Method and device for optimizing performance of a servo control of a mechatronic system based on effective static and dynamic margins
A method for automated optimisation of a servo control system controlled by a setpoint, the servo control system including a corrector in a feedback loop, the method exhibiting satisfactory reliability and performance in terms of stability through an iterative procedure, the most effective corrector being determined from among correctors by developing a current value of the delay margin and by individually testing the correctors on the servo control system of the real mechatronic system and by injecting an excitation signal into the loop and by assessing two effective indicators based on at least one effective static margin and one effective dynamic margin, the two effective indicators being an effective static indicator and an effective dynamic indicator, the iterative procedure being stopped on a corrector, which is then the optimal corrector, when the two effective indicators become greater than respective thresholds determined for a current delay margin value.
1. A method for automated optimization of a servo control of a real mechatronic system controlled by a setpoint Y c (t) (P(t), V(t)), said servo control including a linear corrector in a feedback loop including the real mechatronic system, the linear corrector being defined by corrector parameters, the method comprising:
determining a nominal transfer function between an input control U(t) and an output variable Y(t) that is measured for servo control, the real mechatronic system modelled by the nominal transfer function; and
determining corrector parameters of the linear corrector using the nominal transfer function to achieve a robustness and a performance of the feedback loop, the robustness of the feedback loop applied to the nominal transfer function being dependent on a modulus margin, the performance of the feedback loop applied to the nominal transfer function being dependent on a nominal delay margin,
wherein, by an iterative procedure, a most performant optimum corrector is determined among a plurality of correctors, said iterative procedure comprising
varying a current value of the delay margin, for the same modulus margin,
individually testing the linear corrector having the nominal delay margin corresponding to a current value on the servo control of the real mechatronic system,
injecting an excitation signal w(t) into the feedback loop, and
evaluating two effective indicators based on at least an effective static margin M st and an effective dynamic margin M dyn , the effective static margin M st and the effective dynamic margin M dyn characterizing the robustness of the feedback loop, the two effective indicators being:
an effective static indicator Ind S that is the effective static margin M st , and
an effective dynamic indicator Ind D that is a function of the effective dynamic margin M dyn ,
the iterative procedure being stopped on the most performant optimum corrector when the two effective indicators Ind S and Ind D become higher than respective thresholds S s and S D determined for a current value of the nominal delay margin that is the lowest possible, for a same level of the nominal modulus margin, and for the highest performance.
2. The method according to claim 1 , wherein, during each evaluation, an effective complementary sensitivity function T yp (s) is estimated and the two effective indicators Ind S and Ind D are calculated based on said effective complementary sensitivity function T yp (s), the effective static indicator Ind S being the effective static margin M st that is equal to the inverse of the norm H ∞ of the effective complementary sensitivity function:
M
st
=
1
max
ω
T
yp
(
j
ω
)
,
and
the effective dynamic indicator Ind D being a ratio between, in the numerator, the effective dynamic margin M dyn and, in the denominator, a parameter chosen from the nominal delay margin and the nominal dynamic margin M dyn0 ,
the effective dynamic margin M dyn being equal to the inverse of the maximum of the gain of the product of the effective complementary sensitivity function by the frequency ω:
M
dyn
=
1
max
ω
ω
T
yp
(
j
ω
)
,
the nominal delay margin MRC and the nominal dynamic margin M dyn0 being obtained by calculation on the feedback loop applied to the nominal transfer function.
3. The method according to claim 1 , wherein the nominal transfer function of the real mechatronic system is a simple-integrator or double-integrator function.
4. The method according to claim 1 , wherein the excitation signal is calculated and is a white noise.
5. The method according to preceding claim 1 , wherein the effective complementary sensitivity function T yp (s) is estimated by an identification method, said identification method being chosen from one of:
a method of real-time recursive identification, by a parametric identification method, and
a method of non-parametric identification by spectral identification, using a sliding discrete Fourier transform.
6. The method according to claim 5 , wherein the identification method is implemented in real-time or in deferred time.
7. The method according to claim 1 , wherein a calculator is implemented within the feedback loop, said calculator comprising a correction calculation part corresponding to the linear corrector, the linear corrector receiving as an input or using a signal resulting from the difference computed by the calculator between the setpoint Y c (t) and the output variable Y(t) that is measured for servo control, and producing a control signal U(t) as an output, said calculator being configured so that, during tests, the excitation signal w(t) is added to the control signal before sending to the real mechatronic system.
8. A servo-control system for a real mechatronic system controlled by d setpoint Y c (t) (P(t), V(t)), said servo control system comprising:
a linear corrector in a feedback loop including the real mechatronic system, the linear corrector being defined by corrector parameters, the real mechatronic system configured to be modelled by a nominal transfer function, between an input control U(t) and an output variable Y(t) measured for servo control; and
a calculator configured to execute the method according to claim 1 and in which, during tests on the real mechatronic system, the calculator ensures the servo control by processing signals using a tested corrector receiving as an input, or using, a signal resulting from the difference computed by the calculator between the setpoint Y c (t) and the output variable Y(t) that is measured for servo control, and producing as an output a control signal U(t), said calculator being furthermore configured so that, during the tests, an excitation signal w(t) is added to the control signal before sending to the mechatronic system.
9. The servo-control system according to claim 8 , wherein the calculator is configured to evaluate two effective indicators based on at least an effective static margin M st and an effective dynamic margin M dyn , the effective static margin M st and the effective dynamic margin M dyn characterizing the robustness of the feedback loop, the two effective indicators being:
an effective static indicator Ind S that is the effective static margin M st , and
an effective dynamic indicator Ind D that is a function of the effective dynamic margin M dyn .
10. The servo-control system according to claim 9 , wherein the calculator is further configured to execute an iterative procedure of the tests and evaluations, said iterative procedure being stopped on an optimum corrector when the two effective indicators Ind S and Ind D become higher than respective thresholds S s and S D determined for a current value of nominal delay margin that is the lowest possible value, and hence for the highest performance.
11. The method according to claim 2 , wherein the nominal transfer function of the real mechatronic system is a simple-integrator or double-integrator function.
12. The method according to claim 2 , wherein the excitation signal is calculated and is a white noise.
13. The method according to preceding claim 2 , wherein the effective complementary sensitivity function T_yp (s) is estimated by an identification method, said identification method being chosen from one of:
a method of real-time recursive identification, by a parametric identification method, and
a method of non-parametric identification by spectral identification, using a sliding discrete Fourier transform.
14. The method according to claim 13 , wherein the identification method is implemented in real-time or in deferred time.
15. The method according to claim 2 , wherein a calculator is implemented within the feedback loop, said calculator comprising a correction calculation part corresponding to the linear corrector, the linear corrector receiving as an input or using a signal resulting from the difference computed by the calculator between the setpoint Y c (t) and the output variable Y(t) that is measured for servo control, and producing a control signal U(t) as an output, said calculator being configured so that, during tests, the excitation signal w(t) is added to the control signal before sending to the real mechatronic system.