JP7621611B2 - Controller Design Method - Google Patents

Description

The present invention relates to a controller design method .

The engine bench system connects the engine under test and a dynamometer with a connecting shaft, and measures various engine characteristics by using the dynamometer as a power absorber and controlling the throttle opening of the engine with a throttle actuator. The connecting shaft is equipped with an axle torque meter that detects the axle torque, which is the torsional torque, and when the dynamometer is used as a power absorber, axle torque control is performed to make this axle torque match a specified axle torque command.

Patent Document 1 shows a method for designing a shaft torque controller using the I-PD control method. In an engine bench system, resonance may occur in the coupled shaft due to pulsating torque generated in the engine. In the design method of Patent Document 1, the characteristics of the engine bench system are expressed by a two-inertia system transfer function, and the gain parameters used in I-PD control are set by specifying the pole frequency of the fourth-order closed loop transfer function obtained by coupling this transfer function with the I-PD control device to approximately the mechanical resonance frequency of the engine bench system. As a result, the design method of Patent Document 1 makes it possible to design a shaft torque controller capable of shaft torque control with a resonance suppression effect.

In a typical engine bench system, the connecting shaft that connects the engine and dynamometer includes a clutch whose spring stiffness tends to fluctuate greatly. The shaft torque controller of Patent Document 1 allows stable control even when the spring stiffness of the connecting shaft fluctuates. However, in the design method of Patent Document 1, the gain parameters are set using the mechanical resonance frequency when the spring stiffness is low as a guide. For this reason, the design method of Patent Document 1 only produces conservative results, and the shaft torque controller designed using this method has poor control responsiveness.

In response to this, Patent Document 2 by the present applicant discloses a controller design method that can be designed while explicitly specifying the variation range of parameters that characterize the input/output characteristics of the controlled object. The controller design method disclosed in Patent Document 2 is based on a so-called robust controller design method that defines a feedback control system in which a variation part that gives unbounded complex variation to model parameters included in a generalized plant or a nominal plant is specified, and designs a controller by imposing sufficient conditions for robust stability derived from the small gain theorem as design conditions on this feedback control system. In particular, the controller design method disclosed in Patent Document 2 makes it possible to design a controller while explicitly specifying the variation range of model parameters by using bounded complex variation obtained by Cayley transformation as a variation output signal.

JP 2009-133714 A International Publication No. 2020/070963

According to the controller design method shown in Patent Document 2, in principle it is possible to handle the fluctuations of multiple model parameters, but in this case it is necessary to derive a transfer function for the multi-input multi-output system (more specifically, the transfer function described in Patent Document 2 as the "phase adjustment transfer function"), which is difficult. For this reason, Patent Document 2 shows an example in which the controlled object is approximated by a two-inertia system model, and only the fluctuations of one model parameter included in this two-inertia system model are handled.

On the other hand, the test system assumed as the controlled object in Patent Document 2 can be approximated with high accuracy by a two-inertia system model in the low frequency band including the low-order resonant frequencies, but cannot be approximated by a two-inertia system model in the high frequency band including the high-order resonant frequencies. For this reason, a controller designed by the method shown in Patent Document 2 may react sensitively to fluctuations in model parameters that are not included in the two-inertia system model, and stability in the high frequency band cannot be guaranteed.

An object of the present invention is to provide a controller design method capable of approximating a nominal plant using a low-order model having a small number of model parameters, while designing a controller with guaranteed stability in high frequency bands that cannot be adequately reproduced by the low-order model.

(1) The controller design method according to the present invention is a method for designing a controller by a computer so as to satisfy a predetermined design condition in a feedback control system including a nominal plant that mimics the input/output characteristics of a controlled object, a generalized plant including a fluctuation part that gives fluctuations to at least one fluctuation model parameter included in the nominal plant, and a controller that gives an input to the generalized plant based on an output from the generalized plant, wherein the nominal plant includes a low-order model that includes the fluctuation model parameters and mimics the input/output characteristics of the controlled object in a low-frequency band, and a fluctuation element that does not include the fluctuation model parameters and gives fluctuations to the output of the low-order model, and the transfer function of the fluctuation element is set so that the gain is larger in at least a part of a high-frequency band higher than the low-frequency band than a differential transfer function defined based on the difference between the transfer function of the high-order model that mimics the input/output characteristics of the controlled object in the high-frequency band and the transfer function of the low-order model.

(2) In this case, in the nominal plant, the variable element imparts a multiplicative variation to the output of the low-order model, and when a transfer function of the low-order model is P _L and a transfer function of the high-order model is P _H , it is preferable that the differential transfer function δ is defined by the following equation (1):

(3) In this case, in the nominal plant, the variable element applies an additive variation to the output of the low-order model, and when a transfer function of the low-order model is P _L and a transfer function of the high-order model is P _H , it is preferable that the differential transfer function δ is defined by the following equation (2):

(4) In this case, in the variable element setting step of setting the transfer function of the variable element, it is preferable to set the transfer function of the variable element so that the gain is greater than all of the multiple differential transfer functions obtained by varying the value of a model parameter other than the variable model parameter among the multiple model parameters included in the high-order model within a predetermined variation range.

(5) In this case, the nominal plant includes a nominal value multiplication unit that multiplies a predetermined input signal by the nominal value of the fluctuation model parameter, and an adder that adds the fluctuation output signal of the fluctuation unit and the output signal of the nominal value multiplication unit, and it is preferable that the fluctuation unit generates the fluctuation output signal by using a mapping by a Cayley transform of a complex fluctuation.

(6) In this case, it is preferable that the variation unit includes a bounded variation generating unit that generates a bounded variation signal by multiplying a predetermined input signal by the mapping, a phase adjustment unit that changes the phase of the variation signal using a phase adjustment transfer function, and a normalization unit that limits the norm of the variation output signal to within a predetermined range using the output signal of the phase adjustment unit and the input signal of the nominal value multiplication unit.

(7) In this case, it is preferable to provide a phase adjustment transfer function setting process in which the computer sets the phase adjustment transfer function so that the transfer function from the fluctuation signal to the input signal to the bounded fluctuation generating unit in the feedback control system becomes a positive real function, a sub-controller design process in which the computer designs a sub-controller so that the design conditions are satisfied in the feedback control system, and a controller synthesis process in which the controller is designed by connecting n sub-controllers in parallel, which are designed by alternately repeating the phase adjustment transfer function setting process and the sub-controller design process n times (n is an integer equal to or greater than 2).

(8) In this case, in the first phase adjustment transfer function setting step, the phase adjustment transfer function is set in a state where the controller is separated from the feedback control system, and in the first sub-controller design step, the sub-controller is designed in a state where the feedback control system includes the phase adjustment transfer function set through the first phase adjustment transfer function setting step, and in the second or subsequent phase adjustment transfer function setting steps, the phase adjustment transfer function is set in a state where one or more sub-controllers designed through the first to previous sub-controller design steps are connected in parallel to the generalized plant, and in the second or subsequent sub-controller design steps, the sub-controller is preferably designed in a state where the feedback control system includes the phase adjustment transfer function set through the previous phase adjustment transfer function setting step and the generalized plant includes one or more sub-controllers designed through the first to previous sub-controller design steps.

