Method of setting a controller with setpoint weighting

Abstract

The invention relates to a method for the closed-loop control of a proportional integral-type controller (2) in an instrumentation and control device (1) of a closed-loop control system (3), in particular a servovalve-actuator system, said controller (2) including a setpoint-weighting coefficient (β), said closed-loop control method comprising the consecutive steps of assigning (11) a unit value to the set-point weighting coefficient (β), optimizing (12) a closed-loop control of the controller (2) satisfying at least one predefined performance criterion, defining a characteristic tracking error (εTC) making it possible to respond to the performance constraints of the system to be closed-loop controlled, and assigning (132) a setpoint weighting coefficient (β) value, depending on the characteristic tracking error (εTC) and the closed-loop control of the controller (2).

Claims

1. A method for controlling a control command device of a servo-controlled system, the method comprising: setting of a proportional integral-type corrector in the control command device, the proportional integral-type corrector including a setpoint weighting coefficient, a proportional gain and an integral gain, the method including the successive steps of: setting the setpoint weighting coefficient at a unit value, setting the proportional gain and the integral gain of the corrector meeting at least one predefined performance criterion, defining a characteristic tracking error allowing to meet performance constraints of the servo-controlled system, setting the setpoint weighting coefficient at a setpoint weighting coefficient value according to the characteristic tracking error and the proportional gain and the integral gain previously set, and controlling the control command device based on the setpoint weighting coefficient.

2. The method according to claim 1, wherein the step of setting the proportional gain and the integral gain of the corrector further comprises the following steps: determining and setting the proportional and integral gains at initial values, and adjusting by iteration proportional and integral gains, so as to optimize at least one predefined performance criterion.

3. The method according to claim 2, wherein the step of determining the initial values of the proportional and integral gains is carried out by an empirical method of Ziegler-Nichols or by an empirical method of Takahashi.

4. The method according to claim 1, further comprising a step of determining a safety margin, and wherein the step of setting the setpoint weighting coefficient at the setpoint weighting coefficient value is carried out according to a theoretical error of the command control device and the safety margin.

5. The method according to claim 4, wherein the safety margin is determined according to the behavioral gap between the real system and its linearized model.

6. The method according to claim 1, wherein the corrector includes no derivative component.

7. The method according to claim 1, the method being carried out automatically by means of a setting module including one or more memory units, in which setpoints are stored allowing the execution of the automatic setting method, the setpoints being executed by means of at least one processor.

8. The method according to claim 1, wherein the servo-controlled system is a servo valve-cylinder system.

9. A control command device of a servo-controlled system, the control command device including a setpoint inputted into a corrector, an output signal of the corrector being inputted into the servo-controlled system, the servo-controlled system producing a response, the response also being inputted into the corrector, in which the corrector is a proportional integral-type corrector comprising a setpoint weighter, the setpoint weighter including a setpoint weighting coefficient, the control command device comprising at least one processor configured to at least: set the setpoint weighting coefficient at a unit value, set the proportional gain and the integral gain of the corrector meeting at least one predefined performance criterion, define a characteristic tracking error allowing to meet the performance constraints of the servo-controlled system, set the setpoint weighting coefficient at a setpoint weighting coefficient value according to the characteristic tracking error and the proportional gain and the integral gain previously set, and control the control command device based on the setpoint weighting coefficient.

10. The command device according to claim 9, wherein the corrector is configured to generate a command corresponding to the sum of: the error integrated and modified by an integral gain, the difference between a weighted setpoint weighted by the setpoint weighting coefficient and the response of the servo-controlled system, the difference being modified by a proportional gain, wherein the integral gain, the proportional gain and the setpoint weighting coefficient are parameters of the corrector that can be set.

Description

PRESENTATION OF THE FIGURES

(1) Other characteristics and advantages of the invention will emerge from the following description, which is purely illustrative and not limiting, and should be read with reference to the appended figures in which:

(2) FIG. 1 is a diagram of a servo-control chain according to the invention;

(3) FIG. 2 is a diagram detailing a method for the automatic setting of a corrector according to the invention;

(4) FIG. 3 shows a setting module allowing to carry out a method in accordance with the invention;

DESCRIPTION OF ONE OR MORE EMBODIMENTS

(5) Generalities:

(6) With reference to FIG. 1, a control command chain 1 includes a corrector 2 and a servo-controlled system 3.

(7) In a preferred embodiment, the servo-controlled system 3 includes an integrator.

(8) In the embodiment shown, the corrector 2 is of the proportional integral type with setpoint weighting.

(9) A setpoint X is inputted at the input of the corrector 2, which transforms the setpoint X into a command U, the command U being inputted into the servo-controlled system 3.

(10) The servo-controlled system 3 reacts depending on the command U received, the response Y of the servo-controlled system being measured and returned to the corrector 2.

(11) More specifically, the corrector 2 performs a proportional action 4 and an integral action 5 in parallel, which are inputted into an adder 6.

(12) The adder 6 thus generates the command U, which is inputted into the servo-controlled system 3.

(13) The setpoint X and the response Y are both inputted into each of the proportional 4 and integral 5 action chains.

