Method for controlling an active control system and system...

Details Method for controlling an active control system and system... Method for controlling an active control system and system...

2003-05-09

2004-12-14

Mei, Xu (Department: 2644)

Electrical audio signal processing systems and devices

Acoustical noise or sound cancellation

Counterwave generation control path

C381S071800

Reexamination Certificate

active

06831983

ABSTRACT:

AREA AND BACKGROUND OF THE INVENTION
The present invention relates to a method for controlling a control arrangement controlling a predetermined system, the control arrangement comprising a controller, M output sensors providing an output signal vector y(t), L control actuators controlled by a control signal vector u(t) provided by the controller and N reference signal generators for providing a reference signal vector z(t) to the controller, L, M, N being positive integers, the output signal vector y(t) being defined as:
y
(
t
)=
d
(
t
)+
H
(
q
−1
)
u
(
t
)
with:
d(t)=a disturbance signal vector of dimension M×1;
H(q
−1
)=a transfer matrix of the predetermined system of dimension M×L in a backward shift operator q
−1
;
the control signal vector u(t) being defined as:
u
(
t
)=&PHgr;
T
(
t
)·
w
(
t
)
with:
&PHgr;
T
(t)=a block diagonal matrix of dimension L×LNI built up of L row vectors
&phgr;
T
, each vector &phgr;
T
being the transpose of NI×1 vector p containing the last I
samples of the N reference signals z
n
(t), I being an integer,
w(t)=a vector containing all controller coefficients for the controller.
Active control systems are generally formed by a number of actuators and sensors. The actuator outputs are controlled by actuator signals from a controller, based on inputs from both sensor signals and reference signals. Generally, the actuator signals are controlled such that desired sensor signals are obtained.
In e.g. active sound suppression systems the signal detected by the sensors should be minimal, which is obtained by adapting the actuator signals dependent on the reference signals and sensor signals. However, to obtain such a result, it might be necessary to control the actuators with high amplitude signals.
Certain actuators are limited with respect to the amplitude (or energy) with which they are controlled, and controlling the actuators with too high a signal might lead to non-linear behaviour (which is undesirable) or might even damage actuators.
Moreover, high amplitude control signals may weaken the robustness of the control method, and small variations in control parameters may lead to serious performance degradation.
SUMMARY OF THE INVENTION
It is, therefore, an object of the present invention to provide a method for controlling an active control system, in which the combination of the energy from the sensors and the energy to the actuators is optimised.
This object is achieved by a method according to the preamble of claim
1
, characterised in that the method comprising the step of minimizing a criterion function J defined as a mixture of energy of an observed output error signal vector &egr;
1
(t) and energy of a control error signal vector &egr;
2
(t), defined as:
&egr;
1
(
t
)=
P
(
q
−
)
y
(
t
)
&egr;
2
(
t
)=
Q
(
q
−1
)
u
(
t
)
with:
P(q
−1
)=an M×M dimensional rational weighting matrix of the output sensor signals,
Q(q
−1
)=an L×L dimensional rational weighting matrix of the actuator signals, the step of minimising the criterion function J comprising the step of recursively updating the controller coefficients in w(t) proportional to the observed output error signal vector &egr;
1
and proportional to the control error signal vector &egr;
2
.
Minimising the criterion function J will provide a robust control method, enabling limitation of the drive signal to actuators while maintaining performance of the control method.
In an embodiment of the present method, the output error signal vector &egr;
1
(t) is equal to &egr;
1
(t)=P(q
−1
)y(t|w(t)), in which y(t|w(t)) is a prediction output signal vector, corresponding to the output signal vector y(t) of the sensors (
4
) at time t in the case that the controller coefficients w(t) have been held constant for a period longer than a response time of the predetermined system. If the controller coefficients are time varying (as may occur during adaptation) y(t|w(t)) may differ significantly from the true sensor output y(t).
This embodiment requires some additional computational effort, but provides a more stable control method behaviour.
In an embodiment of the present method, the contributions to the criterion function J of output error signal vector &egr;
1
(t) and control error signal vector &egr;
2
(t) are tuned by nonnegative entries in diagonal matrices K and &Lgr;, respectively in the criterion function J, the criterion function being defined as
J
=
lim
T
→
∞
⁢
1
2
⁢
T
⁢
∑
t
=
0
T
⁢
 