(9) In this case, in the phase adjustment transfer function setting step, it is preferable to set the phase adjustment transfer function using a metaheuristic algorithm.

(10) In this case, the low-order model is constructed based on an i-inertia system consisting of i (i is an integer equal to or greater than 2) or more inertial bodies characterized by a predetermined moment of inertia connected in series with i-1 or more shafts characterized by a predetermined spring stiffness and damping coefficient, and the high-order model is constructed based on a j-inertia system consisting of j (j is an integer greater than i) or more inertial bodies characterized by a predetermined moment of inertia connected in series with j-1 or more shafts characterized by a predetermined spring stiffness and damping coefficient, and the variable model parameters are preferably at least one of the moment of inertia, the spring stiffness, and the damping coefficient.

(11) In this case, the controlled object is a test system including a test specimen that generates torque in response to a test specimen input, a dynamometer that generates torque in response to a torque current command signal, a connecting shaft that connects the test specimen and the dynamometer, and a shaft torque meter that generates a shaft torque detection signal in response to the shaft torque on the connecting shaft, and the low-order model is constructed based on an i-inertia system consisting of i (i is an integer of 2 or more) inertial bodies connected in series with i-1 shaft bodies characterized by a predetermined spring stiffness, the high-order model is constructed based on a j-inertia system consisting of j (j is an integer greater than i) inertial bodies connected in series with j-1 shaft bodies characterized by a predetermined spring stiffness, the fluctuation model parameter is the spring stiffness, and the controller is preferably a shaft torque controller that outputs the torque current command signal when the shaft torque detection signal and a shaft torque command signal for the shaft torque detection signal are input.

(1) In the present invention, in a feedback control system including a nominal plant that imitates the input/output characteristics of a controlled object, a generalized plant that includes a fluctuation part that imparts fluctuations to at least one fluctuation model parameter included in the nominal plant, and a controller that imparts an input to the generalized plant based on an output from the generalized plant, a controller is designed by a computer to satisfy a predetermined design condition. In the present invention, a nominal plant is used that includes a low-order model that includes a fluctuation model parameter and imitates the input/output characteristics in the low-frequency band of the controlled object. This makes it possible to design a controller whose stability is guaranteed against fluctuations in the model parameters in the low-frequency band that can be sufficiently approximated by the low-order model. In addition, in the present invention, a nominal plant is used that includes a fluctuation element that does not include a fluctuation parameter and imparts fluctuations to the output of the low-order model in addition to the above-mentioned low-order model, and the transfer function of this fluctuation element is set so that its gain is larger than that of a differential transfer function defined based on the difference between the transfer function of a high-order model that imitates the input/output characteristics in the high-frequency band of the controlled object and the transfer function of the low-order model. This makes it possible to design a controller whose stability is guaranteed even in the high-frequency band that cannot be sufficiently approximated by the low-order model alone.

(2) In the present invention, the transfer function of the variable element that imparts a multiplicative variation to the output of the low-order model is set so that its gain is greater than the differential transfer function δ defined by the above formula (1). This makes it possible to design a controller that further guarantees stability in the high frequency band.

(3) In the present invention, the transfer function of the variable element that imparts additive variation to the output of the low-order model is set so that its gain is greater than the differential transfer function δ defined by the above formula (2). This makes it possible to design a controller with even greater guaranteed stability in the high frequency band.

(4) In the present invention, in the variable element setting step of setting the transfer function of the variable element, the transfer function of the variable element is set so that the gain is greater than all of the multiple differential transfer functions obtained by varying the value of a model parameter other than the variable model parameter among the multiple model parameters included in the high-order model within a predetermined variation range. This makes it possible to prevent control in the high frequency band from becoming unstable due to the variation of a model parameter that is not included in the low-order model but is included in the high-order model.

(5) In conventional robust controller design methods such as H∞ control and μ design, a feedback control system is defined in which a fluctuation part etc. that gives an unbounded complex fluctuation to the model parameters included in a generalized plant or a nominal plant is specified, and a sufficient condition for robust stability derived based on the small gain theorem is imposed as a design condition on this feedback control system, and a controller is designed to satisfy this design condition (see, for example, Liu Kangzhi, "Linear Robust Control", Corona Publishing, 2002). In this way, conventional robust controller design methods handle unbounded complex fluctuations, but this is equivalent to considering the fluctuation range of the model parameters to infinity on the imaginary axis in design, which is not realistic. In contrast, in the controller design method of the present invention, an additive fluctuation is given to the fluctuation model parameters of the low-order model by the fluctuation output signal output from the fluctuation part, and the fluctuation output signal is generated by using a mapping by the Cayley transform of the complex fluctuation. According to the Cayley transform, the unbounded complex fluctuation over the right half plane of the complex plane is mapped into a unit circle. Therefore, according to the controller design method of the present invention, the bounded complex fluctuation obtained by the Cayley transform can be used as the fluctuation output signal, so that the controller can be designed while explicitly specifying the fluctuation range of the fluctuation model parameters.

(6) In the controller design method of the present invention, a variation is given to the variation model parameters by using a variation unit that includes a bounded variation generating unit that generates a bounded variation signal by multiplying a predetermined input signal by a mapping based on the Cayley transform, a phase adjustment unit that changes the phase of the variation signal using a phase adjustment transfer function, and a normalization unit that limits the norm of the variation output signal to a predetermined range using the output signal of the phase adjustment unit and the input signal of the nominal value multiplication unit. According to the controller design method of the present invention, when the upper and lower limits of the variation range of the variation model parameters are known in advance, a controller that conforms to reality can be designed by limiting the norm of the variation output signal to a range determined using these upper and lower limits in the normalization unit.

(7) In the controller design method described in Patent Document 2 by the applicant of the present application, a controller is designed through a phase adjustment transfer function setting process in which a phase adjustment transfer function in a phase adjustment unit is set by a computer so that the transfer function from the bounded variation signal, which is the output of the bounded variation generating unit, to the input signal to the bounded variation generating unit becomes a positive real function when the controller is separated from the generalized plant, and a controller design process in which a controller is designed by a computer so as to satisfy the design conditions. Here, when a controller designed through these two processes is incorporated into an actual system, its phase changes. This means that the phase adjustment transfer function set in a state in which the controller is separated from the generalized plant is not optimal for the actual system in which the controller is incorporated. For this reason, a controller designed based on the controller design method described in Patent Document 2 may not be able to exhibit sufficient performance.

In contrast, in the present invention, a controller is designed by connecting n sub-controllers designed by alternately repeating the phase adjustment transfer function setting process and the sub-controller design process n times (n is an integer equal to or greater than 2) in parallel. This makes it possible to optimize the phase adjustment transfer function and the controller.

