Patent Grant
11956605
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 an associated method.
Passivity describes the fact that a system cannot spontaneously create energy, but only store it and/or dissipate it. As an illustration, a network of resistances, diodes, coils or capacitors (linear or not) connected to a speaker will modify the mechanical and acoustic behavior of the speaker, but without generating sustained oscillations (Larsen effect) or instabilities. The passivity ensures this robustness. More generally, a passive physical system satisfies a power balance of type dE(t)/dt=Pext(t)−Pdis(t) (temporal variation of the stored energy=power contributed from the outside−dissipated power) with a positive dissipated power Pdis (or zero in the conservative case).
In the case of complex controls, the controls may be implemented in a real-time digital form, that is to say, using embedded systems comprising analog-digital converters, electric signal generators and a hardware digital computer. The calculation of the control signal is then rendered after a latency time, equivalent to a delay, which here is denoted T. Such a delay is inherent to any control done by digital hardware systems (microprocessor, DSP, microcontroller, FPGA) due to the time taken for the calculation.
Now, including a delay in a feedback loop may deteriorate the passivity property and thus make the control ineffective, or even cause destabilization thereof.
There is therefore a need for a device allowing passive control of a system.
To this end, the present description relates to a device for generating a control signal for an electrical system, the generation device comprising:
According to other advantageous aspects, the generation device comprises one or more of the following features, considered alone or according to all technically possible combinations:
The invention also relates to an audio system, such as a speaker, comprising a device as previously described.
The invention also relates to a method for generating a control signal for an electrical system from a generation device as previously described, the method comprising:
Other features and advantages of the invention will appear upon reading the following description of embodiments of the invention, solely as an example and done in reference to the drawings, which are:
The principle of the invention consists in artificially encapsulating the delay T, intrinsic to the hardware computer, in a virtual passive electrical transmission line 30, shown in
The system S (Sc, respectively) has (at least) one electrical port characterized by a voltage Vs and a current Is (respectively voltage Vsc and current Isc). Let us virtually connect these two systems on either side of the transmission line. The propagation is described by two transport equations, the solutions of which are outbound/return waves, denoted W+/− (where, for a given system S or Sc, W+ will designate the outbound wave and W− the inbound wave). A lossless, unidimensional transmission will be considered here, in a characteristic impedance medium r (in Ohms).
The variables of outbound/return waves associated with S and Sc are denoted Ws+/− and Wsc+/−, respectively. The incoming wave in Sc at the instant t is equal to the outgoing wave of S at instant t−T/2, or Wsc−(t)=Ws+(t−T/2), and reciprocally, Ws−(t)=Wsc+(t−T/2) from S to Sc, which implies a total round-trip duration T.
The voltages (Vs, Vsc) and currents (Is, Isc) are converted into inbound/outbound wave variables Ws+/− and Wsc+/− via the following variable change:
which depends on the chosen characteristic impedance r. In particular, the conversion at the electrical port of S is expressed:
In (2), an instantaneous relationship (without delay) appears between Vs and Is through r. This relationship will be done physically by placing a passive analog component between S and the computer.
The rest of the conversion is implanted digitally in the computer, i.e. (i) the conversion (2) removed from the instantaneous relationship between Vs and Is, (ii) conversion (1) for Sc, linking (Vc, Ic) to (Wsc+, Wsc−).
Additionally, for stationary systems Sc, the delay T/2 between Ws+ and Wsc− can be propagated between Wsc+ and Ws−, so as to equivalently consider a delay T between Wsc+ and Ws− (and no delay between Ws+ and Wsc−).
Thus, rather than interfacing the physical system S directly with the passive digital controller Sc, the principle of the invention consists in:
This configuration allows integration of the intrinsic delay into the hardware computer in passive form.
Implementation of the General Principle
The generation device 40 is a system of the admittance type or of the impedance type. A system of the admittance type is a system able to receive a voltage and to return a current. A system of the admittance type is a system able to receive a voltage and to return a current.
The generation device 40 comprises 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 able to receive an input signal Vc, Ic originating from the electrical system S. The input signal Vc, Ic is an analog signal representative of a voltage Vc when the generation device 40 is of the admittance type and representative of a current Ic when the generation device 40 is of the impedance type.
The output 44 is able to send 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.
The analog block 46 is connected to the input 42 and to the output 44 of the generation device 40.
As illustrated by
In particular, as illustrated by
In the example illustrated by
In the example illustrated by
In a variant, the passive analog 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 specifically, the passive analog 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, Ic in the passive analog component 62. In the Norton case, the first component is a current I1. In the Thevenin case, the first component is a voltage 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 control received by the generator 66. The control is generated by the digital block 50, as will be described in the remainder of the description. The generator 66 is thus controlled by the digital block 50 and generates the second component as a function of the received control originating from the digital block 50. In the Norton case, the second component is a current I2. In the Thevenin case, the second component is a voltage 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, Ic done by the measuring component 64 of the analog block 46 to obtain a converted input signal SE-C 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 specifically, the controllable component 70 is a computer.
