EP4062651B1 - Device for generating a control signal for an electrical system - Google Patents

Description

The present invention relates to a device for generating a control signal for an electrical system. The present invention also relates to an audio system comprising such a device. The present invention also relates to a related method.

Passivity describes the fact that a system cannot spontaneously create energy but only store and/or dissipate it. As an illustration, a network of resistors, diodes, coils or capacitors (linear or not) connected to a loudspeaker will modify the mechanical and acoustic behavior of the loudspeaker but without generating sustained oscillations (feedback effect) or instabilities . Passivity ensures this robustness. More generally, a passive physical system satisfies a power balance of the type dE(t)/dt= Pext(t)-Pdis(t) (temporal variation of the stored energy = power supplied from the outside - dissipated power) with a positive dissipated power Pdis (or zero in the conservative case).

In the case of complex servo-controls, the servo-controls are likely to be implemented in a real-time digital form, that is to say by means of on-board systems comprising analog-digital converters, electrical signal generators and a hardware digital calculator (in French “computer hardware”). The calculation of the servo signal is then rendered after a latency time, equivalent to a delay, which is here denoted T. Such a delay is inherent to any servo produced by digital hardware systems (microprocessor, DSP, micro-controller, FPGA) due to the time taken by the calculation.

However, the inclusion of a delay in a feedback loop is likely to deteriorate the passivity property and thus make the control ineffective or even cause its destabilization.

The document US 2010/318205 A1 (published December 16, 2010 ) describes a signal processing apparatus and method for the motional feedback of a loudspeaker. However, it does not describe the characteristic according to which a controllable component of a digital block is configured to generate a digital output signal based on a converted input signal and a modeling of a digital controller connected to a digital passive component having a second passive characteristic impedance, the value of the second characteristic impedance being chosen as a function of the value of a first characteristic impedance.

There is therefore a need for a device making it possible to control a system passively.

• une entrée pour un signal d'entrée en provenance du système électrique, le signal d'entrée étant un signal analogique représentatif d'une tension, respectivement d'un courant,
• une sortie pour le signal de commande, le signal de commande étant un signal analogique représentatif d'un courant, respectivement d'une tension, le signal de commande ayant une première composante et une deuxième composante,
• un bloc analogique connecté à l'entrée et à la sortie du dispositif de génération, le bloc analogique comprenant un circuit électrique comprenant un composant passif analogique ayant une première impédance caractéristique passive, un composant de mesure de tension, respectivement de courant, et un générateur de courant, respectivement de tension,
• un bloc numérique comprenant au moins un composant commandable numériquement,
• un convertisseur analogique-numérique connecté entre le bloc analogique et le bloc numérique, et
• un convertisseur numérique-analogique connecté entre le bloc analogique et le bloc numérique,

• le composant passif analogique du circuit électrique étant configuré pour générer la première composante du signal de commande et le générateur du circuit électrique étant configuré pour générer la deuxième composante du signal de commande, le circuit électrique étant configuré pour sommer la première et de la deuxième composante générées afin d'obtenir le signal de commande,
• le convertisseur analogique-numérique étant configuré pour convertir en numérique une mesure du signal d'entrée effectuée par le composant de mesure du bloc analogique pour obtenir un signal d'entrée converti,
• le composant commandable du bloc numérique étant configuré pour générer un signal de sortie numérique en fonction du signal d'entrée converti et d'une modélisation d'un contrôleur numérique connecté à un composant passif numérique ayant une deuxième impédance caractéristique passive, la valeur de la deuxième impédance caractéristique étant choisie en fonction de la valeur de la première impédance caractéristique,
• le convertisseur numérique-analogique étant configuré pour convertir en analogique le signal de sortie numérique pour obtenir une commande du générateur, la deuxième composante du signal de commande générée par le générateur étant fonction de la commande obtenue à partir du bloc numérique.

For this purpose, the present description relates to a device for generating a control signal for an electrical system, the generation device comprising:

• an input for an input signal coming from the electrical system, the input signal being an analog signal representative of a voltage, respectively of a current,
• an output for the control signal, the control signal being an analog signal representative of a current, respectively a voltage, the control signal having a first component and a second component,
• an analog block connected to the input and output of the generation device, the analog block comprising an electrical circuit comprising an analog passive component having a first passive characteristic impedance, a voltage or current measuring component, respectively, and a generator current, respectively voltage,
• a digital block comprising at least one digitally controllable component,
• an analog-to-digital converter connected between the analog block and the digital block, and
• a digital-analog converter connected between the analog block and the digital block,

• the analog passive component of the electrical circuit being configured to generate the first component of the control signal and the generator of the electrical circuit being configured to generate the second component of the control signal, the electrical circuit being configured to sum the first and the second components generated in order to obtain the control signal,
• the analog-digital converter being configured to convert into digital a measurement of the input signal carried out by the measurement component of the analog block to obtain a converted input signal,
• the controllable component of the digital block being configured to generate a digital output signal based on the converted input signal and a modeling of a digital controller connected to a digital passive component having a second passive characteristic impedance, the value of the second characteristic impedance being chosen as a function of the value of the first characteristic impedance,
• the digital-to-analog converter being configured to convert the digital output signal to analog to obtain control of the generator, the second component of the control signal generated by the generator being a function of the control obtained from the digital block.