(8) In the present invention, in the first phase adjustment transfer function setting process, the phase adjustment transfer function is set in a state where the controller is separated from the feedback control system, and in the first sub-controller design process, the sub-controller is designed in a state where the feedback control system includes the phase adjustment transfer function set through the first phase adjustment transfer function setting process. In the second and subsequent phase adjustment transfer function setting processes, the phase adjustment transfer function is set in a state where one or more sub-controllers designed through the first to previous sub-controller design processes are connected in parallel to the generalized plant, and in the second and subsequent sub-controller design processes, the sub-controller is designed in a state where the feedback control system includes the phase adjustment transfer function set through the previous phase adjustment transfer function setting process and one or more sub-controllers designed through the first to previous sub-controller design process are connected in parallel to the generalized plant. This makes it possible to optimize the phase adjustment transfer function and the controller.

(9) In the controller design method of the present invention, a metaheuristic algorithm is used to set a phase adjustment transfer function so that the transfer function from the fluctuation signal to the input signal becomes a positive real function. This allows the phase adjustment transfer function to be set quickly regardless of the designer's skill.

(10) In the controller design method of the present invention, a low-order model is constructed based on an i-inertia system consisting of i (i is an integer of 2 or more) inertial bodies connected in series with i-1 or more shaft bodies, and a high-order model is constructed based on a j-inertia system consisting of j (j is an integer greater than i) inertial bodies connected in series with j-1 or more shaft bodies. In addition, in the present invention, at least one of the inertia moment of the inertial body and the spring stiffness and damping coefficient of the shaft body is set as a variable model parameter that is fluctuated by a variable part, and a controller is designed to control the multi-inertia system. This makes it possible to design a controller that can achieve stable and highly responsive control even when the inertia moment, spring stiffness, damping coefficient, etc. fluctuate.

(11) In the controller design method of the present invention, a test system including a test specimen that generates torque in response to a test specimen input, a dynamometer that generates torque in response to a torque current command signal, a connecting shaft that connects the test specimen and the dynamometer, and a shaft torque meter that generates a shaft torque detection signal in response to the shaft torque in the connecting shaft is treated as a control target, a low-order model is constructed based on the i-inertia system, a high-order model is constructed based on the j-inertia system, the spring stiffness of the shaft of the low-order model is set as a variable model parameter that is fluctuated by a fluctuating part, and a controller is designed that outputs a torque current command signal in response to the shaft torque detection signal and the shaft torque command signal. As described above, the connecting shaft that connects the test specimen and the dynamometer includes a clutch, and its spring stiffness has the characteristic of fluctuating greatly. In contrast, the controller design method of the present invention makes it possible to design a controller for a test system that can achieve stable and highly responsive control.

1 is a diagram showing a configuration of a test system equipped with a shaft torque controller designed by applying a controller design method according to an embodiment of the present invention. FIG. 1 is a diagram showing an example of the relationship between the torsion angle of a bond shaft and axial torque. FIG. 2 is a diagram showing a configuration of a feedback control system used when designing a shaft torque controller. FIG. 4 is a diagram showing a configuration of a controller derived based on the feedback control system of FIG. 3 . FIG. 1 is a diagram showing the configuration of a generalized plant. FIG. 2 is a diagram showing a detailed configuration of a nominal plant. FIG. 1 illustrates an example of a high-order model. 1 is a Bode diagram comparing input/output characteristics of a two-inertia system model adopted as a low-order model and a four-inertia system model adopted as a high-order model. FIG. 1 is a Bode plot comparing the input/output characteristics of the fluctuation elements and three differential transfer functions. FIG. 2 is a diagram showing the configuration of a variable section. FIG. 13 is a diagram showing mapping by the Cayley transform of a complex variation. 4 is a flowchart showing a specific procedure of a controller design method. FIG. 13 is a diagram for explaining the procedure of a sub-controller synthesis process. FIG. 13 is a diagram showing another example of a nominal model.

Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings.
1 is a diagram showing the configuration of a test system S equipped with an axle torque controller 7 designed by applying the controller design method according to this embodiment. The test system S includes an engine E as a test specimen, a dynamometer 2, a connecting shaft 3, an inverter 4, an axle torque meter 5, a throttle actuator 6, and the axle torque controller 7. The test system S is a so-called engine bench system that measures various characteristics of the engine E by using the dynamometer 2 as a power absorber for the engine E while controlling the throttle opening of the engine E with the throttle actuator 6.

When a throttle opening command signal corresponding to a command for the throttle opening of engine E is input, throttle actuator 6 controls the throttle opening of engine E to realize this, thereby causing engine E to generate engine torque corresponding to the throttle opening command signal.

The connecting shaft 3 connects the output shaft of the engine E and the output shaft of the dynamometer 2. The connecting shaft 3 includes a clutch, and therefore its spring stiffness has the characteristic of fluctuating within a predetermined range. FIG. 2 is a diagram showing an example of the relationship between the torsion angle [rad] of the connecting shaft and the shaft torque [Nm]. In FIG. 2, the inclination corresponds to the spring stiffness. As shown in FIG. 2, the spring stiffness of the connecting shaft has the characteristic of being small in a low stiffness region including a torsion angle of 0 [rad], and being large in a high stiffness region outside this low stiffness region. That is, in the example of FIG. 2, the lower limit k _min of the fluctuation range of the spring stiffness corresponds to the spring stiffness when the connecting shaft is in the low stiffness region, and the upper limit k _max corresponds to the spring stiffness when the connecting shaft is in the high stiffness region.

Returning to FIG. 1, the shaft torque meter 5 generates a shaft torque detection signal corresponding to the shaft torque in the connected shaft 3 and transmits it to the shaft torque controller 7. The shaft torque controller 7 uses the shaft torque command signal and the shaft torque detection signal to generate a torque current command signal equivalent to a command for the torque generated by the dynamometer 2 so that the shaft torque control deviation, which is the difference between a predetermined shaft torque command signal and the shaft torque detection signal from the shaft torque meter 5, is eliminated, and inputs this to the inverter 4. The inverter 4 supplies power corresponding to the torque current command signal input from the shaft torque controller 7 to the dynamometer 2, thereby causing the dynamometer 2 to generate a dynamo torque corresponding to the torque current command signal.

The shaft torque controller 7 that performs the above-described shaft torque control defines a feedback control system 8 as shown in FIG. 3, and is configured by implementing a controller designed to satisfy predetermined design conditions in this feedback control system 8 in hardware equipped with input/output ports such as a digital signal processor or microcomputer.