(14) The proportional action 4 receives as input the setpoint X, which is inputted into a weighter 7 so as to generate a weighted setpoint X′.

(15) The weighter 7 applies a gain, or a setpoint weighting coefficient β, to the setpoint X.

(16) The weighted setpoint X′ and the response Y are inputted into a subtractor 9, generating a weighted error e′, that is to say the difference between the weighted setpoint X′ and the response Y.

(17) The weighted error e′ is inputted into a proportional gain K.sub.P, then into the adder 6.

(18) The integral action 5 receives as input the setpoint X, which is inputted into a subtractor 10 with the response Y, generating an error ε corresponding to the difference between the setpoint X and the response Y.

(19) In this specific case, the error E is a tracking error ε.sub.T, the setpoint X being of the ramp type.

(20) The error ε is then inputted into an integral gain K.sub.I, then into an integrator block 8. The output of the integrator 8 is inputted into the adder 6.

(21) It is possible in other embodiments that the weighter 7 is located on the integral action 5, or upstream of the corrector, or that each of the proportional 4 and integral 5 actions includes a weighter 7 each having a weighting coefficient setpoint p, these coefficients being mutually different.

(22) Corrector Setting:

(23) As is well known, the dimensioning of the proportional K.sub.P and integral K.sub.I gains has an impact on the stability, the response time and the robustness of the control chain 1.

(24) The setting of the degrees of freedom of the corrector 2 allows optimizing the criteria of stability, response time and robustness of the system, as well as minimizing the overshoot and the tracking error.

(25) A method for the automatic setting of these parameters includes a plurality of steps carried out sequentially. This method is illustrated in FIG. 2.

(26) An assignment step 11 is performed firstly, during which the setpoint weighting coefficient β is fixed at a unit value. In this way, the corrector has a behavior of a conventional proportional integral corrector.

(27) An optimization step 12 is then carried out, during which a setting of the corrector 2 is carried out so as to optimize at least one performance criterion, which can be selected from, for example, robustness, response time, overshoot, or any other criterion or combination of criteria allowing to quantify the performances and the behavior of a servo-controlled system.

(28) During a determination step 121, initial values are determined and assigned to the proportional gain K.sub.P and to the integral gain K.sub.I.

(29) This is a first setting of the corrector 2, achievable by a conventional setting method such as for example an empirical method of Ziegler Nichols or Takahashi, as described below.

(30) During the determination step 121 according to the Takahashi method, the gain margin of the system to be regulated is estimated by increasing the gain until a self-sustaining oscillating system is obtained.

(31) Initial proportional and integral gain values are then defined according to the gain margin values given by the Takahashi method (correspondence table available in the literature).

(32) Any other conventional corrector setting method can be used to carry out this step, the choice of another method being able to lead to a determination of the initial values of proportional and integral gains according to a criterion other than the gain margin, such as for example the overshoot or the response time.

(33) The initial values of the proportional gain K.sub.P and of the integral gain K.sub.I are then refined during an adjustment step 122.

(34) During the adjustment step 122, the proportional gain K.sub.P and integral gain K.sub.I values are refined by iteration, so as to comply with the requirements of stability, response time and robustness which are stipulated by the list of requirements of the control command chain 1. The value of the gains is increased or decreased until a setting which gives satisfactory results in simulation is obtained.

(35) Once the optimal proportional gain K.sub.P and integral gain K.sub.I values obtained, they are fixed, and a weighting setting step 13 is then carried out.

(36) By applying the final value theorem to a system such as a control command chain 1, the setpoint weighting coefficient β can be expressed by the relation:

(37) $\beta =1-\mathrm{.Math.}\times \frac{K_I}{K_P}$

(38) In the embodiment described, the setpoint weighting coefficient β is therefore a function of the proportional gain K.sub.P and of the integral gain K.sub.I, as well as of the system error ε.

(39) The proportional gain K.sub.P and the integral gain K.sub.I being fixed, it is therefore possible to calibrate the value of the setpoint weighting coefficient β so as to reach an error value E corresponding to the criteria of the list of requirements defining the performance to be achieved for the control command chain 1.

(40) In order to obtain a behavior that complies with the criteria specified by the list of requirements, it is necessary to dimension the setting of the corrector for the most unfavorable operating cases.

(41) The most unfavorable operating cases are encountered in the case where the setpoints have the largest gradient.

(42) The setpoint gradient limitations imply that the most demanding setpoints will have the form of ramps with a gradient equal to that of the gradient limiter.

(43) Consequently, the type of error that will be used to size the corrector will be a tracking error, corresponding to the error following the most demanding setpoint model (a ramp).

(44) Prior to the weighting assignment step 132, a modeling step 131 can be carried out, during which the servo-controlled system 3 is assimilated to a theoretical model 3′ representing its operation.

(45) In the selected embodiment, the servo-controlled system model 3′ is a perfect second order linear system associated with an integrator, subjected to a ramp-type setpoint of unit slope. It may for example include an actuator of the servo valve-cylinder type.

(46) The command chain 1 is therefore modeled by a command chain model 1′ including a corrector model 2′ similar to the corrector 2 and the servo-controlled system model 3′.