For example, the digitally controllable component 70 is a microprocessor, a DSP (“Digital Signal Processor”), a microcontroller or an FPGA (“field-programmable gate array”).
The controllable component 70 is configured to generate a digital output signal Ss-num (corresponding to the digital control of the generator 66 of the electrical circuit 60) as a function of the converted input signal SE-C and a model Scr of a digital controller Sc connected to a passive digital component having a second characteristic impedance.
The passive analog component and the passive digital component are of the same nature. For example, each of the passive analog component 62 and the passive digital component is a resistance.
The value of the second characteristic impedance is chosen as a function of 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.
In fact, the transmission line is conservative if the first and the second characteristic impedance are equal. Nevertheless, in practice, the first characteristic impedance is known to within a precision, which prevents strict equality. For example, in the case of resistances, 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)*Ss-num2≥0 where Ss-num is the digital output signal. In the impedance case, r≤R and the power dissipated by the virtual line is given by (R−r)*Ss-num2≥0.
The digital controller Sc is a discrete-time dynamic system, linear or not, intended to control the electrical system S. This digital controller Sc is of the admittance type (voltage input v(n) and current output i(n)) or of the impedance type (current input i(n) and voltage output v(n)).
Advantageously, the digital controller Sc is passive, that is to say, satisfying equation [E(n+1)−E(n)]/T=Pext(n)−Pdis(n) with Pdis(n)≥0, where the power contributed from the outside Pext(n) is the product “input·output,” that is to say, in both cases, v(n)·i(n).
The model Scr of the digital controller Sc connected to the passive digital component corresponds to the addition of a feedback loop to the controller Sc. This model relates the new “voltage w(n) and current j(n)” pair.
In particular, in the example illustrated by
In the example illustrated by
In these examples, the assembly Scr is passive because the passive digital component with impedance r adds dissipation to the controller Sc. In fact, since v(n)i(n)=−Pr(n)+w(n)j(n), the power balance becomes:
[E(n+1)−E(n)]/T=−[Pdis(n)+Pr(n)]+w(n)·j(n)
where w(n)·j(n) represents the power contributed to the assembly Scr from the outside, and where the power dissipated by the assembly Scr is Pdis(n)+Pr(n) Pdis(n) 0.
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 the admittance type with input v(n) and output i(n). Such a controller is represented by:
The energy of the controller Sc is defined by E(n)=H(x(n)). According to (e.1) and (e.2), one may then write
[E(n+1)−E(n)]/T=i(n)v(n)−∇dH(x(n),δx(n))TM(x(n))∇dH(x(n),δx(n))
where ∇dH(x(n), δx(n))T M(x(n)) ∇dH(x(n), δx(n))≥0 (positive or zero dissipated power).
The passivity of the discrete-time system is guaranteed by:
[E(n+1)−E(n)]/T≤i(n)·v(n).
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 by Falaize, A., & Flab, T. (2016). Passive guaranteed simulation of analog audio circuits: A port-Hamiltonian approach. Applied Sciences, 6(10), 273).
In this case, the model for the system Scr comprising the controller Sc connected to the passive digital component with impedance r is given by the following equations. First, the input-output loop associated with the system Scr is written (see
v(n)=w(n)−r·i(n),
which can be injected into equation (e.1), which leads to:
δx(n)/T=[J(x(n))−M*(x(n))]∇dH(x(n),δx(n))+G(x(n))w(n),
with M*(x(n))=M(x(n))+r GT(x(n)) G(x(n))≥0.
Thus, the same solver is usable to simulate Sc and Scr. In fact, to go from Sc to Scr, it suffices to replace M with M*, which have the same property (positive symmetrical matrix).
To generate the digital output signal Ss-num, the controllable component 70 is configured to implement a method comprising, for example, the steps illustrated in the flowchart of
The method comprises a step 100 for converting the converted input signal SE-C originating from the analog-digital converter 48 into a first intermediate signal Sint1 as a function of the second characteristic impedance and representative of a power wave. More specifically, the first intermediate signal Sint1 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.
For example, when the generation device 40 is of the admittance type and the passive digital component is a resistance with impedance r, the first intermediate signal Sint1 is obtained by multiplying the converted input signal SE-C with
and by subtracting a fourth intermediate signal Sint4 obtained at the previous instant. The obtainment of the fourth intermediate signal Sint4 at the present instant is described in the remainder of the description.
For example, when the generation device 40 is of the impedance type and the passive digital component is a resistance with impedance r, the first intermediate signal Sint1 is obtained by multiplying the converted input signal SE-C with √{square root over (2r)} and by adding a fourth intermediate signal Sint4 obtained at the previous instant. The obtainment of the fourth intermediate signal Sint4 at the present instant is described in the remainder of the description.