In the test system S configured as above, the shaft torque controller 7, which is equipped with the controller K described below, generates a torque current command signal and inputs it to the inverter 4 via communication when it receives a shaft torque command signal transmitted from a higher-level controller (not shown) via communication and a shaft torque detection signal transmitted from the shaft torque meter 5 equipped on the dynamometer 2. When the inverter 4, which is electrically connected to the dynamometer 2, receives a torque current command signal from the shaft torque controller 7, it generates a torque in the dynamometer 2 according to the torque current command signal. Note that disturbance elements assumed at this time include noise generated when the shaft torque is measured by the shaft torque meter 5, time delays in each communication path, and nonlinear deviations between the torque current command signal and the generated torque due to the control response of the inverter 4, etc. Note that the above-mentioned shaft torque command signal may be generated by a higher-level controller other than the shaft torque controller 7 as described above, or may be generated by a module constructed separately from the controller K inside the shaft torque controller 7.

The feedback control system 8 in FIG. 3 is constructed by combining a generalized plant P having a nominal plant N that mimics the input/output characteristics of the test system S from the input to the engine E and the input to the dynamometer 2 to the output of the axle torque meter 5, a controller K that provides input and output to this generalized plant P, and a fluctuation section Δ that provides fluctuations to the nominal plant N.

In the generalized plant P, an input consisting of a first disturbance input w1, a second disturbance input w2, and a third disturbance input w3, and an output consisting of a first evaluation output z1, a second evaluation output z2, and a third evaluation output z3 are defined. In the following, a vector quantity having components of the first disturbance input w1, the second disturbance input w2, and the third disturbance input w3 is denoted as w, and a vector quantity having components of the first evaluation output z1, the second evaluation output z2, and the third evaluation output z3 is denoted as z. The specific configuration of the generalized plant P will be described in detail later with reference to FIG. 5 and FIG. 6.

Between the generalized plant P and the controller K, a first observation output y1 corresponding to the shaft torque detection signal, a second observation output y2 corresponding to the shaft torque command signal, and a control input u corresponding to the torque current command signal are defined. By setting the above-mentioned input/output signals between the generalized plant P and the controller K, as shown in FIG. 4, a two-degree-of-freedom control system controller K is derived that is configured by combining two transfer functions Ky1(s) and Ky2(s) and outputs a control input u from the first observation output y1 and the second observation output y2.

Returning to FIG. 3, between the generalized plant P and the fluctuation section Δ, a fluctuation input η, which is a scalar quantity, and a fluctuation output ξ, which is also a scalar quantity, are defined. The fluctuation section Δ generates a fluctuation output ξ based on the fluctuation input η output from the generalized plant P, and provides this fluctuation output ξ to the generalized plant P, thereby providing a fluctuation to the nominal plant N. The specific configuration of this fluctuation section Δ will be described in detail later with reference to FIG. 10.

Figure 5 shows the configuration of the generalized plant P. The generalized plant P is composed of a nominal plant N that mimics the input/output characteristics of the test system S to be controlled, a fluctuation section Δ that imparts fluctuations to at least one fluctuation model parameter included in the nominal plant N, and multiple weighting functions We(s), Wu(s), Wy(s), Wd(s), Wr(s), and Wn(s).

The nominal plant N has input/output characteristics that mimic the input/output characteristics from the dynamo torque corresponding to the torque current command signal to the shaft torque corresponding to the shaft torque detection signal in the test system S in Figure 1.

The nominal plant N comprises a low-order model M1 constructed to simulate the input/output characteristics of the controlled object, particularly the low-frequency band, and a variable element M2 that imparts variation to the output of the low-order model M1. As shown in FIG. 5, the variable part Δ is connected to the low-order model M1 but is not connected to the variable element M2. In other words, the low-order model M1 includes a variable model parameter, whereas the variable element M2 does not include a variable model parameter.

In this embodiment, the case will be described where the variable element M2 gives a multiplicative variation to the output of the low-order model M1 as shown in Fig. 5. That is, when the transfer function of the low-order model M1 is P _L and the transfer function of the variable element M2 is W p , the transfer function P _N of the nominal plant N is expressed by the following formula (3).

FIG. 6 is a diagram showing a detailed configuration of the nominal model N.
As described above, the low-order model M1 is constructed so as to simulate the input/output characteristics of the controlled object in the low frequency band. In this embodiment, the low-order model M1 is constructed based on the equation of motion of a two-inertia system formed by connecting, for example, a first inertial body having an inertial moment JE of an engine _E and a second inertial body having an inertial moment _JD of a dynamometer 2 by one shaft having a spring stiffness of a predetermined nominal value _k0 and a predetermined damping coefficient D. This low-order model M1 is constructed by combining a transfer function G _a1 (s) (see equation (4-1) below) from the sum of engine torque and shaft torque (not shown) to the rotation speed of the first inertia body corresponding to the engine (engine speed), a transfer function G _a2 (s) (see equation (4-2) below) from the difference between dynamo torque and shaft torque to the rotation speed of the second inertia body corresponding to the dynamometer (dynamo speed), and a transfer function G _a3 (s) (see equation (4-3) below) from the difference between the engine speed and dynamo speed to the shaft torque, as shown in Figure 6.

In the low-order model M1 formed by combining three transfer functions, the moments of inertia _JE and _JD are the moments of inertia of the engine E and the dynamometer 2, respectively, obtained by a known method. A predetermined positive value is used as the damping coefficient D of the shaft. The nominal value _k0 of the spring stiffness of the shaft is set to the lower limit _kmin of the assumed fluctuation range of the spring stiffness of the connecting shaft 3 used in the test system S ( _k0 = _kmin ). Here, the lower limit _kmin of the fluctuation range of the spring stiffness is the spring stiffness value when the connecting shaft is in the low stiffness region in the example of FIG. 2.

As described above, in the low-order model M1, four model parameters are defined: the moment of inertia of the engine, the moment of inertia of the dynamometer, the damping coefficient of the coupling shaft, and the spring stiffness of the coupling shaft. The variation unit Δ varies the spring stiffness, which is one of these four model parameters. That is, among the four model parameters included in the low-order model M1, the variation model parameter to which the variation unit Δ varies is the spring stiffness. More specifically, the low-order model M1 includes a nominal value multiplication unit 51 that multiplies an input signal η corresponding to the rotation speed of the coupling shaft by a nominal value k ₀ of the spring stiffness, and a summing unit 52 that sums a variation output signal ξ, which is an output signal of the variation unit Δ, and an output signal of the nominal value multiplication unit 51. When an input signal η to the nominal value multiplication unit 51 is input, the variation unit Δ generates a variation output signal ξ and inputs it to the summing unit 52. As a result, the fluctuation section Δ imparts an additive fluctuation to the spring stiffness, which is a fluctuation model parameter of the low-order model M1.

The variable element M2 is a weighting function that imparts a multiplicative variation in the high frequency band that cannot be simulated by the output of the low-order model M1, which imitates the input/output characteristics of the controlled object in the low frequency band as described above. In other words, the variable element M2 is set so that the input/output characteristics of the controlled object from the low frequency band to the high frequency band can be simulated by the entire nominal plant N, which combines the low-order model M1, which mainly simulates the low frequency band, and the variable element M2.