• le composant passif analogique et le composant passif numérique sont de même nature ;
• chacun du composant passif analogique et du composant passif numérique est une résistance ;
• lorsque le signal d'entrée est représentatif d'une tension et le signal de commande est représentatif d'un courant, la deuxième impédance caractéristique est supérieure ou égale à la première impédance caractéristique, et
• lorsque le signal d'entrée est représentatif d'un courant et le signal de commande est représentatif d'une tension, la deuxième impédance caractéristique est inférieure ou égale à la première impédance caractéristique ;
• lorsque le signal d'entrée est représentatif d'une tension et le signal de commande est représentatif d'un courant, le composant de mesure est un composant de mesure de tension et le générateur est un générateur de courant, le composant passif analogique étant connecté en parallèle de l'entrée et de la sortie et en parallèle du générateur et du composant de mesure, et
• lorsque le signal d'entrée est représentatif d'un courant et le signal de commande est représentatif d'une tension, le composant de mesure est un composant de mesure de courant et le générateur est un générateur de tension, le composant passif analogique étant connecté en série avec le générateur et le composant de mesure entre l'entrée et la sortie ;
• lorsque le signal d'entrée est représentatif d'une tension et le signal de commande est représentatif d'un courant, la modélisation est une modélisation du contrôleur numérique connecté en série du composant passif numérique, et
• lorsque le signal d'entrée est représentatif d'un courant et le signal de commande est représentatif d'une tension, la modélisation est une modélisation du contrôleur numérique connecté en parallèle du composant passif numérique ;
• le composant commandable est configuré pour :
  • convertir le signal d'entrée converti en provenance du convertisseur analogique-numérique en un premier signal intermédiaire fonction de la deuxième impédance caractéristique et représentatif d'une onde de puissance,
  • convertir le premier signal intermédiaire en un deuxième signal intermédiaire fonction de la deuxième impédance caractéristique et représentatif d'une tension, respectivement d'un courant,
  • calculer un troisième signal intermédiaire en fonction du deuxième signal intermédiaire et de la modélisation,
  • convertir le troisième signal intermédiaire en un quatrième signal intermédiaire fonction de la deuxième impédance caractéristique et représentatif d'une onde de puissance, et
  • convertir le quatrième signal intermédiaire en le signal de sortie numérique du composant commandable en fonction de la deuxième impédance caractéristique, le quatrième signal intermédiaire étant représentatif d'une tension, respectivement d'un courant.
• le composant commandable 70 est choisi dans la liste constituée de : un microprocesseur, un processeur de signal numérique, un micro-contrôleur et un réseau de portes programmables.

According to other advantageous aspects, the generation device comprises one or more of the following characteristics, taken individually or in all technically possible combinations:

• the analog passive component and the digital passive component are of the same nature;
• each of the analog passive component and the digital passive component is a resistor;
• when the input signal is representative of a voltage and the control signal is representative of a current, the second characteristic impedance is greater than or equal to the first characteristic impedance, and
• when the input signal is representative of a current and the control signal is representative of a voltage, the second characteristic impedance is less than or equal to the first characteristic impedance;
• when the input signal is representative of a voltage and the control signal is representative of a current, the measurement component is a voltage measurement component and the generator is a current generator, the analog passive component being connected in parallel with the input and output and in parallel with the generator and the measuring component, and
• when the input signal is representative of a current and the control signal is representative of a voltage, the measurement component is a current measurement component and the generator is a voltage generator, the analog passive component being connected in series with the generator and the measuring component between the input and the output;
• when the input signal is representative of a voltage and the control signal is representative of a current, the modeling is a modeling of the digital controller connected in series of the digital passive component, and
• when the input signal is representative of a current and the control signal is representative of a voltage, the modeling is a modeling of the digital controller connected in parallel with the digital passive component;
• the controllable component is configured to:
  • convert the converted input signal coming from the analog-digital converter into a first intermediate signal depending on the second characteristic impedance and representative of a power wave,
  • convert the first intermediate signal into a second intermediate signal depending on the second characteristic impedance and representing a voltage, respectively a current,
  • calculate a third intermediate signal based on the second intermediate signal and the modeling,
  • convert the third intermediate signal into a fourth intermediate signal depending on the second characteristic impedance and representative of a power wave, and
  • convert the fourth intermediate signal into the digital output signal of the controllable component as a function of the second characteristic impedance, the fourth intermediate signal being representative of a voltage, respectively a current.
• the controllable component 70 is chosen from the list consisting of: a microprocessor, a digital signal processor, a micro-controller and an array of programmable gates.

The invention also relates to an audio system, such as a loudspeaker, comprising a device as described above.

• la réception d'un signal d'entrée en provenance du système électrique en entrée du dispositif de génération, le signal d'entrée étant un signal analogique représentatif d'une tension, respectivement d'un courant,
• la conversion en numérique d'une mesure du signal d'entrée effectuée par le composant de mesure du bloc analogique pour obtenir un signal d'entrée converti,
• la génération d'un signal de sortie numérique par le composant commandable du bloc numérique,
• la conversion en analogique du signal de sortie numérique pour obtenir une commande du générateur du circuit électrique,
• la génération de la première composante du signal de commande par le composant passif analogique du circuit électrique,
• la génération de la deuxième composante du signal de commande par le générateur du circuit électrique en fonction de la commande obtenue à partir du bloc numérique, et
• la somme de la première composante et de la deuxième composante générées par le circuit électrique pour obtenir le signal de commande.

The invention also relates to a method for generating a control signal for an electrical system from a generation device as described above, the method comprising:

• receiving an input signal from the electrical system at the input of the generation device, the input signal being an analog signal representative of a voltage, respectively a current,
• the digital conversion of a measurement of the input signal carried out by the measurement component of the analog block to obtain a converted input signal,
• generating a digital output signal by the controllable component of the digital block,
• converting the digital output signal into analog to obtain control of the generator of the electrical circuit,
• generating the first component of the control signal by the analog passive component of the electrical circuit,
• generating the second component of the control signal by the generator of the electrical circuit according to the command obtained from the digital block, and
• the sum of the first component and the second component generated by the electrical circuit to obtain the control signal.

