JP2005293434A - Parameter determination device, controller with the same, parameter determination method, program and recording medium with the program recorded thereon - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain a parameter determination device capable of determining a control parameter of the optimal PID control for a control object having nonlinear characteristics. <P>SOLUTION: The parameter determination device determines a PID parameter of the PID control and is provided with a local linear model construction part 10 which constructs a plurality of local linear models to a nonlinear system, a first parameter calculation part 11 which calculates PID parameters corresponding to the local linear models for every local linear model and a second parameter calculation part 12 which performs weighting corresponding to each difference to each PID parameter calculated by the first parameter calculation part 11 and calculates the PID parameter of the PID control from each PID parameter to which the weighting is performed based on size of each difference between an output value to be outputted from the nonlinear system to input to the nonlinear system and an output value in each local linear model to the input in the case of using each PID parameter calculated by the first parameter calculation part 11. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to determination of control parameters in PID control. In particular, the present invention relates to determination of control parameters when the controlled object is a nonlinear system.

  In recent years, with the development of digital computers, a control system design method having higher-order compensators has been considered with the aim of improving control performance. However, PID control is still used as a mainstream in process control systems represented by chemical processes. As described above, the reason why PID control is used in the process control system includes the following two points. The first point is that a control parameter in PID control (hereinafter also referred to as a PID parameter) is represented by a proportional operation, an integral operation, and a differential operation, and the physical meaning of the control parameter is clear. The second point is that the control structure of PID control is simple and can be easily implemented.

  However, in a process control system, since there are many uncertain systems (control targets) and systems having nonlinear characteristics, it may be difficult to adjust the PID gain appropriately.

  In view of such a situation, Non-Patent Document 1 discloses a self-tuning PID control method using a least square method for a system whose characteristics are unknown. However, since the above control method uses the least square method, it cannot be applied to a system that cannot use the least square method.

  Furthermore, when applying PID control to a system having nonlinear characteristics, it may be necessary to adjust the PID parameters according to the nonlinear characteristics.

Therefore, in an actual control field, as shown in FIG. 14, a plurality of local linear models are constructed for the nonlinear system, and PID parameters corresponding to the respective local linear models are obtained respectively, and the equilibrium point (the same figure) is obtained. A method of switching PID parameters to be used corresponding to the points A and B in the figure) is adopted. In the figure, the horizontal axis represents the control input vector, and the vertical axis represents the system output vector.
Yamamoto, Kaneda: A design of self-tuning PID controller based on generalized minimum variance control law, Journal of System Control Information Society, 11, 1, 1/9 (1998)

  However, in the above-described conventional configuration, it is difficult for the user to grasp the criteria for appropriate switching of the PID parameters, and as a result, switching of the PID parameters must be performed through trial and error. In addition, when there is a range in which a local linear model is not constructed, it is difficult to calculate the PID parameter.

  The present invention has been made in view of the above-described problems, and an object of the present invention is to provide a parameter determination device capable of determining an optimal PID control parameter for a control target having nonlinear characteristics, and a control including the parameter determination device. To provide an apparatus, a program, and a recording medium on which the program is recorded.

  In order to solve the above problem, a parameter determination device according to the present invention is a parameter determination device that determines a control parameter for PID control, and a plurality of local linear models are applied to a control target having nonlinear characteristics. Local linear model construction means to construct, first parameter calculation means for computing a control parameter corresponding to the local linear model for each local linear model, and output output from the control object in response to an input to the control object Based on the magnitude of the difference between the value and the output value of each local linear model with respect to the input when each control parameter calculated by the first parameter calculation unit is used, the first parameter calculation unit The control parameters calculated in step 1 are weighted corresponding to the differences, and the control of PID control is performed from the weighted control parameters. It is characterized in that it comprises a second parameter calculating means for calculating the parameters.

  According to the above configuration, when the second parameter calculation unit uses the output value output from the control target with respect to the input to the control target and the control parameter calculated by the first parameter calculation unit. The control parameters calculated by the first parameter calculation means are weighted according to the magnitude of each difference based on the magnitude of the difference between the input and the output value in each local linear model. A control parameter for PID control is calculated from each control parameter for which the control is performed.

  Here, as the magnitude of the difference between the output value output from the control target and the output value in the local linear model is larger, the control parameter calculated by the first parameter calculation unit is used as the control parameter for PID control. It can be said that it is not appropriate to use. On the other hand, as the magnitude of the difference is smaller, it is preferable to use the control parameter calculated by the first parameter calculation means as a control parameter for PID control.

  Therefore, based on the magnitude of each difference, the control parameters calculated by the first parameter calculation means are weighted corresponding to the differences, and the control parameters for PID control are calculated from the weighted control parameters. By doing so, it is possible to obtain an optimal control parameter for PID control with respect to a controlled object having nonlinear characteristics.