For this reason, the transfer function Wp of the variable element M2 is set based on a differential transfer function δ defined based on the difference between a transfer function P _H of a high-order model M3 (see FIG. 7 described later) that imitates the input/output characteristics of the controlled object in the low frequency band and the high frequency band, and a transfer function P _L of a low-order model M1 that imitates the input/output characteristics of the controlled object in the low frequency band. When the variable element M2 gives a multiplicative fluctuation to the output of the low-order model M1, this differential transfer function δ is defined by the following formula (5).

After defining the differential transfer function δ as shown in the above formula (5), the transfer function Wp of the variable element M2 is set so that the gain is greater than the differential transfer function δ in at least a part of the high frequency band that cannot be simulated by the low-order model M1 among all frequency bands. More specifically, the transfer function Wp of the variable element M2 is set so that the gain is greater across the entire high frequency band than all of the multiple differential transfer functions δ obtained by varying within a predetermined variation range the values of model parameters other than the variable model parameters defined in the low-order model M1 among the multiple model parameters included in the high-order model M3.

Fig. 7 is a diagram showing an example of the high-order model M3. Fig. 7 shows a case where the high-order model M3 is constructed based on the equation of motion of a four-inertia system in _{which four inertia bodies characterized by inertia moments J1, J2 , J3 ,} and _J4 are connected in series with three shaft bodies characterized by spring stiffnesses _{k1, k2, k3, and k4 and damping coefficients D1 , D2 , D3 , and D4} . In the above-mentioned low-order model M1, the spring stiffness _k0 that is varied by the variable part Δ corresponds to the spring stiffness _k3 in the four-inertia system shown in Fig. 7, and the inertia moment _JE of the engine E in the low-order model M1 corresponds to the inertia moment _J4 in the four-inertia system shown in Fig. 7.

Figure 8 is a Bode diagram comparing the input/output characteristics of a two-inertia system model (see solid line) used as the low-order model M1 and a four-inertia system model (see dashed line) used as the high-order model M3. As shown in Figure 8, the two-inertia system model and the four-inertia system model have roughly the same input/output characteristics in the low-frequency band including the first-order resonance frequency f1 of the controlled object. In contrast, in the high-frequency band including the second-order resonance frequency f2 and the third-order resonance frequency f3 of the controlled object, the two-inertia system model and the four-inertia system model have a large difference in input/output characteristics. In other words, the four-inertia system model can reproduce the second-order and third-order resonance points in the high-frequency band of the controlled object, whereas the two-inertia system model cannot reproduce these second-order and third-order resonance points. As described above, the high-order model M3 is constructed to be able to simulate the high-frequency band that cannot be simulated by the low-order model M1.

Note that, in the following, a case will be described in which the low-order model M1 and the high-order model M3 are each constructed based on a multi-inertia system model, but the present invention is not limited to this. In other words, the low-order model is constructed to simulate the input/output characteristics of the control target in the low frequency band, and the high-order model may be any model constructed to simulate the input/output characteristics of the high frequency band that cannot be simulated by the low-order model.

In the following, a case will be described in which the low-order model M1 is constructed based on a two-inertia system model and the high-order model M3 is constructed based on a four-inertia system model, but the present invention is not limited to this. The low-order model may be constructed based on an i-inertia system model consisting of i (i is an integer equal to or greater than 2) or more inertial bodies characterized by a predetermined moment of inertia connected in series with i-1 shaft bodies characterized by predetermined spring stiffness and damping coefficient. In this case, the high-order model may be constructed based on a j-inertia system model consisting of j (j is an integer greater than i) or more inertial bodies characterized by a predetermined moment of inertia connected in series with j-1 shaft bodies characterized by predetermined spring stiffness and damping coefficient.

Fig. 9 is a Bode diagram comparing the input/output characteristics of the variable element M2 and the three differential transfer functions δ1, δ2, and δ3. More specifically, Fig. 9 is a diagram showing an example of setting the variable element M2. In Fig. 9, three differential transfer functions δ1, δ2, and δ3 obtained by varying the spring stiffness _k2 and the moment of inertia _J3 , which are model parameters other than the spring stiffness _k3 corresponding to the variable model parameter _k0 of the low-order model M1, within a predetermined variation range, among the multiple model parameters included in the differential transfer function δ defined by the above formula (5), are plotted in an overlapping manner.

As shown in FIG. 9, the transfer function Wp of the variable element M2 is set so that its gain is greater than that of all three differential transfer functions δ1 to δ3 in the entire frequency band including the first to third resonance frequencies f1 to f3.

In this embodiment, the case has been described where the variable model parameter of the low-order model M1 is the spring stiffness _k0 , and among the multiple model parameters included in the differential transfer function δ, the spring stiffness _k2 and the moment of inertia _J3 are varied within a predetermined variation range, but the present invention is not limited to this. For example, when the variable model parameter of the low-order model M1 is the moment of inertia _JE , among the multiple model parameters included in the differential transfer function δ, the spring stiffnesses _k2 and _k3 are varied within a predetermined variation range to set multiple differential transfer functions, and the transfer function Wp of the variable element M2 may be set so that its gain is larger than all of these differential transfer functions.

Returning to FIG. 5, the generalized plant P has multiple input/output signals defined, which are the first disturbance input w1, the second disturbance input w2, the third disturbance input w3, the first evaluation output z1, the second evaluation output z2, the third evaluation output z3, the control input u, the first observation output y1, the second observation output y2, the fluctuation input η, and the fluctuation output ξ. The correspondence between these input/output signals and the test system S in FIG. 1 is as follows:

The first disturbance input w1 is an input signal to the generalized plant P and corresponds to a disturbance to the control input u output from the controller K. The first disturbance input w1 is weighted by a preset weighting function Wd(s). The second disturbance input w2 is an input signal to the generalized plant P and corresponds to the shaft torque command signal input to the controller K. The second disturbance input w2 is weighted by a preset weighting function Wr(s). The third disturbance input w3 is an input signal to the generalized plant P and corresponds to a disturbance to the shaft torque detection signal input to the controller K. The third disturbance input w3 is weighted by a preset weighting function Wn(s).

The control input u is an input signal from the controller K to the generalized plant P, and corresponds to a torque current command signal. The sum of this control input u and the first disturbance input w1 weighted by the weighting function Wd(s) is input to the nominal plant N. The first observation output y1 is an input signal from the generalized plant P to the controller K, and corresponds to an axial torque detection signal. The first observation output y1 is the sum of the output of the nominal plant N and the third disturbance input w3 weighted by the weighting function Wn(s). The second observation output y2 is an input signal to the controller K, and corresponds to an axial torque command signal. The second disturbance input w2 weighted by the weighting function Wr(s) is used for this second observation output y2.