• [Fig 1] figure 1, une représentation schématique d'une connexion directe entre un système physique S et un contrôleur numérique Sc,
• [Fig 2] figure 2, une représentation schématique d'une connexion du système physique S de la figure 1 au contrôleur numérique Sc via une ligne de transmission passive introduisant un retard (T/2 à l'aller et T/2 au retour),
• [Fig 3] figure 3, une représentation schématique d'une connexion d'un système physique S à un contrôleur passif retardé formé d'un bloc analogique hardware et d'un bloc numérique hardware,
• [Fig 4] figure 4, une représentation schématique du bloc analogique de la figure 3 dans le cas d'un contrôleur de type admittance,
• [Fig 5] figure 5, une représentation schématique du bloc analogique de la figure 3 dans le cas d'un contrôleur de type impédance,
• [Fig 6] figure 6, une représentation schématique d'un système Scr comprenant un contrôleur Sc connecté à un composant passif analogique dans le cas d'un contrôleur de type admittance,
• [Fig 7] figure 7, une représentation schématique d'un système Scr comprenant un contrôleur Sc connecté à un composant passif analogique dans le cas d'un contrôleur de type impédance, et
• [Fig 8] figure 8, une représentation schématique d'un procédé mis en oeuvre par les composants du bloc numérique de la figure 3.

Other characteristics and advantages of the invention will appear on reading the following description of embodiments of the invention, given by way of example only, and with reference to the drawings which are:

• [ Fig 1] figure 1 , a schematic representation of a direct connection between a physical system S and a digital controller Sc,
• [ Fig 2] figure 2 , a schematic representation of a connection of the physical system S of the figure 1 to the digital controller Sc via a passive transmission line introducing a delay (T/2 on the outward journey and T/2 on the return journey),
• [ Fig 3] figure 3 , a schematic representation of a connection of a physical system S to a delayed passive controller formed of a hardware analog block and a hardware digital block,
• [ Fig 4] figure 4 , a schematic representation of the analog block of the Figure 3 in the case of an admittance type controller,
• [ Fig 5] figure 5 , a schematic representation of the analog block of the Figure 3 in the case of an impedance type controller,
• [ Fig 6] figure 6 , a schematic representation of a system Scr comprising a controller Sc connected to an analog passive component in the case of an admittance type controller,
• [ Fig 7] figure 7 , a schematic representation of a system Scr comprising a controller Sc connected to an analog passive component in the case of an impedance type controller, and
• [ Fig 8] figure 8 , a schematic representation of a process implemented by the components of the digital block of the Figure 3 .

General principle

There figure 1 illustrates the state of the art. On this figure 1 , a physical system S to be electrically controlled is connected directly to a discrete-time passive digital controller Sc via a real-time digital hardware computer 20 and analog-digital converters 22 and digital-analog converters 24. As shown in this figure 1 , a delay T in the signal returned to the system S deteriorates the passivity property.

The principle of the invention consists of artificially encapsulating the delay T, intrinsic to the hardware computer, in a virtual passive electrical transmission line 30 represented in figure 2 . Such a transmission line introduces a delay of T/2 on the outward journey and of T/2 on the return journey. The principle behind the artificial encapsulation of the delay T in a transmission line is summarized in the following.

The system S (respectively Sc) has (at least) one electrical port characterized by a voltage Vs and a current Is (respectively voltage Vsc and current Isc). Let's virtually connect these two systems on either side of the transmission line. Propagation is described by two transport equations, the solutions of which are round-trip waves, denoted W ^+/- (where, for a given system S or Sc, W ⁺ will designate the wave which leaves it and W ^- the wave entering it). Here we consider lossless transmission, one-dimensional and in a medium with characteristic impedance r (in Ohm).

The round-trip wave variables associated with S and Sc are denoted Ws ^+/- and Wsc ^+/- , respectively. The incoming wave in Sc at time t is equal to the outgoing wave in S at time tT/2, i.e. Wsc ^- (t) = Ws ⁺ (tT/2) and vice versa, Ws ^- (t) = Wsc ⁺ (tT/2) from S to Sc, which implies a total round trip time T.

qui dépend de l'impédance caractéristique r choisie. En particulier, la conversion au niveau du port électrique de S s'exprime : $$\mathrm{Vs}\left(\mathrm{t}\right)=\sqrt{\frac{\mathrm{r}}{2}}{\mathrm{Wsc}}^{+}\left(\mathrm{t}-\mathrm{T}/2\right)+\mathrm{r}\mathrm{ls}\left(\mathrm{t}\right).$$

The voltages (Vs, Vsc) and currents (Is, Isc) are converted into forward/return wave variables Ws ^+/- and Wsc ^+/- via the following variable change: $${\mathrm{W}}^{+/-}\left(\mathrm{t}\right)=\sqrt{\frac{2}{\mathrm{r}}}\left[\mathrm{V}\left(\mathrm{t}\right)+/-\mathrm{r}\mathrm{L}\left(\mathrm{t}\right)\right],$$

which depends on the characteristic impedance r chosen. In particular, the conversion at the electrical port of S is expressed: $$\mathrm{Vs.}\left(\mathrm{t}\right)=\sqrt{\frac{\mathrm{r}}{2}}{\mathrm{Wsc}}^{+}\left(\mathrm{t}-\mathrm{T}/2\right)+\mathrm{r}\mathrm{ls}\left(\mathrm{t}\right).$$

In (2) an instantaneous relationship (without delay) appears between Vs and Is through r. This relationship will be achieved physically by placing an analog passive component between S and the computer.

The rest of the conversion is implemented numerically in the calculator, that is to say (i) conversion (2) removing the instantaneous relationship between Vs and Is, (ii) conversion (1) for Sc, linking (Vc , Ic) to (Wsc ⁺ , Wsc ^- ).

Furthermore, for stationary Sc systems, the delay T/2 between Ws ⁺ and Wsc ^- can be propagated between Wsc ⁺ and Ws ^- , in order to consider equivalently a delay T between Wsc ⁺ and Ws ^- (and no delay between Ws ⁺ and Wsc ^- ).