  In addition, the user himself / herself does not have to switch the control parameter according to the input to the control target, which has been conventionally performed by the user.

  Further, the parameter determination device according to the present invention is characterized in that, in the parameter determination device, the first parameter calculation means calculates each control parameter using a parameter included in each local linear model. Yes.

  According to said structure, the control parameter corresponding to this local linear model can be calculated for every local linear model using a local linear model.

  Therefore, it is possible to easily calculate a control parameter corresponding to the local linear model.

  In order to solve the above problem, a parameter determination device according to the present invention is a parameter determination device that determines a control parameter for PID control, and a plurality of local linear models are applied to a control target having nonlinear characteristics. Local linear model construction means to be constructed, first parameter calculation means for computing a control parameter corresponding to the local linear model for each local linear model, and control of each local linear model calculated by the first parameter calculation means A control parameter for PID control using a neural network constructed with a parameter as a teacher signal and an input to a control object corresponding to each local linear model and an output from the control object corresponding to the input as learning data And a second parameter calculating means for calculating.

  According to the above configuration, the neural network uses the control parameter of each local linear model calculated by the first parameter calculating unit as a teacher signal, and inputs to the control target corresponding to each local linear model, and The output from the controlled object corresponding to the input is constructed as learning data.

  Therefore, the second parameter calculation means inputs the input to the controlled object and the output from the controlled object with respect to the input to the neural network, so that the controlled object having nonlinear characteristics as the output from the modular network. As a result, it is possible to obtain an optimal PID control parameter.

  In addition, the user himself / herself does not have to switch the control parameter according to the input to the control target, which has been conventionally performed by the user.

  In the parameter determination device according to the present invention, in the parameter determination device, the local linear model is constructed by dividing a range of input to the control target into a plurality of ranges, and the range in each range A local linear model is constructed as an input to the control object as the learning data in each range, which is constructed based on an input to the control object and an output from the control object with respect to the input. It is characterized by using the input to the control object used at the time.

  According to said structure, the same input used when constructing | assembling a local linear model can be input into control object as learning data.

  Therefore, when the neural network is constructed, the neural network can be made to learn accurately. Therefore, there is an effect that a highly accurate control parameter can be obtained.

  The parameter determination device according to the present invention is characterized in that the parameter determination device includes a neural network construction means for constructing the neural network.

  According to said structure, the parameter determination apparatus is equipped with the neural network construction means to construct | assemble the said neural network.

  Therefore, there is an effect that a neural network can be constructed in the parameter determination device. Further, it is not necessary to provide a separate device for constructing the neural network.

  In order to solve the above-described problem, a control device according to the present invention includes the parameter determination device and controls the control target using a control parameter for PID control calculated by the second parameter calculation unit. It is characterized by.

  According to said structure, a control apparatus is equipped with the said parameter determination apparatus, and controls the said control object using the control parameter of PID control which the said 2nd parameter calculation means calculated.

  Therefore, the control target can be controlled using the optimum PID control parameters determined by the parameter determination device.

  In order to solve the above problems, a parameter determination method according to the present invention is a parameter determination method for determining a control parameter for PID control, and a plurality of local linear models for a control target having nonlinear characteristics. A local linear model constructing step for constructing, a first parameter calculating step for computing a control parameter corresponding to the local linear model for each local linear model, and an output to the control target being output from the control target Based on the magnitude of each difference between the output value and the output value in each local linear model for the input when using each control parameter calculated in the first parameter calculating step, the first parameter calculation is performed. Each control parameter calculated in step is weighted corresponding to each difference, and each weighted control parameter is used. It is characterized in that it comprises a second parameter calculating step of calculating a control parameter of the ID control.

  According to the above method, when the second parameter calculation step uses the output value output from the control target with respect to the input to the control target and the control parameter calculated in the first parameter calculation step The control parameters calculated in the first parameter calculation step are weighted according to the magnitude of each difference based on the magnitude of the difference between the input and the output value in each local linear model. A control parameter for PID control is calculated from each control parameter for which the control is performed.

  Here, as the magnitude of the difference between the output value output from the control target and the output value in the local linear model is larger, the control parameter calculated in the first parameter calculation step is used as a control parameter for PID control. It can be said that it is not appropriate to use. On the other hand, it is preferable that the control parameter calculated in the first parameter calculation step is used as a control parameter for PID control as the difference is smaller.

  Therefore, based on the magnitude of each difference, the control parameters calculated in the first parameter calculation step are weighted corresponding to the differences, and the control parameters for PID control are calculated from the weighted control parameters. By doing so, it is possible to obtain an optimal control parameter for PID control with respect to a controlled object having nonlinear characteristics.

  In addition, the user himself / herself does not have to switch the control parameter according to the input to the control target, which has been conventionally performed by the user.