The first evaluation output z1 is an output signal of the generalized plant P and corresponds to a weighted shaft torque control deviation. The deviation obtained by subtracting the control input u corresponding to the torque current command signal from the second observation output y2 corresponding to the shaft torque command signal is weighted by a preset weighting function We(s) and used as the first evaluation output z1. The second evaluation output z2 is an output signal of the generalized plant P and corresponds to a weighted torque current command signal. The second evaluation output z2 is a control input u corresponding to the torque current command signal weighted by a preset weighting function Wu(s) as described above and used as the second evaluation output z2. The third evaluation output z3 is an output signal of the generalized plant P and corresponds to a weighted shaft torque detection signal. The third evaluation output z3 is a nominal plant N output weighted by a preset weighting function Wy(s).

Figure 10 shows the configuration of the variation unit Δ. The variation unit Δ includes a bounded variation generating unit 61, a phase adjusting unit 62, and a normalizing unit 63, which are used to generate a variation output signal ξ from an input signal η input from the nominal plant N, and input the variation output signal ξ to the nominal plant N.

The bounded variation generating unit 61 generates a bounded variation signal ξ1 by multiplying the input signal η1 input from the normalizing unit 63 by a mapping by the Cayley transform of the unbounded complex variation Δg, and outputs the bounded variation signal ξ1 to the phase adjusting unit 62. More specifically, the bounded variation generating unit 61 generates the variation signal ξ1 by multiplying the input signal η1 by a mapping Δp by the Cayley transform of the complex variation Δg, as shown in the following formula (6). According to the Cayley transform shown in the following formula (6), the unbounded complex variation Δg across the right half plane of the complex plane is mapped into a unit circle with a radius of 1 centered at the origin, as shown in FIG.

The phase adjustment unit 62 changes the phase of the fluctuation signal ξ1 by multiplying the bounded fluctuation signal ξ1 generated by the bounded fluctuation generation unit 61 by a predetermined phase adjustment transfer function W _scope (s). As will be described later with reference to FIG. 12, the function form of this phase adjustment transfer function W _scope (s) is set so that the transfer function M(s) from the fluctuation signal ξ1 output from the bounded fluctuation generation unit 61 to the input signal η1 input to the bounded fluctuation generation unit 61 is a positive real function. Here, when the following inequality (7) is satisfied for the transfer function M(s), the transfer function M(s) is defined as a positive real function. Here, M ^* (s) is the complex conjugate of M(s).

The normalization unit 63 uses the output signal of the phase adjustment unit 62 and the input signal η input from the nominal plant N to limit the norm of the fluctuation output signal ξ output from the fluctuation unit Δ to a predetermined range. The normalization unit 63 inputs a signal η1 obtained by multiplying the input signal η by a predetermined second norm N2 and then multiplying the output signal of the phase adjustment unit 62 by a predetermined first norm N1 to the bounded fluctuation generation unit 61, and also generates a fluctuation output signal ξ by multiplying the output signal of the phase adjustment unit 62 by a predetermined third norm N3, and inputs the generated fluctuation output signal ξ to the nominal plant N. Here, the norms N1, N2, and N3 are set, for example, as shown in the following formula (8). As a result, the norm of the fluctuation output signal ξ generated by the fluctuation unit Δ is limited to a range between 0 and k _max -k _min .

Figure 12 is a flowchart showing the specific steps of the controller design method according to this embodiment.

First, in S1, the designer sets the low-order model M1 and the variable element M2 by using a computer, and sets the nominal plant N as shown in FIG. 6 by combining the low-order model M1 and the variable element M2. More specifically, the designer sets the low-order model M1 and the high-order model M3 by using a computer, and sets the differential transfer function δ according to the above formula (5) by using the low-order model M1 and the high-order model M3, and sets the transfer function of the variable element M2 based on this differential transfer function δ. More specifically, the designer sets multiple differential transfer functions by varying the values of model parameters other than the variable model parameters among the multiple model parameters included in the high-order model M3 within a predetermined variation range, and sets the transfer function Wp of the variable element M2 so that the gain is larger than all of the multiple differential transfer functions in all frequency bands including the low frequency band and the high frequency band, as described with reference to FIG. 9. After that, the designer sets the nominal plant N by combining the low-order model M1 and the variable element M2 as shown in FIG. 6 by using a computer.

Next, in S2, the designer uses a computer to set the variable part Δ and the weighting functions Wd(s), Wr(s), Wn(s), We(s), Wu(s), and Wy(s) as shown in Figures 5 and 10.

Next, in S3 to S7, the designer uses a computer to alternately repeat the phase adjustment transfer function setting process (S3 and S5) and the subcontroller design process (see S4 and S6) n times (n is an integer equal to or greater than 2) (see S7) to design a total of n subcontrollers.

More specifically, in the first phase adjustment transfer function setting step (see S3), the designer uses a computer to combine the nominal plant N, the fluctuation part Δ, and the weight function Wd(s) set in S1 and S2 as shown in Fig. 5 to define a feedback control system, and sets the phase adjustment transfer function W _scope (s) based on this feedback control system. More specifically, in the first phase adjustment transfer function setting step, in a state where the controller K, which is the design target, is separated from the feedback control system, the phase adjustment transfer function W scope (s) is set so that the transfer function M(s) from the fluctuation signal ξ1 output from the bounded fluctuation generating part 61 of the fluctuation part Δ to the input signal η1 input to the bounded fluctuation generating part 61 becomes a positive real function. More specifically, the phase adjustment transfer function W _scope (s) is set so that the transfer function M(s) becomes a positive real function by utilizing a known metaheuristic algorithm such as a genetic algorithm or a particle _swarm optimization method.

Next, in the first sub-controller design step (see S4), the designer uses a computer to design the sub-controller. More specifically, the designer uses a computer to design the sub-controller so that predetermined design conditions are satisfied that are set so as to realize robust stability in a feedback control system that includes the phase adjustment transfer function W _scope (s) set through the first phase adjustment transfer function setting step shown in S3 and is connected to a sub-controller that is the design target as controller K. More specifically, such a sub-controller is derived, for example, by performing iterative calculations based on the D-K iteration method on a computer.

Next, in the second or subsequent phase adjustment transfer function setting process (see S5), one or more sub-controllers designed through the first to previous sub-controller design process are connected in parallel to the generalized plant, and the phase adjustment transfer function W _scope (s) is reset using a procedure similar to that of the first phase adjustment transfer function setting process.

Next, in the second or subsequent sub-controller design process (see S6), the feedback control system includes the phase adjustment transfer function W _scope (s) set through the previous phase adjustment transfer function setting process, and one or more sub-controllers designed through the first to previous sub-controller design processes and the sub-controller to be designed this time are connected in parallel to the generalized plant, and a sub-controller is designed using the same procedure as in the first sub-controller design process.

The designer repeats the above-described phase adjustment transfer function setting process and sub-controller design process n times alternately, and when the design of a total of n sub-controllers is completed, the process proceeds to S8.

Next, in the subcontroller synthesis process shown in S8, the designer uses a computer to design controller K by connecting in parallel subcontroller K1 designed through the first subcontroller design process, subcontroller K2 designed through the second subcontroller design process, and subcontroller Kn designed through the nth subcontroller design process, as shown in FIG. 13.