• interfacer le système physique S à un circuit analogique comprenant un générateur et un composant passif analogique, l'impédance du composant passif analogique étant destinée à représenter l'impédance caractéristique de la ligne de transmission électrique virtuelle,
• modifier le calculateur numérique hardware 20 (selon un algorithme approprié) de sorte que le contrôleur Sc soit vu au travers de la ligne de transmission. Cette modification consiste à simuler un système Scr (et non plus Sc) encapsulé dans une suite d'opérations algébriques reproduisant l'équation (1) précédente.

Thus, rather than directly interfacing the physical system S to the passive digital controller Sc, the principle of the invention consists of:

• interface the physical system S to an analog circuit comprising a generator and an analog passive component, the impedance of the analog passive component being intended to represent the characteristic impedance of the virtual electrical transmission line,
• modify the hardware digital computer 20 (according to an appropriate algorithm) so that the controller Sc is seen through the transmission line. This modification consists of simulating a system Scr (and no longer Sc) encapsulated in a series of algebraic operations reproducing the previous equation (1).

This configuration makes it possible to integrate the intrinsic delay into the hardware computer in a passive form.

Implementation of the general principle

There Figure 3 illustrates a device 40 for generating a control signal for an electrical system S. By the term “electrical system” is meant an electrically controlled system.

The generation device 40 is an admittance type or impedance type system. An admittance type system is a system capable of receiving a voltage and returning a current. An impedance type system is a system capable of receiving a current and returning a voltage.

The generation device 40 includes an input 42, an output 44, an analog block 46, an analog-digital converter 48, a digital block 50 and a digital-analog converter 52.

The input 42 is capable of receiving an input signal Vc, le coming from the electrical system S. The input signal Vc, le is an analog signal representative of a voltage Vc when the generation device 40 is of type admittance and representative of a current when the generation device 40 is of the impedance type.

The output 44 is capable of sending a control signal Is, Vs to the electrical system S. The control signal Is, Vs is an analog signal representative of a current Is when the generation device 40 is of the admittance type and representative of a voltage Vs when the generation device 40 is of the impedance type.

Analog block 46 is connected to input 42 and output 44 of generation device 40.

As illustrated by the figures 4 And 5 , the analog block 46 comprises a hardware electrical circuit 60 comprising an analog passive component 62, a component 64 for measuring the input signal Vc, and a generator 66.

In particular, as illustrated by the Figure 4 (Norton type), when the generation device 40 is of the admittance type, the measurement component 64 is a voltage measuring component, such as a voltmeter, and the generator 66 is a current generator. The analog passive component 62 is connected in parallel between the input 42 and the output 44 and in parallel with the generator 66 and the measuring component 64.

In the example illustrated by Figure 5 (Thévenin type), when the generation device 40 is of the impedance type, the measurement component 64 is a current measurement component, such as an ammeter, and the generator 66 is a voltage generator. The analog passive component 62 is connected in series with the generator 66 and with the measurement component 64 between input 42 and output 44.

In the example illustrated by the figures 4 And 5 , the analog passive component 62 is a dissipative component such as a resistor.

Alternatively, the analog passive component 62 is a capacitor or a coil.

The electrical circuit 60 is configured to generate the control signal Is, Vs of the electrical system S resulting from the sum of a first component and a second component both generated by components of the electrical circuit 60.

More precisely, the analog passive component 62 of the electrical circuit 60 is configured to generate the first component of the control signal Is, Vs, resulting from the passage of the input signal Vc, le in the analog passive component 62. In the Norton case, the first component is a current I1. In the Thévenin case, the first component is a tension T1.

The generator 66 of the electrical circuit 60 is configured to generate the second component of the control signal Is, Vs as a function of a command received by the generator 66. The command is generated by the digital block 50, as will be described below of the description. The generator 66 is thus controlled by the digital block 50 and generates the second component as a function of the command received from the digital block 50. In the Norton case, the second component is a current I2. In the Thévenin case, the second component is a tension T2.

The analog-digital converter 48 is connected between the output of the analog block 46 and the input of the digital block 50.

The analog-digital converter 48 is configured to convert into digital a measurement of the input signal Vc, carried out by the measurement component 64 of the analog block 46 to obtain a converted input signal S _EC readable by the digital block 50.

The digital block 50 comprises at least one digitally controllable component 70. The controllable component 70 is a physical element. More precisely, the controllable component 70 is a calculator.

For example, the digitally controllable component 70 is a microprocessor, a DSP (from the English "Digital Signal Processor" translated into French as "digital signal processor"), a micro-controller or even an FPGA (from the English " field-programmable gate array” translated into French as “programmable gate array”).

The controllable component 70 is configured to generate a digital output signal S _s-num (corresponding to the digital control of the generator 66 of the electrical circuit 60) as a function of the converted input signal S _EC and a modeling Scr of a digital controller Sc connected to a digital passive component having a second characteristic impedance.

The analog passive component and the digital passive component are of the same nature. For example, each of the analog passive component 62 and the digital passive component is a resistor.

The value of the second characteristic impedance is chosen according to the value of the first characteristic impedance.

In particular, when the generation device 40 is of the admittance type, the second characteristic impedance is greater than or equal to the first characteristic impedance. When the generation device 40 is of the impedance type, the second characteristic impedance is less than or equal to the first characteristic impedance.

Indeed, the transmission line is conservative if the first and second characteristic impedance are equal. However, in practice, the first characteristic impedance is known to a precision, which prevents strict equality. For example, in the case of resistors, the first characteristic impedance is denoted R and the second characteristic impedance is denoted r. In the admittance case, r ≥ R and the power dissipated by the virtual line is given by (1/R-1/r) *S _s-num ² ≥ 0 where S _s-num is the digital output signal. In the impedance case, r ≤ R and the power dissipated by the virtual line is given by (Rr) *S _s-num ² ≥ 0.

The digital controller Sc is a discrete-time dynamic system, linear or not, intended for controlling the electrical system S. This digital controller Sc is of the admittance type (voltage input v(n) and current output i(n)) or impedance (current input i(n) and voltage output v(n)).