  In order to solve the above problems, a parameter determination method according to the present invention is a parameter determination method for determining a control parameter for PID control, and a plurality of local linear models for a control target having nonlinear characteristics. A local linear model constructing step for constructing, a first parameter calculating step for calculating a control parameter corresponding to the local linear model for each local linear model, and each of the local linear models calculated in the first parameter calculating step Control of PID control using a neural network constructed with control parameters as teacher signals and inputs to the control objects corresponding to the local linear models and outputs from the control objects corresponding to the inputs as learning data And a second parameter calculating step for calculating a parameter.

  According to the above method, the neural network uses the control parameter of each local linear model calculated in the first parameter calculating step as a teacher signal, and inputs to the control target corresponding to each local linear model, and The output from the controlled object corresponding to the input is constructed as learning data.

  Therefore, in the second parameter calculation step, by inputting an input to the control object and an output from the control object with respect to the input to the neural network, a control having nonlinear characteristics as an output from the neural network. There is an effect that it is possible to obtain an optimal control parameter of PID control for the target.

  In addition, the user himself / herself does not have to switch the control parameter according to the input to the control target, which has been conventionally performed by the user.

  As described above, the program according to the present invention is for causing a computer to function as each means of the parameter determination device.

  By loading the program into the computer system, the parameter determining device can be provided.

  The program according to the present invention is for causing a computer to execute the parameter determination method as described above.

  By loading the program into a computer system, the parameter determining method can be provided.

  The recording medium recording the program according to the present invention records the program as described above.

  By loading the program recorded on the recording medium into the computer system, the parameter determining device, the control device, and the parameter determining method can be provided.

  As described above, the parameter determination apparatus according to the present invention is a parameter determination apparatus that determines a control parameter for PID control, and is configured to construct a plurality of local linear models for a controlled object having nonlinear characteristics. A linear model construction means; a first parameter calculation means for calculating a control parameter corresponding to the local linear model for each local linear model; an output value output from the control object in response to an input to the control object; When each control parameter calculated by the first parameter calculation unit is used, the first parameter calculation unit calculates the difference between the input value and the output value of each local linear model with respect to the input. The control parameters are weighted corresponding to the differences, and the control parameters for PID control are determined from the weighted control parameters. A configuration and a second parameter calculation means for output.

  The parameter determination device according to the present invention is a parameter determination device that determines control parameters for PID control as described above, and constructs a plurality of local linear models for a control target having nonlinear characteristics. Local linear model constructing means, first parameter calculating means for calculating for each local linear model a control parameter corresponding to the local linear model, and control parameters for each local linear model calculated by the first parameter calculating means And a control parameter for PID control using a neural network constructed with the input to the controlled object corresponding to each local linear model and the output from the controlled object corresponding to the input as learning data And a second parameter calculating means for calculating.

  As described above, the parameter determination method according to the present invention is a parameter determination method for determining a control parameter for PID control, and is a method for constructing a plurality of local linear models for a controlled object having nonlinear characteristics. A linear model construction step; a first parameter calculation step for calculating a control parameter corresponding to the local linear model for each local linear model; an output value output from the control target with respect to an input to the control target; When the control parameters calculated in the first parameter calculation step are used, the control parameters are calculated in the first parameter calculation step based on the magnitudes of the differences between the input values and the output values in the local linear models. Each control parameter is weighted corresponding to each difference, and PID control is performed from each weighted control parameter. A method and a second parameter calculating step of calculating a control parameter.

  The parameter determination method according to the present invention is a parameter determination method for determining a control parameter for PID control as described above, and constructs a plurality of local linear models for a controlled object having nonlinear characteristics. A local linear model construction step, a first parameter calculation step for calculating a control parameter corresponding to the local linear model for each local linear model, and a control parameter for each local linear model calculated in the first parameter calculation step And a control parameter for PID control using a neural network constructed with the input to the controlled object corresponding to each local linear model and the output from the controlled object corresponding to the input as learning data And a second parameter calculating step for calculating.

Therefore, by using the parameter determination device or the parameter determination method, the optimal control parameter for PID control can be determined for a control target having nonlinear characteristics. The control device according to the present invention includes the parameter determination device. And controlling the object to be controlled.

  Therefore, the control target can be controlled using the optimal PID control parameters determined by the parameter determination device.

  As described above, the program according to the present invention is for causing a computer to function as each unit of the parameter determination device. Therefore, the parameter determination device is provided by loading the program into a computer system. There is an effect that becomes possible.

  Since the program according to the present invention is for causing a computer to execute the parameter determination method as described above, the parameter determination method can be provided by loading the program into a computer system. The effect of becoming.

  Since the recording medium recording the program according to the present invention records the program as described above, the parameter determination is performed by loading the program recorded on the recording medium into a computer system. There is an effect that it is possible to provide a device, a control device, and a parameter determination method.

[Embodiment 1]
One embodiment of the present invention is described below with reference to FIGS.