(47) During the modeling step 131, the corrector model 2′ has the settings established during the assignment 11 and optimization 12 steps.

(48) The setpoint weighting coefficient β is fixed at a unit value, the proportional K.sub.P and integral K.sub.I gains are fixed at the values obtained after the optimization step 12.

(49) A theoretical error ε.sub.TH of the command chain model 1′ can be deduced conventionally, which will then be used in order to proceed with the setting of the setpoint coefficient β.

(50) The theoretical error ε.sub.TH can also be a specification of the list of requirements and be extracted directly from the list of requirements.

(51) However, it is possible in other embodiments to apply a setpoint on a ramp with a non-unit slope.

(52) In the selected embodiment of a ramp setpoint, the theoretical error of the model is therefore a characteristic tracking error ε.sub.TC.

(53) The setpoint weighting coefficient β can therefore be defined during the weighting assignment step 132 for a value expressed according to the formula:

(54) $\beta =1-\left({\mathrm{.Math.}}_{\mathrm{TC}}\right)\times \frac{K_I}{K_P}$

(55) The value thus expressed will be assigned to the weighter 7 of the control chain 1.

(56) Under the effect of the setting of the value of the setpoint weighting coefficient β, the command chain 1 will have a tracking error ET which will tend to the value of the characteristic tracking error ε.sub.TC.

(57) Optionally, the theoretical error ε.sub.TH can be associated with a safety margin σ defined so as to take into account the non-linearity of the operation of the servo-controlled system 3. It is necessary to take into account its imperfections in the synthesis of the corrector 2. The setpoint weighting coefficient β is then defined according to the formula:

(58) $\beta =1-\left({\mathrm{.Math.}}_{\mathrm{TH}}+\sigma \right)\times \frac{K_I}{K_P}$

(59) In the embodiment where the servo-controlled system 3 is modeled as a perfect second order linear system with an integrator subjected to a ramp setpoint, the setpoint weighting coefficient β can then be defined by the relation:

(60) $\beta =1-\left({\mathrm{.Math.}}_{\mathrm{TC}}+\sigma \right)\times \frac{K_I}{K_P}$

(61) The structure of this embodiment of the corrector 2 allows modifying the setpoint weighting coefficient β without having any effect on the performance in terms of stability and robustness of the corrector 2.

(62) The optimal setting of the setpoint weighting coefficient β allows optimizing the response time, the overshoot and the tracking error ε.sub.T, more specifically it allows defining the performance expected for the tracking error ε.sub.T without degrading the performance in response time and overshoot matter previously obtained by the proportional K.sub.P and integral K.sub.I gain setting.

(63) More particularly, the overshoot is highly contained while retaining a response time similar to a corrector 2 without weighter 7.

(64) In this embodiment, the corrector 2 preserves its properties of stability and robustness with or without a weighter 7.

(65) By avoiding adding a derivative component, the sensitivity of the system to measurement noise is greatly limited.

(66) Taking into account the theoretical error ε.sub.TH in the setting of the corrector 2 allows obtaining an optimal overshoot/error ε compromise compared to the specifications of the list of requirements.

(67) In the embodiment in which the servo-controlled system 3 is modeled as a perfect second order linear system with an integrator subjected to a ramp setpoint, taking into account the characteristic tracking error ε.sub.TC in the setting of the corrector 2 allows obtaining an optimal overshoot/tracking error ε.sub.T compromise compared to the specifications of the list of requirements.

(68) The automated setting method allows greatly limiting the duration of the operation, in addition to simplifying the process.

(69) The structure of the setting is simple, which limits its development and maintainability costs.

(70) The automatic setting method of the corrector 2 is carried out by means of a setting unit or module 14 including one or more memory units 15, in which setpoints are stored allowing the execution of the automatic setting method.

(71) The setpoints are executed by means of at least one processor 16, which implements the automatic setting method of the corrector 2. The processor 16 and the memory 15 are typically part of the engine computer, but it is alternatively possible that they are integrated into a specific module physically separate from the engine control unit.

(72) Similarly, if there is an existing setting of a PI corrector with setpoint weighting for an integrator system, then it is possible to know the tracking error that we will be obtained, for a ramp setpoint, thanks to the relation:

(73) ${\mathrm{.Math.}}_T=\frac{K_p}{K_I}\left(1-\beta \right)$

(74) Now, knowledge of the servo-control performance and therefore of the tracking error ET is essential for the design of the fallback modes of the turbomachine.

(75) When a fault is detected on the machine, a fallback must be carried out quickly to preserve the machine by avoiding keeping it for too long in a degraded state.

(76) Conversely, a too rapid reduction in the propeller speed relative to the power delivered by the gas generator is also dangerous because it may cause additional torques in the propeller shafts.

(77) Knowing the profile of decelerations in advance via knowledge of the tracking error ε.sub.T therefore allows optimizing the design of the propellers, whether from the point of view of piloting (synchronization between the propellers and the gas generator) or the mechanical design since the torques that will be present in the propeller shafts during rapid transients can be known in advance.