Advantageously, the digital controller Sc is passive, that is to say, satisfying the equation [E(n+1) - E(n)] / T = Pext(n) - Pdis(n) with Pdis(n ) ≥ 0, where the power supplied from the outside Pext(n) is the “input.output” product, that is to say in both cases, v(n).i(n).

The Scr modeling of the digital controller Sc connected to the digital passive component corresponds to the addition of a feedback loop to the controller Sc. This modeling relates the new couple “voltage w(n) and current j(n)”.

In particular, in the example illustrated by the Figure 6 , the digital passive component is a resistor of impedance r and the generation device 40 is of the admittance type. In this case, the modeling Scr is a modeling of the digital controller Sc connected in series of the digital passive component of impedance r. The looping is expressed in the form: w(n)= v(n)+ri(n) & j(n) = i(n). The power dissipated by the digital passive component is given by: Pr(n)= r. i(n) ² .

In the example illustrated by Figure 7 , the digital passive component is a resistor of impedance r and the generation device 40 is of the impedance type. In this case, the modeling Scr is a modeling of the digital controller Sc connected in parallel with the digital passive component of impedance r. The looping is expressed in the form: w(n)=v(n) & j(n) = i(n)+v(n)/r. The power dissipated by the digital passive component is given by: Pr(n)= v(n) ² /r.

où w(n).j(n) représente la puissance apportée à l'ensemble Scr par l'extérieur, et où la puissance dissipée par l'ensemble Scr est Pdis(n)+ Pr(n) ≥ Pdis(n) ≥ 0.In these examples, the whole Scr is passive because the digital passive component of impedance r adds dissipation to the controller Sc. Indeed, since v(n)i(n)= -Pr(n) + w(n) j(n), the power balance becomes: $$\left[\mathrm{E}\left(\mathrm{not}+1\right)-\mathrm{E}\left(\mathrm{not}\right)\right]/\mathrm{T}=-\left[\mathrm{Pdis}\left(\mathrm{not}\right)+\mathrm{Pr}\left(\mathrm{not}\right)\right]+\mathrm{w}\left(\mathrm{not}\right).\mathrm{j}\left(\mathrm{not}\right)$$

where w(n).j(n) represents the power brought to the set Scr from the outside, and where the power dissipated by the set Scr is Pdis(n)+ Pr(n) ≥ Pdis(n) ≥ 0.

• un vecteur d'état x(n) de dimension N_x,
• une équation sur la dynamique de son état en fonction de l'entrée v(n): $$\mathrm{\delta }\mathrm{x}\left(\mathrm{n}\right)/\mathrm{T}=\left[\mathrm{J}\left(\mathrm{x}\left(\mathrm{n}\right)\right)-\mathrm{M}\left(\mathrm{x}\left(\mathrm{n}\right)\right)\right]{\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{n}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{n}\right)\right)+\mathrm{G}\left(\mathrm{x}\left(\mathrm{n}\right)\right)\mathrm{v}\left(\mathrm{n}\right)$$
  
  avec
  • $$\mathrm{x}\left(\mathrm{n}+1\right)=\mathrm{x}\left(\mathrm{n}\right)+\mathrm{\delta }\mathrm{x}\left(\mathrm{n}\right);$$
    
  • J : matrice antisymétrique de taille N_x x N_x ;
  • M : matrice symétrique positive de taille N_x x N_x ;
  • G : vecteur de taille N_x ;
  • H : fonction régulière scalaire définie positive ;
  • ∇_d: opérateur tel que ∇_dH(x(n), δx(n)). δx(n) = H(x(n+1)) - H(x(n)).
• une équation sur sa sortie i(n): $$\mathrm{i}\left(\mathrm{n}\right)=\mathrm{G}{\left(\mathrm{x}\left(\mathrm{n}\right)\right)}^{\top }{\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{n}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{n}\right)\right).$$
  

In one example, the digital controller Sc is described by the following equations. These equations are given in the case of a digital controller of input admittance v(n) and output i(n). Such a controller is represented by:

• a state vector x(n) of dimension N _x ,
• an equation on the dynamics of its state as a function of the input v(n): $$\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)/\mathrm{T}=\left[\mathrm{J}\left(\mathrm{x}\left(\mathrm{not}\right)\right)-\mathrm{M}\left(\mathrm{x}\left(\mathrm{not}\right)\right)\right]{\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{not}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)\right)+\mathrm{G}\left(\mathrm{x}\left(\mathrm{not}\right)\right)\mathrm{v}\left(\mathrm{not}\right)$$
  
  with
  • $$\mathrm{x}\left(\mathrm{not}+1\right)=\mathrm{x}\left(\mathrm{not}\right)+\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right);$$
    
  • J: antisymmetric matrix of size N _x x N _x ;
  • M: positive symmetric matrix of size N _x x N _x ;
  • G: vector of size N _x ;
  • H: positive definite scalar regular function;
  • ∇ _d : operator such as ∇ _d H(x(n), δx(n)). δx(n) = H(x(n+1)) - H(x(n)).
• an equation on its output i(n): $$\mathrm{i}\left(\mathrm{not}\right)=\mathrm{G}{\left(\mathrm{x}\left(\mathrm{not}\right)\right)}^{\top }{\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{not}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)\right).$$
  

où ∇_dH(x(n), δx(n))^T M(x(n)) ∇_dH(x(n), δx(n)) ≥ 0 (puissance dissipée positive ou nulle).The energy of the controller Sc is defined by E(n) = H(x(n)). According to (e.1) and (e.2), we can then write $$\left[\mathrm{E}\left(\mathrm{not}+1\right)-\mathrm{E}\left(\mathrm{not}\right)\right]/\mathrm{T}=\mathrm{i}\left(\mathrm{not}\right)\mathrm{v}\left(\mathrm{not}\right)-{\nabla }_{\mathrm{d}}\mathrm{H}{\left(\mathrm{x}\left(\mathrm{not}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)\right)}^{\top }\mathrm{M}\left(\mathrm{x}\left(\mathrm{not}\right)\right){\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{not}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)\right)$$

where ∇ _d H(x(n), δx(n)) ^T M(x(n)) ∇ _d H(x(n), δx(n)) ≥ 0 (positive or zero dissipated power).

