( ).

10. The method according either Claim 8 or Claim 9, characterized in that said step of generating an approximation ( ) comprises the operations of: defining the functions: f {^χ> r) _t™3, (⁵ _* ⁺ \^x - ^χk II)

calculating; γ = inf γ /,,(- )≥"A=ι M generating an estimate of said control law (/) given by:

where / and are said control law and said approximation, respectively.

11. A method for controlling a semiactive suspension by controlling (U) a force of reaction exerted by the suspension (A) as a function of a set (P) of input variables which identify the suspension- system state ( x ) , in which: - said input variables comprise variables detected via an accelerometer ( z^c , z^w ) and variables ( z^c,z^w ) indicating parameters of position of the suspension; - said state is estimated via an observer (14, 16) ; and - where reliable values for said variables of position ( z^c,z^w ) are not available, the relative value in said observer is set at a given reference value, preferably zero.

12. The method according to Claim ₁₁, characterized in that said observer is a filter H applied to dynamic equations representing the kinematic relations between positions, velocities and accelerations of the structure.

13. A system for controlling a semiactive suspension by controlling (U) a force of reaction exerted by the suspension (A) as a function of a set (P) of input variables, characterized in that it comprises at least one electronic control unit (14, 16) configured for controlling (U) said force of reaction as a function of said set (P) of input variables with a control law of a predictive type.

14. The system according to Claim 13 , characterized in that said at least one electronic control unit (14, 16) is configured for implementing a control model in discrete-time state equations.

15. The system according to Claim 13 or Claim 14, characterized in that said at least one electronic control unit (14, 16) is configured for implementing a control model of an MPC type.

16. The system according to any one of the preceding Claims 13 to 15, characterized in that said at least one electronic control unit (14, 16) is configured for operating on the basis of an objective function of the control ( J ) , which includes at least one quantity chosen in the set consisting of: acceleration of the sprung mass ( z^c ) , deflection of the suspension [z^c - z^w] , and acceleration of the unsprung mass ( z^w ) .

17. The system according to any one of the preceding Claims 13 to 16, characterized in that said at least one electronic control unit (14, 16) is configured for operating on the basis of an objective function of the control ( J ) expressed by a quadratic function.

18. The system according to any one of the preceding Claims 13 to 17, characterized in that said at least one electronic control unit (14, 16) is configured for imposing, in said suspension-control law, the passivity constraints as linear inequalities on said force of reaction ( u ) and at least one of the state variables of the system ( ).

19. The system according to any oi-e of the preceding Claims 13 to 18, characterized i that said at least one electronic control unit (14, 16) is configured for imposing, in said suspension-control law, the passivity constraints in a different way according to the sign of the predicted relative velocity ( v__|/+A|, = Cx_tJ, ) of the suspension.

20. The system according to any one of the preceding Claims 13 to 19, characterized in that said at least one electronic control unit (14, 16) is configured for controlling (U) said force of reaction as a function of said set (P) of input variables using an approximation ( ) of said control law ( ) determined as state function ( x, ) of the suspension, said approximation being generated starting from a set of points ( x_k ) chosen on a grid of a region in which said state ( x_t ) may evolve.

21. The system according to Claim 20, characterized in that: - the system is configured for installation on board a structure (10) provided with said suspension; - the system is configured for implementing said approximation (/) of said control law i f ) , said approximation ( ) having been generated in a remote position with respect to the structure (10) ; and - the system is configured for controlling (U) in real time, on board the structure (10) , said force of reaction as a function of said set (P) of input variables using said approximation (/) of said control law (/) .

22. A system for controlling a semiactive suspension by controlling (TJ) a force of reaction exerted by the suspension (A) as a function of a set (P) of input variables which identify the suspension- system state (x), in which: - the system can be associated to a set of sensors (18) comprising accelerometer sensors, and said input variables comprise, in addition to variables detected via an accelerometer ( z° , z^w ) , variables ( z^c,z^w ) indicating parameters of position of the suspension; - the system comprises an observer (14, 16) for estimating said state; and - the observer is configured in such a way that, where reliable values for said variables of position ( z ,z^w ) are not available, the relative value in said observer is set at a given reference value, preferably zero.

23. The system according to Claim 22, characterized in that said observer (14, 16) is a filter H_∞ applied to dynamic equations representing the kinematic relations between positions, velocities and accelerations of the structure.

24. A structure (10) equipped with a system according to any one of Claims 13 to 23.

25. The structure according to Claim 24, in the form of a vehicle, such as a motor vehicle (10) .

26. A computer-program product loadable into the memory of at least one computer (16) and comprising software code portions for implementing the steps of the method according to any one of Claims 1 to 12.

27. A computer-program product loadable into the memory of at least one computer (16) and comprising software code portions for implementing said approximation ( ) of said control law (/) according to any one of Claims 8 to 10.