The method comprises a step 110 of converting the first intermediate signal Sinti into a second intermediate signal Sint2 as a function of the second characteristic impedance 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 passive digital component is a resistance with impedance r, the second intermediate signal Sint2 is obtained by multiplying the first intermediate signal Sint1 with √{square root over (2r)}.
For example, when the generation device 40 is of the impedance type and the passive digital component is a resistance with impedance r, the second intermediate signal Sint2 is obtained by multiplying the first intermediate signal Sint1 with
The method comprises a step 120 of calculating a third intermediate signal Sint3 as a function of a second intermediate signal Sint2 and of the model Scr. The third intermediate signal Sint3 is therefore obtained by simulating the digital signal Scr, which reproduces the original passive system Sc interfaced with the transmission line of characteristic impedance r. This step thus makes it possible to obtain the current or voltage value output by the assembly formed by the controller Sc connected to the passive digital component.
When the generation device 40 is of the admittance type, the third intermediate signal Sint3 is representative of a current. When the generation device 40 is of the impedance type, the third intermediate signal Sint3 is representative of a voltage.
The method comprises a step 130 for converting the third intermediate signal Sinn into a fourth intermediate signal Sint4 as a function of the second characteristic impedance r and representative of a power wave.
For example, when the generation device 40 is of the admittance type and the passive digital component is a resistance with impedance r, the fourth intermediate signal Sint4 is obtained by multiplying the third intermediate signal Sint3 with 2r and by adding the first intermediate signal Sinti.
For example, when the generation device 40 is of the impedance type and the passive digital component is a resistance with impedance r, the fourth intermediate signal Sint4 is obtained by multiplying the third intermediate signal Sint3 with
and by subtracting the first intermediate signal Sinti.
The method comprises a step 140 for converting the fourth intermediate signal Sint4 into the digital output signal Ss-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 passive digital component is a resistance with impedance r, the digital output signal Ss-num is obtained by multiplying the third intermediate signal Sint3 with
For example, when the generation device 40 is of the impedance type and the passive digital component is a resistance with impedance r, the digital output signal Ss-num is obtained by multiplying the third intermediate signal Sint3 with (−√{square root over (2r)}).
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-digital converter 48 and the digital-analog converter 52 are synchronized on a common clock signal.
The digital-analog converter 52 is configured to convert, into analog, the digital output signal Ss-num to obtain an analog control 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, Ic originating from the electrical system S.
The passive analog 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 received control originating from the digital block 50.
The generated first component and second component are summed at the output of the electrical circuit 60 to form the control signal Is, Vs.
The control of the generator 66 is obtained by the following steps. A measurement of the input signal Vc, Ic is converted into digital by the analog-digital converter 48 to obtain a converted input signal SE-C.
The controllable component 70 of the digital block 50 next generates a digital output signal Ss-num corresponding to the digital control of the generator 66.
The digital output signal Ss-num is converted into analog by the digital-analog converter 52, which makes it possible to obtain the analog control of the generator 66. As a function of the received control, the generator 66 generates the second component of the control signal Is, Vs.
Thus, the generation device 40 has been designed to passively regulate an electrically controlled system S. It in particular allows preservation of 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 causes the results of the state of the art not to 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 allows realization of a “half-physical, half-digital” passive virtual transmission line.
The generation device 40 also accounts for the difficulty in combining the characteristic impedance of the transmission line in its physical hardware form R and its digital clone r by distinguishing them artificially in the development of the method. This approach combined with a dissipativity analysis leads to an order relationship between R and r: the method provides the conditions that make it possible to ensure passivity in view of the uncertainties regarding R (potential sensitivity to temperature, variations over time, etc.).
The generation device 40 is in particular intended to be used to control audio systems, such as speakers, in particular speakers corrected for hi-fi, acoustic absorbers for studios and concert halls, augmented musical instruments, or for the physical reconstruction of the linear or nonlinear impedance load of virtual instruments
More generally, the generation device 40 is adaptable to any actuated physical system, such as vibration absorbers and acoustic absorbers for aeronautics and transportation, vibrating surface controllers (acoustic diffusion without speaker) or mechatronic system stabilizers.
One skilled in the art will understand that the invention is not limited to the examples described in the description. For example, it should be noted that additional information from physical sensors (signals conditioned and converted to digital) collected or not from the physical system S or digital signals (target trajectory, setting or other type of information) may be supplied to the controller Sc. It should also be noted that the digital controller could be replaced by a passive or balanced power system having a digital connection port.
| Number | Date | Country | Kind |
|---|---|---|---|
| 1913122 | Nov 2019 | FR | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/EP2020/082758 | 11/19/2020 | WO |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2021/099509 | 5/27/2021 | WO | A |
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| 20100318205 | Kazunobu et al. | Dec 2010 | A1 |
| 20130259245 | Chih-Chiang et al. | Oct 2013 | A1 |
| Number | Date | Country |
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| 103945306 | Jul 2014 | CN |
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| Number | Date | Country | |
|---|---|---|---|
| 20220408186 A1 | Dec 2022 | US |