  First, PID control will be described. In general, the control is to apply a required operation to a target object so as to meet a certain purpose. A target machine, process, system, or the like is a control target, a device that performs control in combination with the target machine, process, system, or the like is referred to as a control device, and an entire system that combines control targets / control devices is referred to as a control system.

  FIG. 2 is a block diagram showing the configuration of the PID control system. In the configuration shown in the figure, the operation amount u is determined by the control device so that the control amount z that is the output of the control object matches the given target value r. At this time, disturbance w may be included in the manipulated variable, or noise v may be mixed into the observed quantity y 1 observed using a sensor or the like. Therefore, it is required to realize appropriate control. In the following description, the manipulated variable is described as an input to the controlled object, and the observed variable is described as an output from the controlled object with respect to the input.

  The control device in the figure is made up of a PID controller. As the name suggests, this PID controller is P (Proportional, proportional) operation, I (Integral, integration) operation, D operation (Derivative, differentiation). Is to do.

  In the P operation, the difference between the target value and the observation amount in the operation control is called a deviation (control deviation), and the operation amount is determined based on this deviation. If the deviation is small, the manipulated value is small, and if the deviation is large, it is appropriate to increase the manipulated value accordingly. Therefore, the control law includes a term proportional to the deviation.

  However, if the controlled object has self-balance (the property that the controlled variable finally settles to a constant value when the operation manipulated variable is maintained at a constant value), if only the P action (proportional control) is performed, the target value and disturbance Since a constant deviation (steady deviation) remains with respect to the step-like change, a term proportional to the integral of the deviation is included in the control law in order to remove this deviation. This is the I operation.

Further, in addition to the P action and I action, the control side also includes a term proportional to the derivative of the deviation in order to improve the control characteristics by reflecting the increase / decrease trend of the deviation in the determination of the operation amount. This is the D operation and corresponds to a kind of foreseeing operation.

  As described above, the control law of the PID control system including the three operations of P, I, and D is as shown in Expression 1 when the deviation is e.

In Equation 1, k _c , K _I and K _D are proportional constants. It is customary to express Equation 1 as Equation 2.

In Equation 2, k _c is called proportional gain, T _I is called integration time, and T _D is called differentiation time. Therefore, the design of the PID control system can be summarized as determining three parameters (control parameters): proportional gain, integration time, and differentiation time. In the following, the above three parameters are referred to as PID parameters.

  In the present embodiment, a system having nonlinear characteristics, specifically, a nonlinear discrete-time system (hereinafter referred to as a nonlinear system) represented by Expression 3 will be described as an example of a control target.

  In Equation 3, G is a nonlinear function. U represents a control input vector, and Y represents a system output vector corresponding to the control input vector. Note that k in Equation 4 is a dead time.

  FIG. 1 is a functional block diagram of the parameter determination apparatus according to the present embodiment. That is, this figure is a block diagram showing the function performed by the parameter determination device. In addition, the figure has shown the structure with which the parameter determination apparatus is provided in the control apparatus. However, the configuration is not limited to this configuration, and the parameter determination device may be any configuration that is provided outside the control device and can exchange data with the control device (for example, a configuration that is communicably connected). .

  As shown in FIG. 1, the parameter determination device 1 includes a local linear model construction unit 10, a first parameter calculation unit 11, and a second parameter calculation unit 12.

  The local linear model construction unit 10 is a functional block that constructs a plurality of local linear models for a nonlinear system. Hereinafter, the process performed in the local linear model construction part 10 is demonstrated concretely.

  When identifying the system to be controlled, if the structure of the nonlinear function G is known, the identification may be possible directly. However, when the structure of the nonlinear function G is unknown, it is difficult to identify it directly. Considering the design of the control system, it is not preferable to perform identification using a complicated mathematical model because the structure of the control device becomes complicated.

  Therefore, in the present embodiment, an identification model having linear characteristics represented by Expression 5 is used.

In Equation 5, u (t), y (t), and, k _m, respectively, the control inputs to the system, the output from the system, and shows a minimum estimate of the dead time. Incidentally, if no any information is available about the dead time, and k m _{= 0.} Ξ (t) is Gaussian white noise having an average of zero and a variance of σ ² . Further, A (z ⁻¹ ) and B (z ⁻¹ ) are polynomials represented by the following Expression 6. In Equation 6, z ⁻¹ represents a time delay operator, and for example, z ⁻¹ y (t) means y (t−1).

  By the way, when identification is performed using the linear identification model shown in Equation 5 for the nonlinear system shown in Equation 3, a local model around a certain equilibrium point is obtained, which is global to the nonlinear system. The characteristic cannot be expressed. Therefore, in this embodiment, a plurality of linear models (local linear models) are prepared locally, and the characteristics of the nonlinear system are approximately expressed using these local linear models.