Next, in S9, the designer designs the shaft torque controller 7 by implementing the controller K designed by combining n subcontrollers in a digital signal processor.

The controller design method according to this embodiment provides the following advantages:

(1) In this embodiment, in a feedback control system including a nominal plant N simulating the input/output characteristics of a controlled object, a generalized plant P including a fluctuation part Δ that gives fluctuations to at least one fluctuation model parameter included in the nominal plant N, and a controller K that gives an input to the generalized plant P based on an output from the generalized plant P, the controller K is designed by a computer so as to satisfy a predetermined design condition. In the present invention, the nominal plant N is one that includes the fluctuation model parameters and has a low-order model M1 that simulates the input/output characteristics of the controlled object in a low-frequency band. This makes it possible to design a controller K whose stability against fluctuations in the model parameters is guaranteed in a low-frequency band that can be sufficiently approximated by the low-order model M1. In this embodiment, in addition to the above-mentioned low-order model M1, a nominal plant N is used that includes a variable element M2 that does not include a variable parameter and causes a fluctuation in the output of this low-order model M1, and the transfer function Wp of this variable element M2 is set so that its gain is larger than the differential transfer function δ defined based on the difference between the transfer function P _H of the high-order model M3 that imitates the input/output characteristics of the controlled object in a high-frequency band and the transfer function P _L of the low-order model M1. This makes it possible to design a controller K whose stability is guaranteed even in a high-frequency band that cannot be sufficiently approximated by the low-order model M1 alone.

(2) In this embodiment, the transfer function Wp of the variable element M2 that imparts a multiplicative variation to the output of the low-order model M1 is set so that its gain is greater than the differential transfer function δ defined by the above formula (5). This makes it possible to design a controller K with even greater guaranteed stability in the high frequency band.

(3) In this embodiment, in the variable element setting step (see S1 in FIG. 12) for setting the transfer function Wp of the variable element M2, the transfer function Wp of the variable element M2 is set so that the gain is greater than all of the multiple differential transfer functions obtained by varying within a predetermined variation range the value of a model parameter other than the variable model parameter among the multiple model parameters included in the high-order model M3. This makes it possible to prevent control in the high frequency band from becoming unstable due to the variation of a model parameter that is not included in the low-order model M1 but is included in the high-order model M3.

(4) In this embodiment, the fluctuation output signal ξ output from the fluctuation unit Δ gives an additive fluctuation to the fluctuation model parameters of the low-order model M1, and the fluctuation unit Δ generates the fluctuation output signal ξ by using a mapping Δp by the Cayley transform of the complex fluctuation Δg. According to the Cayley transform, the unbounded complex fluctuation Δg across the right half plane of the complex plane is mapped within a unit circle. Therefore, according to this embodiment, the bounded complex fluctuation obtained by the Cayley transform can be used as the fluctuation output signal ξ, so that the controller K can be designed while explicitly specifying the fluctuation range of the fluctuation model parameters.

(5) In this embodiment, a variation is given to the variation model parameters by using a variation _unit Δ including a bounded variation generating unit 61 that generates a bounded variation signal ξ1 by multiplying a predetermined input signal η1 by a mapping Δp by a Cayley transform, a phase adjusting unit 62 that changes the phase of the variation signal ξ1 by using a phase adjustment transfer function W scope (s), and a normalizing unit 63 that limits the norm of the variation output signal ξ to a predetermined range by using an output signal of the phase adjusting unit 62 and an input signal η of the nominal value multiplier 51. According to this embodiment, when the upper and lower limits of the variation range of the variation model parameters are known in advance, a controller K that conforms to reality can be designed by limiting the norm of the variation output signal ξ in the normalizing unit 63 to a range determined by using these upper and lower limits.

(6) In this embodiment, the phase adjustment transfer function setting step (see S3 and S5 in FIG. 12) and the sub-controller design step (see S4 and S6 in FIG. 12) are alternately repeated n times (n is an integer of 2 or more), and n sub-controllers K1 to Kn designed by these steps are connected in parallel to design the controller K. This makes it possible to optimize the phase adjustment transfer function W _scope (s) and the controller K.

(7) In this embodiment, in the first phase adjustment transfer function setting step, the phase adjustment transfer function W _scope (s) is set in a state where the controller K is separated from the feedback control system, and in the first sub-controller design step, the sub-controller K1 is designed in a state where the phase adjustment transfer function W _scope (s) set through the first phase adjustment transfer function setting step is included in the feedback control system. In the second and subsequent phase adjustment transfer function setting steps, the phase adjustment transfer function W _{scope (s) is set in a state where one or more sub-controllers designed through the first to previous sub-controller design steps are connected in parallel to the generalized plant, and in the second and subsequent sub-controller design steps, the sub-controller is designed in a state where the phase adjustment transfer function W scope} (s) set through _the previous phase adjustment transfer function setting step is included in the feedback control system and one or more sub-controllers designed through the first to previous sub-controller design steps are connected in parallel to the generalized plant. This makes it possible to optimize the phase adjustment transfer function W _scope (s) and the controller K.

(8) In this embodiment, a metaheuristic algorithm is used to set the phase adjustment transfer function W _scope (s) so that the transfer function M(s) from the fluctuation signal ξ1 to the input signal η1 becomes a positive real function. This allows the phase adjustment transfer function W _scope (s) to be set quickly regardless of the designer's skill.

(9) In this embodiment, a low-order model M1 is constructed based on an i-inertia system consisting of i (i is an integer of 2 or more) inertial bodies connected in series with i-1 or more shafts, and a high-order model M3 is constructed based on a j-inertia system consisting of j (j is an integer greater than i) inertial bodies connected in series with j-1 or more shafts. In this embodiment, at least one of the inertia moment of the inertial body and the spring stiffness and damping coefficient of the shaft is set as a variable model parameter that is fluctuated by a fluctuation part Δ, and an axial torque controller 7 is designed to control the multi-inertia system. This makes it possible to design an axial torque controller 7 that can achieve stable and highly responsive control even when the inertia moment, spring stiffness, damping coefficient, etc. fluctuate.

(11) In this embodiment, a test system S including an engine E that generates torque in response to a throttle opening command signal, a dynamometer 2 that generates torque in response to a torque current command signal, a connecting shaft 3 that connects the engine E and the dynamometer 2, and a shaft torque meter 5 that generates a shaft torque detection signal in response to the shaft torque on the connecting shaft 3 is used as a control target, a low-order model M1 is constructed based on a two-inertia system configured by connecting two inertia bodies in series with one or more shaft bodies, a high-order model M3 is constructed based on a four-inertia system, the spring stiffness k ₀ of the shaft body of the two-inertia system is set as a fluctuation model parameter that is fluctuated by the fluctuation part Δ, and a shaft torque controller 7 is designed that outputs a torque current command signal in response to the shaft torque detection signal and the shaft torque command signal. As described above, the connecting shaft that connects the engine E and the dynamometer 2 includes a clutch, and its spring stiffness k ₀ has a characteristic that fluctuates greatly. In contrast, according to the controller design method, a shaft torque controller 7 of the test system S that can realize stable and highly responsive control can be designed.