The passivity of the discrete-time system is guaranteed by: $$\left[\mathrm{E}\left(\mathrm{not}+1\right)-\mathrm{E}\left(\mathrm{not}\right)\right]/\mathrm{T}\le \mathrm{i}\left(\mathrm{not}\right).\mathrm{v}\left(\mathrm{not}\right).$$

The solver construction for equations (e.1) and (e.2) can be found in the literature (see for example the article by Itoh, T., & Abe, K. (1988). Hamiltonian-conserving discrete canonical equations based on variational difference quotients. Journal of Computational Physics, 76(1), 85-102 ; or the article from Falaize, A., & Hélie, T. (2016). Passive guaranteed simulation of analog audio circuits: A port-Hamiltonian approach. Applied Sciences, 6(10), 273 ).

que l'on peut injecter dans l'équation (e.1), ce qui mène à : $$\mathrm{\delta }\mathrm{x}\left(\mathrm{n}\right)/\mathrm{T}=\left[\mathrm{J}\left(\mathrm{x}\left(\mathrm{n}\right)\right)-\mathrm{M}\left(\mathrm{x}\left(\mathrm{n}\right)\right)\right]{\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{n}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{n}\right)\right)+\mathrm{G}\left(\mathrm{x}\left(\mathrm{n}\right)\right)\mathrm{w}\left(\mathrm{n}\right),$$

avec $${\mathrm{M}}^{*}\left(\mathrm{x}\left(\mathrm{n}\right)\right)=\mathrm{M}\left(\mathrm{x}\left(\mathrm{n}\right)\right)+\mathrm{r}{\mathrm{G}}^{\mathrm{T}}\left(\mathrm{x}\left(\mathrm{n}\right)\right)\mathrm{G}\left(\mathrm{x}\left(\mathrm{n}\right)\right)\ge 0.$$

In this case, the modeling for the system Scr including the controller Sc connected to the digital passive component of impedance r is given by the following equations. Firstly, the input-output loop associated with the Scr system is written (see Figure 6 ): $$\mathrm{v}\left(\mathrm{not}\right)=\mathrm{w}\left(\mathrm{not}\right)-\mathrm{r}.\mathrm{i}\left(\mathrm{not}\right),$$

which can be injected into equation (e.1), which leads to: $$\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)/\mathrm{T}=\left[\mathrm{J}\left(\mathrm{x}\left(\mathrm{not}\right)\right)-\mathrm{M}\left(\mathrm{x}\left(\mathrm{not}\right)\right)\right]{\nabla }_{\mathrm{d}}\mathrm{H}\left(\mathrm{x}\left(\mathrm{not}\right),\mathrm{\delta }\mathrm{x}\left(\mathrm{not}\right)\right)+\mathrm{G}\left(\mathrm{x}\left(\mathrm{not}\right)\right)\mathrm{w}\left(\mathrm{not}\right),$$

with $${\mathrm{M}}^{*}\left(\mathrm{x}\left(\mathrm{not}\right)\right)=\mathrm{M}\left(\mathrm{x}\left(\mathrm{not}\right)\right)+\mathrm{r}{\mathrm{G}}^{\mathrm{T}}\left(\mathrm{x}\left(\mathrm{not}\right)\right)\mathrm{G}\left(\mathrm{x}\left(\mathrm{not}\right)\right)\ge 0.$$

Thus, the same solver can be used to simulate Sc and Scr. Indeed, to go from Sc to Scr, it is enough to substitute M by M*, which have the same property (positive symmetric matrix).

To generate the digital output signal S _s-num , the controllable component 70 is configured to implement a method comprising, for example, the steps illustrated in the flowchart of the figure 8 .

The method comprises a step 100 of converting the converted input signal S _EC coming from the analog-digital converter 48 into a first intermediate signal S _int1 function of the second characteristic impedance and representative of a power wave. More precisely, the first signal intermediate S _int1 represents the power wave of the virtual transmission line, that is to say the wave transmitted from the physical system S to the digital controller Sc by the virtual transmission line of characteristic impedance r.

et par soustraction d'un quatrième signal intermédiaire S_int4 obtenu à l'instant précédent. L'obtention du quatrième signal intermédiaire S_int4 à l'instant présent est décrit dans la suite de la description.For example, when the generation device 40 is of the admittance type and the digital passive component is a resistance of impedance r, the first intermediate signal S _int1 is obtained by multiplication of converted input signal S _EC with $\sqrt{\frac{2}{\mathrm{r}}}$

and by subtraction of a fourth intermediate signal S _int4 obtained at the previous instant. Obtaining the fourth intermediate signal S _int4 at the present time is described in the remainder of the description.

et par addition d'un quatrième signal intermédiaire S_int4 obtenu à l'instant précédent. L'obtention du quatrième signal intermédiaire S_int4 à l'instant présent est décrit dans la suite de la description.For example, when the generation device 40 is of the impedance type and the digital passive component is a resistor of impedance r, the first intermediate signal S _int1 is obtained by multiplication of converted input signal S _EC with $\sqrt{2\mathrm{r}}$

and by addition of a fourth intermediate signal S _int4 obtained at the previous instant. Obtaining the fourth intermediate signal S _int4 at the present time is described in the remainder of the description.

The method comprises a step 110 of converting the first intermediate signal S _int1 into a second intermediate signal S _int2 as a function of the second characteristic impedance and representative of a voltage or a current to be applied to the controller Sc.