Specifically, first, the range of the control input (u) to be used is divided into n areas. Further, it creates an input signal series center values of the respective regions is average, _{they, U 1, U 2, U} 3, ···, and U _n. Then, U ₁ , U ₂ , U ₃ ,..., U _n are input to the nonlinear system shown in Equation 3, so that the corresponding output series Y ₁ , Y ₂ , Y ₃ ,. , Y _n is obtained. U _i and Y _i (1 ≦ i ≦ n) are a control input vector and a system output vector, respectively.

Then, using U _i and Y _i obtained as described above, the system is identified by the collective least square method to obtain a local linear model y _i (t) (1 ≦ i ≦ n). That is, y ₁ (t), y ₂ (t), y ₃ (t),..., Y _n (t) are obtained.

  As described above, the local linear model construction unit 10 constructs a plurality of local linear models.

  The first parameter calculation unit 11 calculates PID parameters corresponding to a plurality of local linear models constructed by the local linear model construction unit 10 for each local linear model. Hereinafter, the process performed by the first parameter calculation unit 11 will be specifically described.

First, the PID control method represented by the following Expression 7 is applied to the nonlinear system represented by Expression 3. Here, e (t) in Equation 7 represents a control error signal as shown in Equation 8 below. In Expression 8, r (t) is the target value, _{k c} is a proportional gain, _{T I} is the integral time, _{T D} is the derivative time, _{T S} is the sampling time.

  In calculating the PID parameter here, as an example, a PID parameter adjustment method based on the generalized minimum variance control (GMVC) method is used. Note that the calculation of the PID parameter is not limited to the adjustment method described above. Hereinafter, a method for adjusting the PID parameter based on the generalized minimum variance control method will be described.

First, the GMVC rule is derived based on the minimization of the evaluation criterion shown in the following Expression 9. The GMVC rule is one of the self-tuning control methods. For details, see DW Clarke and PJ Gawthrop: “Self-Tuning Control”, Proc. IEE, Vol. 126D, No. 6, pp. 633-640 (1979). In Equation 9, E [•] represents a spatial average. _{Also, φ (t + k m +1} ) is a generalized output, given by equation 10 below.

Here, λ is a design parameter representing a control weight coefficient, and is a parameter greatly related to the stability of the control system. P (z ⁻¹ ) is a design polynomial given by the following expression 11. Further, P (1) in Expression 10 is a static gain of P (Z ⁻¹ ), and is expressed by Expression 12 below.

A control law based on the minimization of Expression 8 is given as u (t) that satisfies Expression 13 below. Here, E (z ⁻¹ ) and F (z ⁻¹ ) in Equation 13 are obtained by solving the following Diophantine equation in Equation 14.

However, E (z ⁻¹ ) and F (z ⁻¹ ) are represented by the following Expression 15.

  In other words, solving the Diophantine equation of Equation 14 means calculating the coefficients ei and fi of Equation 15 by comparing both sides of Equation 14.

Here, Equation 7 is rewritten as Equation 16 below. However, C (z ⁻¹ ) in Expression 16 is defined by Expression 17 below.

Next, consider Equation 18 in which E (z ⁻¹ ) B (z ⁻¹ ) in the second term on the left side of Equation 13 is replaced with steady gain E (1) B (1).

  Furthermore, using ν according to Equation 19, Equation 13 can be written as Equation 20.

Therefore, comparing Equation 16 and Equation 20, if C (z ⁻¹ ) is designed as shown in Equation 21, the GMVC law and the PID control law are equivalent, although approximate. At this time, PID parameters (that is, k _c , T _I , and T _D ) are calculated as the following Expression 22 from the relationship between Expression 16 and Expression 20.

  As described above, the PID parameter can be adjusted based on the GMVC rule.

As described above, in the PID parameter adjustment method based on the generalized minimum variance control method, the parameters of the linear approximation model of the controlled object (nonlinear system) (a ₁ , a ₂ , b ₀ , b ₁ ,..., b _m ). Therefore, the first parameter calculation unit 11 calculates PID parameters (control parameters) using parameters included in the local linear model y _i (t).

Thus, for each of the local linear models y ₁ (t), y ₂ (t), y ₃ (t),..., Y _n (t), PID parameters (ie, k _c , T _I , And a combination of T _D ).

Hereinafter, a PID parameter calculated using parameters included in the local linear model y _i (t) will be described as a PID parameter (i).

  The second parameter calculation unit 12 responds to the input when the output value output from the nonlinear system with respect to the input to the nonlinear system and each PID parameter calculated by the first parameter calculation unit 11 is used. Based on the magnitude of each difference from the output value in each local linear model, each PID parameter calculated by the first parameter calculation unit 11 is weighted corresponding to each difference, and each weighting is performed. A PID parameter for PID control is calculated from the PID parameter.

  Hereinafter, the process performed in the 2nd parameter calculation part 12 is demonstrated concretely. In addition, the following processing content is an example, Comprising: It is not limited to this.