⁢
E
⁢
{
ϵ
T
⁡
(
t
)
⁢
(
K
T
⁢
K
0
0
Λ
T
⁢
Λ
)
⁢
ϵ
⁡
(
t
)
}
,
 
⁢
with
⁢
 
⁢
ϵ
⁡
(
t
)
=
[
ϵ
1
⁡
(
t
)
⁢
ϵ
2
⁡
(
t
)
]
T
.
In this embodiment it is possible to tune the relative importance of each individual output error &egr;
1
and of each individual control error &egr;
2
in the criterion function J.
A further embodiment of the present method implements the tuning of matrices K and &Lgr; by a supervisory control layer, adapting the nonnegative entries in matrices K and &Lgr; in relation to the transfer function H of the predetermined system and the characteristics of the reference signal vector z(t), the output signal vector y(t) and the control signal vector u(t).
This embodiment allows maintaining the desired control behaviour by varying elements in the matrices K and &Lgr;. E.g., changes in the transfer matrix H of the predetermined system or the frequency contents of reference signal vector z(t) may necessitate adaptation of the elements in the matrices K and &Lgr;. The supervisory control layer may be extensively trained beforehand. Although normally the matrices K and &Lgr; are tuned off line, the supervisory control layer may adjust the values of the elements in the matrices K and &Lgr; yielding time variant weight characteristics of matrices K(t) and &Lgr;(t).
In a preferred embodiment, the controller coefficients in w(t) are recursively updated according to
w
(
t+
1)=
w
(
t
)−&ggr;(
t
)[
F
1
(
q
−1
,t
)
K
(
t
)&egr;
1
(
t
)+
F
2
(
q
−1
,t
)&Lgr;(
t
)&egr;
2
(
t
)]
in which F
1
(q
−1
,t) and F
2
(q
−1
,t) are time-variant rational matrices of dimensions LNI×M and LNI×L, respectively, and &ggr;(t) is a positive scalar used to tune the rate of convergence of the control method.
This method allows an adaptation of the scalar &ggr;(t) to influence the convergence behaviour of the control method.
In a further embodiment of the present invention, F
1
(t) and F
2
(t) have a structure according to
F
1
(
t
)=
F
3
−1
(
K
(
t
)&PSgr;
1
(
t
))
T
;F
2
(
t
)=
F
3
−1
(&Lgr;(
t
)&PSgr;
2
(
t
))
T
; and
 
F
3
=E{&PSgr;
1
T
(
t
)
K
T
(
t
)
K
(
t
)&PSgr;
1
(
t
)+&PSgr;
2
T
(
t
)&Lgr;
T
(
t
)&Lgr;(
t
)&PSgr;
2
(
t
)}
in which &PSgr;
1
(t)=PH&PHgr;
T
(t), and &PSgr;
2
(t)=Q&PHgr;
T
(t).
In this embodiment, the controller will be stable, and have an optimal convergence and tracking speed, by selecting a specific structure for the transfer matrices F
1
(t) and F
2
(t), which control the feedback of errors &Dgr;
1
and &egr;
1
to the controller coefficients w(t).
Preferably, the matrix inversion F
3
−1
is calculated off-line, stored in a memory and retrieved when needed, such that the total real-time computational demand is smaller.
Preferably, F
1
, F
2
(t), F
3
(t) and its inverse F
3
−1
(t) are tuned simultaneously with the tuning of K and &Lgr;, as this will maintain the favourable characteristic of convergence rate equalisation and stability of the control method.
Also, in a further embodiment, F
3
(t) is preferably updated as function of matrices K and &Lgr; by using a rank one updating algorithm, e.g. the rank one QR update algorithm as described in G. H. Golub and C. F. van Loon, “Matrix computations”, Johns Hopkins University Press,

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