.For example, when the generation device 40 is of the admittance type and the digital passive component is a resistor of impedance r, the second intermediate signal S _int2 is obtained by multiplication of the first intermediate signal S _int1 with $\sqrt{2\mathrm{r}}$

.

.For example, when the generation device 40 is of the impedance type and the digital passive component is a resistor of impedance r, the second intermediate signal S _int2 is obtained by multiplication of the first intermediate signal S _int1 with $\sqrt{\frac{2}{\mathrm{r}}}$

.

The method comprises a step 120 of calculating a third intermediate signal S _int3 as a function of the second intermediate signal S _int2 and the modeling Scr. The third intermediate signal S _int3 is therefore obtained by simulation of the digital system Scr which reproduces the original passive system Sc interfaced to the transmission line of characteristic impedance r. This step thus makes it possible to obtain the current or voltage value at the output of the assembly formed by the controller Sc connected to the digital passive component.

When the generation device 40 is of the admittance type, the third intermediate signal S _int3 is representative of a current. When the generation device 40 is of the impedance type, the third intermediate signal S _int3 is representative of a voltage.

The method comprises a step 130 of converting the third intermediate signal S _int3 into a fourth intermediate signal S _int4 as a function of the second characteristic impedance r and representative of a power wave.

et par ajout du premier signal intermédiaire S_int1.For example, when the generation device 40 is of the admittance type and the digital passive component is a resistor of impedance r, the fourth intermediate signal S _int4 is obtained by multiplication of the third intermediate signal S _int3 with $\sqrt{2\mathrm{r}}$

and by adding the first intermediate signal S _int1 .

et par soustraction du premier signal intermédiaire S_int1.For example, when the generation device 40 is of the impedance type and the digital passive component is a resistor of impedance r, the fourth intermediate signal S _int4 is obtained by multiplication of the third intermediate signal S _int3 with $\sqrt{\frac{2}{\mathrm{r}}}$

and by subtraction of the first intermediate signal S _int1 .

The method comprises a step 140 of converting the fourth intermediate signal S _int4 into the digital output signal S _s-num of the controllable component 70 as a function of the second characteristic impedance.

.For example, when the generation device 40 is of the admittance type and the digital passive component is a resistance of impedance r, the digital output signal S _s-num is obtained by multiplication of the third intermediate signal S _int3 with $\left(-\sqrt{\frac{2}{\mathrm{r}}}\right)$

.

.For example, when the generation device 40 is of the impedance type and the digital passive component is a resistor of impedance r, the digital output signal S _s-num is obtained by multiplication of the third intermediate signal S _int3 with $\left(-\sqrt{2\mathrm{r}}\right)$

.

The digital-analog converter 52 is connected between the input of the analog block 46 and the output of the digital block 50.

Advantageously, the analog-to-digital converter 48 and the digital-to-analog converter 52 are synchronized to a common clock signal.

The digital-to-analog converter 52 is configured to convert the digital output signal S _s-num to analog to obtain a command analog of the generator 66 inducing the generation of the second component of the control signal Is, Vs by the generator 66.

The operation of the generation device 40 will now be described.

Initially, the generation device 40 receives as input an input signal Vc, le coming from the electrical system S.

The analog passive component 62 of the electrical circuit 60 generates the first component of the control signal Is, Vs as a function of the input signal Vc, Ic.

The generator 66 of the electrical circuit 60 generates the second component of the control signal Is, Vs as a function of a command received from the digital block 50.

The first component and the second component generated are summed at the output of the electrical circuit 60 to form the control signal Is, Vs.

Control of generator 66 is obtained by the following steps. A measurement of the input signal Vc, the is converted to digital by the analog-to-digital converter 48 to obtain a converted input signal S _EC .

The controllable component 70 of the digital block 50 then generates a digital output signal S _s-num corresponding to the digital control of the generator 66.

The digital output signal S _s-num is converted to analog by the digital-analog converter 52, which makes it possible to obtain analog control of the generator 66. Depending on the command received, the generator 66 generates the second component of the control signal Is, Vs.

Thus, the generation device 40 was designed to passively control an electrically controlled system S. It makes it possible in particular to preserve the passivity of the connection in the presence of a delay between a continuous time system to be controlled and a discrete time controller. The “continuous time/discrete time” specificity means that the results of the state of the art do not apply because they concern either only the continuous domain, or only the digital domain.

By combining analog hardware elements (on the continuous time part), digital hardware elements and algorithmic elements (on the discrete time part), the generation device 40 makes it possible to create a passive virtual transmission line “half-physical, half-digital”.

The generation device 40 also takes into account the difficulty of marrying the characteristic impedance of the transmission line in its physical hardware form R and its digital clone r by artificially distinguishing them in the development of the process. This approach combined with a dissipativity analysis leads to an order relationship between R and r: the process gives the conditions which make it possible to ensure passivity taking into account the uncertainties in R (potential sensitivity to temperature, variations over time , etc).

The generation 40 device is particularly intended to be used to control audio systems, such as speakers, in particular speakers corrected for HIFI, acoustic absorbers for studios and concert halls, augmented musical instruments or again for the physical reconstruction of the linear or non-linear impedancial load of virtual instruments.

More generally, the generation 40 device is adaptable to any actuated physical system, such as vibration absorbers and acoustic absorbers for aeronautics and transport, controllers of vibrating surfaces (acoustic diffusion without loudspeaker) or mechatronic system stabilizers.

It should be noted that additional information coming from physical sensors (signals conditioned and converted to digital) taken or not from the physical system S or digital signals (target trajectory, adjustment or other type of information) may be provided. to the Sc controller. It should also be noted that the digital controller Sc could be replaced by a passive or balanced power balance system having a digital connection port.