First, the second parameter calculation unit 12 associates the PID parameter (i) calculated by the first parameter calculation unit 11 with the local linear model y _i (t) as shown in FIG. In the figure, the PID parameter (i) is described as PID _i, and the local linear model y _i (t) is described as the local linear model i. Then, as shown in the figure, the second parameter calculation unit 12 receives the actual output value output from the nonlinear system in response to the input (u (t)) to the nonlinear system, and the PID parameter (i). That is, the difference (ε _i (t): estimation from the output value (estimated output value) from the local linear model y _i (t) with respect to the input when the PID parameter calculated by the first parameter calculation unit 11 is used. Error) is calculated for each local linear model.

Next, the second parameter calculation unit 12 calculates η _i (t) by Expression 23. Then, ω _i (weight) is calculated by Equation 24 using the calculated η _i (t). However, ω _i shall satisfy Expression 25.

Here, if the PID parameter (i) corresponding to the local linear model y _i (t) is described as k _ci , T _Ii , and T _Di , the PID parameter (k _{c (t )} , T _{I (t)} , T _{D (t)} ) are expressed by Equation 26.

  As described above, the optimum PID parameter used for the nonlinear system is determined (adjusted).

Then, by substituting the PID parameters (k _{c (t)} , T _{I (t)} , T _{D (t)} ) shown in Expression 26 into Expression 7, Δu (t) is obtained. Therefore, an optimal control input (u (t)) can be obtained by adding Δu (t) to u (t−1).

In the above description, ω _i is calculated from (ε _i (t)) ² as shown in Expression 23. However, for example, ω _i may be calculated from | ε _i (t) |. Any configuration that calculates the weight (ω _i ) based on the size of the estimation error (ε _i (t)) may be used.

  Furthermore, in the above description, the difference between the actual output value and the estimated output value is directly obtained, and the weight is calculated based on the magnitude of the difference. However, the present invention is not limited to this. Any configuration may be used as long as the weight is calculated based on the difference between the actual output value and the estimated output value.

  Here, calculating the weight based on the magnitude of the difference between the actual output value and the estimated output value is a two-dimensional table having the actual output value and the estimated output value as elements, and the actual output value. This includes the case where the weight is determined using a table in which the weight is determined in advance according to the difference between the value and the estimated output value. The same applies to a case where not only a two-dimensional table but also a function using actual output values and estimated output values as parameters is used.

  As described above, the parameter determination device 1 is a parameter determination device that determines a PID parameter (control parameter) for PID control, and a plurality of local alignments for a nonlinear system (a control target having nonlinear characteristics). A local linear model construction unit (local linear model construction means) 10 that constructs a model, and a first parameter calculation unit (first parameter calculation) that calculates a PID parameter (control parameter) corresponding to the local linear model for each local linear model (Means) 11, output values output from the nonlinear system with respect to the input to the nonlinear system, and the respective PID parameters calculated by the first parameter calculation unit 11. Each PID calculated by the first parameter calculation unit 11 based on the magnitude of each difference from the output value at Performs the weighting corresponding to each difference parameter, a configuration and a second parameter calculating section that calculates the PID parameters of the PID control from the PID parameter by weighting (second parameter calculation means) 12.

  According to the above configuration, the second parameter calculation unit 12 uses the output value output from the nonlinear system in response to the input to the nonlinear system and each PID parameter calculated by the first parameter calculation unit 11. The PID parameters calculated by the first parameter calculation unit 11 are weighted to correspond to the differences based on the magnitudes of the differences between the input and the output values of the local linear models. A PID parameter for PID control is calculated from each PID parameter that has been performed and weighted.

  Here, as the difference between the output value output from the nonlinear system and the output value in the local linear model is larger, the PID parameter calculated by the first parameter calculation unit 11 is changed to the PID parameter for PID control. It can be said that it is not appropriate to use as. On the other hand, it is preferable to use the PID parameter calculated by the first parameter calculation unit 11 as the PID parameter for PID control as the difference is smaller.

  Therefore, based on the magnitude of the difference, each PID parameter calculated by the first parameter calculation unit 11 is weighted corresponding to each difference, and a PID parameter for PID control is calculated from each weighted PID parameter. By doing so, it is possible to obtain an optimal PID parameter of PID control for a system having nonlinear characteristics.

  In addition, the user himself / herself does not have to switch the PID parameter according to the input to the nonlinear system, which is conventionally performed by the user.

  Further, when the second parameter calculation unit 12 uses the output value output from the nonlinear system in response to the input to the nonlinear system and each PID parameter calculated by the first parameter calculation unit 11, A difference calculation unit that calculates each difference between the input value and the output value of each local linear model with respect to the input, and the second parameter calculation unit 12 performs the first calculation based on the magnitude of each difference calculated by the difference calculation unit. The PID parameter calculated by the one parameter calculation unit 11 may be weighted corresponding to each difference, and the PID parameter for PID control may be calculated from each weighted PID parameter.