Although one embodiment of the present invention has been described above, the present invention is not limited to this. The detailed configuration may be modified as appropriate within the scope of the spirit of the present invention.

For example, in the above embodiment, the case has been described where the variable element M2 in the nominal plant N provides a multiplicative variation to the output of the low-order model M1, but the present invention is not limited to this. For example, as shown in Fig. 14, in the nominal plant N', the variable element M2' may provide an additive variation to the output of the low-order model M1. When the nominal model N' is defined as shown in Fig. 14, the differential transfer function δ is defined by the following equation (9).

P...Generalized plant N, N'...Nominal plant M1...Low-order model M2, M2'...Variation factor M3...High-order model 51...Nominal value multiplication unit 52...Addition unit Δ...Variation unit 61...Bounded variation generation unit 62...Phase adjustment unit 63...Normalization unit K...Controller
K1, ..., Kn... sub-controllers (sub-controllers)
S: Test system E: Engine (test specimen)
2... Dynamometer 3... Connecting shaft 5... Shaft torque meter 7... Shaft torque controller

Claims (11)

A controller design method for a feedback control system including a nominal plant simulating an input/output characteristic of a controlled object, a generalized plant including a fluctuation unit that fluctuates at least one fluctuation model parameter included in the nominal plant, and a controller that provides an input to the generalized plant based on an output from the generalized plant, the method comprising the steps of: designing the controller by a computer so as to satisfy a predetermined design condition,
the nominal plant comprises a low-order model including the variable model parameters and simulating an input/output characteristic in a low frequency band of the controlled object, and a variable element not including the variable model parameters and causing a fluctuation in an output of the low-order model,
a transfer function of the variable element is set so that, in at least a part of a high frequency band higher than the low frequency band, the transfer function has a larger gain than a differential transfer function defined based on the difference between a transfer function of a high-order model that imitates input/output characteristics of the controlled object in the high frequency band and a transfer function of the low-order model. In the nominal plant, the variation component imparts a multiplicative variation to the output of the reduced-order model;
2. The controller design method according to claim 1, wherein, when a transfer function of the low-order model is P _L and a transfer function of the high-order model is P _H , the differential transfer function δ is defined by the following equation (1):

In the nominal plant, the variation component provides an additive variation to the output of the low-order model;
2. The controller design method according to claim 1, wherein, when a transfer function of the low-order model is P _L and a transfer function of the high-order model is P _H , the differential transfer function δ is defined by the following equation (2):

A controller design method according to any one of claims 1 to 3, characterized in that in the variable element setting step of setting the transfer function of the variable element, the transfer function of the variable element is set so that its gain is greater than all of the multiple differential transfer functions obtained by varying the values of model parameters other than the variable model parameters among the multiple model parameters included in the high-order model within a predetermined variation range. the nominal plant comprises a nominal value multiplication unit that multiplies a predetermined input signal by a nominal value of the fluctuation model parameter, and an adder that adds a fluctuation output signal of the fluctuation unit and an output signal of the nominal value multiplication unit,
5. The controller design method according to claim 1, wherein the variation unit generates the variation output signal by using a mapping according to a Cayley transform of a complex variation. The controller design method according to claim 5, characterized in that the variation unit includes a bounded variation generating unit that generates a bounded variation signal by multiplying a predetermined input signal by the mapping, a phase adjustment unit that changes the phase of the variation signal using a phase adjustment transfer function, and a normalization unit that limits the norm of the variation output signal to within a predetermined range using an output signal of the phase adjustment unit and an input signal of the nominal value multiplication unit. a phase adjustment transfer function setting step of setting the phase adjustment transfer function by the computer so that a transfer function from the fluctuation signal to an input signal to the bounded fluctuation generating unit in the feedback control system becomes a positive real function;
a sub-controller design process for designing a sub-controller by the computer so as to satisfy the design conditions in the feedback control system;
The controller design method according to claim 6, further comprising a controller synthesis process of designing the controller by connecting in parallel n sub-controllers designed by alternately repeating the phase adjustment transfer function setting process and the sub-controller design process n times (n is an integer equal to or greater than 2). In the first phase adjustment transfer function setting step, the phase adjustment transfer function is set in a state in which the controller is separated from the feedback control system;
In the first sub-controller design step, the sub-controller is designed in a state in which the phase adjustment transfer function set through the first phase adjustment transfer function setting step is included in the feedback control system;
In the second or subsequent phase adjustment transfer function setting steps, the phase adjustment transfer function is set in a state in which one or more of the sub-controllers designed through the first to previous sub-controller design steps are connected in parallel to the generalized plant,
The controller design method according to claim 7, characterized in that in the sub-controller design process from the second time onwards, the sub-controller is designed in a state in which the phase adjustment transfer function set via the previous phase adjustment transfer function setting process is included in the feedback control system and one or more sub-controllers designed via the sub-controller design process from the first time to the previous time are connected in parallel to the generalized plant. The controller design method according to claim 7 or 8, characterized in that in the phase adjustment transfer function setting step, the phase adjustment transfer function is set by a metaheuristic algorithm. The low-order model is constructed based on an i-inertia system configured by connecting i or more inertial bodies (i is an integer of 2 or more) characterized by a predetermined moment of inertia in series with i-1 or more shaft bodies characterized by a predetermined spring stiffness and reduction coefficient;
The high-order model is constructed based on a j-inertial system configured by connecting j or more inertial bodies (j is an integer greater than i) characterized by a predetermined moment of inertia in series with j-1 or more shaft bodies characterized by predetermined spring stiffness and damping coefficient,
10. The controller design method according to claim 1, wherein the variable model parameter is at least one of the moment of inertia, the spring stiffness, and the damping coefficient. the controlled object is a test system including a test specimen that generates a torque in response to a test specimen input, a dynamometer that generates a torque in response to a torque current command signal, a connecting shaft that connects the test specimen and the dynamometer, and a shaft torque meter that generates a shaft torque detection signal in response to a shaft torque in the connecting shaft,
The low-order model is constructed based on an i-inertial system configured by connecting i inertial bodies (i is an integer equal to or greater than 2) in series with i-1 shaft bodies characterized by a predetermined spring stiffness;
The high-order model is constructed based on a j-inertial system configured by connecting j inertial bodies (j is an integer greater than i) in series with j-1 shaft bodies characterized by a predetermined spring stiffness,
the variation model parameter is the spring stiffness,
10. The controller design method according to claim 1, wherein the controller is a shaft torque controller that outputs the torque current command signal when the shaft torque detection signal and a shaft torque command signal corresponding to the shaft torque detection signal are input.

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