Claims (10)

1. A device (40) for generating a control signal (Is; Vs) for an electrical system (S), the generation device (40) comprising:

   - an input (42) for an input signal (Vc; Ic) originating from the electrical system (S), the input signal (Vc; Ic) being an analog signal representative of a voltage, of a current, respectively,

   - an output (44) for the control signal (Is; Vs), the control signal (Is; Vs) being an analog signal representative of a current, of a voltage, respectively, the control signal (Is; Vs) having a first component and a second component,

   - an analog block (46) connected to the input (42) and to the output (44) of the generation device (40), the analog block (46) comprising an electrical circuit (60) comprising a passive analog component (62) having a first passive characteristic impedance (R), a voltage, current, respectively, a measuring component (64) and a current, voltage, respectively, generator (66),

   - a digital block (50) comprising at least one digitally controllable component (70),

   - an analog-digital converter (48) connected between the analog block (46) and the digital block (50), and

   - a digital-analog converter (52) connected between the analog block (46) and the digital block (50),

   the passive analog component (62) of the electrical circuit (60) being configured so as to generate the first component of the control signal (Is; Vs) and the generator (66) of the electrical circuit (60) being configured so as to generate the second component of the control signal (Is; Vs), the electrical circuit (60) being configured so as to sum the first and the second component that are generated in order to obtain the control signal (Is; Vs),

   the analog-digital converter (48) being configured to convert, into digital, a measurement of the input signal (Vc; Ic) done by the measuring component (64) of the analog block (46) to obtain a converted input signal (S_E-C),

   the controllable component (70) of the digital block (50) being configured to generate a digital output signal (S_s-num) as a function of the converted input signal (S_E-C) and a model (Scr) of a digital controller (Sc) connected to a passive digital component having a second passive characteristic impedance (r), the value of the second characteristic impedance (r) being chosen as a function of the value of the first characteristic impedance (R),

   the digital-analog converter (52) being configured to convert, into analog, the digital output signal (S_s-num) to obtain a control of the generator (66), the second component of the control signal (Is; Vs) generated by the generator (66) being a function of the control obtained from the digital block (50).
2. The device (40) according to claim 1, wherein the passive analog component (62) and the passive digital component are of the same nature.
3. The device (40) according to claim 1 or 2, wherein each of the passive analog component (62) and the passive digital component is a resistance.
4. The device (40) according to any one of claims 1 to 3, wherein:

   - when the input signal (Vc) is representative of a voltage and the control signal (Is) is representative of a current, the second characteristic impedance (r) is greater than or equal to the first characteristic impedance (R), and

   - when the input signal (Ic) is representative of a current and the control signal (Vs) is representative of a voltage, the second characteristic impedance (r) is less than or equal to the first characteristic impedance (R).
5. The device (40) according to any one of claims 1 to 4, wherein:

   - when the input signal (Vc) is representative of a voltage and the control signal (Is) is representative of a current, the measuring component (64) is a voltage measuring component and the generator (66) is a current generator, the passive analog component (62) being connected in parallel with the input (42) and the output (44) and in parallel with the generator (66) and the measuring component (64), and

   - when the input signal (Ic) is representative of a current and the control signal (Vs) is representative of a voltage, the measuring component (64) is a current measuring component and the generator (66) is a voltage generator, the passive analog component (62) being connected in series with the generator (66) and the measuring component (64) between the input (42) and the output (44).
6. The device (40) according to any one of claims 1 to 5, wherein:

   - when the input signal (Vc) is representative of a voltage and the control signal (Is) is representative of a current, the model (Scr) is a model of the digital controller (Sc) connected in series with the passive digital component, and

   - when the input signal (Ic) is representative of a current and the control signal (Vs) is representative of a voltage, the model (Scr) is a model of the digital controller (Sc) connected in parallel with the passive digital component.
7. The device (40) according to any one of claims 1 to 6, wherein the controllable component (70) is configured to:

   - convert the converted input signal (S_E-C) originating from the analog-digital converter (48) into a first intermediate signal (S_int1) representative of a power wave, as a function of the second characteristic impedance (r),

   - convert the first intermediate signal (S_int1) into a second intermediate signal (S_int2) representative of a voltage, of a current, respectively, as a function of the second characteristic impedance (r),

   - calculate a third intermediate signal (S_int3) as a function of the second intermediate signal (S_int2) and of the model (Scr),

   - convert the third intermediate signal (S_int3) into a fourth intermediate signal (S_int4) representative of a power wave, as a function of the second characteristic impedance (r), and

   - convert the fourth intermediate signal (S_int4) into the digital output signal (S_s-num) of the controllable component (70) as a function of the second characteristic impedance (r), the fourth intermediate signal (S_int4) being representative of a voltage, of a current, respectively.
8. The device (40) according to claim 7, wherein the controllable component 70 is chosen from the list consisting of: a microprocessor, a digital signal processor, a microcontroller and an array of programmable gates.
9. An audio system, such as a speaker, comprising a device (40) according to any one of claims 1 to 8.
10. A method for generating a control signal (Is; Vs) for an electrical system (S) from a generation device (40) according to any one of claims 1 to 8, the method comprising:

    - receiving an input signal (Vc; Ic) originating from the electrical system (S) at the input (42) of the generation device (40), the input signal (Vc; Ic) being an analog signal representative of a voltage, of a current, respectively,

    - converting, into digital, a measurement of the input signal (Vc; Ic) done by the measuring component (64) of the analog block (46) to obtain a converted input signal (S_E-C),

    - generating a digital output signal (S_s-num) via the controllable component (70) of the digital block (50),

    - converting, into analog, the digital output signal (S_s-num) to obtain control of the generator (66) of the electrical circuit (60),

    - generating the first component of the control signal (Is; Vs) via the passive analog component (62) of the electrical circuit (60),

    - generating the second component of the control signal (Is; Vs) via the generator (66) of the electrical circuit (60) as a function of the control obtained from the digital block (50), and

    - summing the first component and the second component generated by the electrical circuit (60) to obtain the control signal (Is; Vs).

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