  Next, the flow of the PID parameter determination method in the parameter determination apparatus 1 will be described with reference to FIG.

  First, the local linear model construction unit 10 constructs a plurality of local linear models for the nonlinear system (S1). After S1, the first parameter calculation unit 11 calculates a PID parameter corresponding to the local linear model for each local linear model (S2). After S2, the second parameter calculation unit 12 uses the output value output from the nonlinear system and the PID parameters calculated by the first parameter calculation unit 11 with respect to the input to the nonlinear system. In this case, each PID parameter calculated by the first parameter calculation unit 11 is made to correspond to each difference based on the magnitude of each difference (estimation error) from the output value of each local linear model with respect to the input. Weighting is performed, and PID parameters for PID control are calculated from the weighted PID parameters (S3).

  Through these steps (S1 to S3), the optimum PID parameter can be determined.

  Next, the effect in the case of using the optimum PID parameter obtained by the parameter determination device 1 was confirmed. Here, a Hammerstein model represented by the following Expression 27 was used as the nonlinear system. In addition, ξ (t) in Equation 27 is Gaussian white noise having an average of zero and a variance of 0.0001.

  Further, for the nonlinear system represented by Expression 27, a linear model represented by Expression 28 below was used.

  First, as a comparison, one identification model (linear nominal model) was created without dividing the control input range (that is, without creating a local linear model). FIG. 5 shows the static characteristics of the nonlinear system represented by Expression 27 and the linear nominal model. In the figure, the solid line is the static characteristic of the nonlinear system, and the broken line is the static characteristic of the linear nominal model. As shown in the figure, the linear model represented by Expression 28 is a linearized version of the Hammerstein model near u (t) = 1.0.

Here, the PID control results y (t) and u (t) using the fixed parameters of the linear nominal model (a ₁ , a ₂ , b ₀ , b ₁ in Equation 28) are respectively shown in FIG. Shown in (b). The PID parameter at this time is expressed by the following equation 29.

  Next, the control result in the control apparatus using the optimum parameters will be described.

First, the local linear model construction unit 10 divided the system represented by Expression 27 into four. That is, the range of the control input to be used was divided into four areas. Then, the local linear model construction unit 10 applied the collective least square method to the linear model of Expression 28 to create four local linear models (y _i (t)). Note that white noise is used as the control input (u (t)), the variance of the white noise is 0.09 in each region, and the average of the white noise is 0.5, 1.0, 1.5 and 2.0.

  And the 1st parameter calculation part 11 calculated the PID parameter corresponding to the created four local linear models for every local linear model. Further, the second parameter calculation unit 12 adds the estimation error (e) to each PID parameter calculated by the first parameter calculation unit 11 based on the magnitude of each estimation error (e (t)) (each difference). A weight corresponding to each difference) was performed, and a PID parameter for PID control was calculated from each weighted PID parameter. Then, using the optimum PID parameter calculated by the second parameter calculation unit 12, the optimum control input u (t) was obtained based on Expression 7.

Here, PID control results y (t) and u (t) by the control device using the optimum PID parameters are shown in FIGS. 7A and 7B, respectively. 8A, 8B, and 8C show the calculation results (k _c , T _I , T _D ) of the PID gain at this time.

  When a fixed parameter, which is a comparative control, is used, as shown in FIGS. 5A and 5B, the control result deteriorates as the target value increases due to the nonlinearity of the system. On the other hand, when the control device is used, as shown in FIGS. 7A and 7B, the control result does not deteriorate even when the target value increases, and FIGS. ) As shown in (c), it can be seen that the PID gain is appropriately adjusted with respect to the nonlinearity of the system.

As a result, by using the control device, it is possible to perform control with higher accuracy than in the past.
[Embodiment 2]
Another embodiment of the present invention will be described below with reference to FIGS. For convenience of explanation, members having the same functions as those described in the first embodiment are given the same reference numerals, and descriptions thereof are omitted.

  FIG. 9 is a functional block diagram of the parameter determination device according to the present embodiment. In addition, the figure has shown the structure with which the parameter determination apparatus is provided in the control apparatus. However, the configuration is not limited to this configuration, and the parameter determination device may be any configuration that is provided outside the control device and can exchange data with the control device (for example, a configuration that is communicably connected). .

  As shown in the figure, the parameter determination apparatus 1 'includes a local linear model construction unit 10, a first parameter calculation unit 11, a neural network construction unit 13, and a second parameter calculation unit 12'. Note that the neural network construction unit 13 is not necessarily provided in the parameter determination device 1 ′, and may be provided outside.

  That is, the parameter determination device 1 ′ is newly provided with a neural network construction unit 13 as compared with the parameter determination device 1 of the first embodiment, and the second parameter calculation unit 12 ′ is replaced with the second parameter calculation unit 12. It has a configuration with. Other configurations are the same as those of the parameter determination apparatus 1. Therefore, below, a different point from the parameter determination apparatus 1 of Embodiment 1 is demonstrated.

  The neural network construction unit 13 constructs a neural network using the PID parameters for each local linear model calculated by the first parameter calculation unit 11. Specifically, the neural network construction unit 13 uses the PID parameter of each local linear model calculated by the first parameter calculation unit 11 as a teacher signal and inputs to the system corresponding to each local linear model, and A neural network is constructed using the output from the system corresponding to the input as learning data.

  In this embodiment, as shown in FIG. 10, a radial basis function (RBF) network is used as the neural network. The RBF network is a network composed of an input layer, an intermediate layer, and an output layer as shown in FIG. The RBF network is an example of a neural network and is not limited to this.

First, the RBF network will be described. The j-th intermediate layer from the top in the figure has an output h _j called a basis function represented by the following Expression 30.

However, in Expression 30, x and c _j indicate the input to the RBF network and the intermediate value in the intermediate layer, respectively. Furthermore, σ is a parameter indicating the spread of the base function. On the other hand, the output O _k from k-th output layer from the top of the figure is given by Equation 31 below.

Here, w _jk is a connection weight from the jth intermediate layer to the kth output layer. Note that the learning of the connection weight can be performed by the calculation shown in the following Expression 32 if the number of intermediate layers is the same as the number of sets of data to be used.

In Equation 32, W _k and T are a weight vector input to the k-th output layer and a teacher signal vector for the k-th output layer, respectively. Furthermore, H is a matrix having all the outputs of the intermediate layer as elements, as represented by the following Expression 33.

  Here, the neural network construction unit 13 uses an RBF network having two input layers, four intermediate layers, and three output layers.

As the learning data for constructing the neural network, the input signal series (that is, the local linear model construction unit 10 used when constructing a plurality of local linear models (U ₁ , U ₂ , U ₃ ,. , U _n )) and the output sequence corresponding to the input (that is, (Y ₁ , Y ₂ , Y ₃ ,..., Y _n ) corresponding to the input signal sequence). Then, Ui and Yi (1 ≦ i ≦ n) are input as learning data to the first and second input layers, respectively.

When Ui and Yi are input as learning data, the PID parameter corresponding to the local linear model y _i (t) calculated by the first parameter calculation unit 11 is used as the teacher signal.

Then, for example, the teacher signal output and k _c from the first output layer and a teacher signal output and T _I from the second output layer, the output and T _D from the third output layer An RBF network is constructed by comparing the teacher signals with each other.

The second parameter calculation unit 12 ′ calculates PID parameters for PID control using the constructed RBF network. Specifically, an input (u (t−1)) and an output (y (t−1)) to the nonlinear system are input to the input layer, and the optimum PID parameters (k _c (t), T _I (t), T _D (t)) is calculated.

  As described above, the parameter determination device 1 ′ is a parameter determination device that determines a PID parameter (control parameter) for PID control, and a plurality of non-linear systems (control objects having characteristics of nonlinearity). A local linear model building unit (local linear model building unit) 10 that builds a local linear model, and a first parameter calculating unit (first parameter calculating unit) that calculates a PID parameter corresponding to the local linear model for each local linear model ) 11 and the PID parameter of each local linear model calculated by the first parameter calculation unit 11 as a teacher signal, and an input to a nonlinear system corresponding to each local linear model, and a nonlinear system corresponding to the input Using a neural network constructed with the output from the learning data as the learning data The second parameter calculating section that calculates the ID parameter is a structure and a (second parameter calculation means) 12.

  According to the above configuration, the neural network uses the PID parameter of each local linear model calculated by the first parameter calculation unit 11 as a teacher signal and inputs to the nonlinear system corresponding to each local linear model, An output from the nonlinear system corresponding to the input is constructed as learning data.

  Therefore, the second parameter calculation unit 12 inputs an input to the nonlinear system and an output from the nonlinear system in response to the input to the neural network, so that an optimum PID for the nonlinear system is output as the output from the neural network. There is an effect that the PID parameter of the control can be obtained.

  In addition, the user himself / herself does not have to switch the PID parameter according to the input to the nonlinear system, which is conventionally performed by the user.

  Further, the parameter determination device 1 ′ is constructed such that the local linear model is constructed by dividing the range of the input to the nonlinear system into a plurality of ranges, the input to the nonlinear system in each range, and the input to the input It is constructed based on the output from the nonlinear system, and the input to the nonlinear system used when constructing the local linear model is used as the input to the nonlinear system as the learning data in each range. It is a configuration.

  According to said structure, the same input used when constructing | assembling a local linear model can be input into a system as learning data.

  Therefore, when the neural network is constructed, the neural network can be accurately learned, and a highly accurate PID parameter can be obtained.

  Further, the parameter determination device 1 ′ has a configuration including a neural network construction unit 13 that constructs the neural network.

  According to said structure, there exists an effect that a neural network can be constructed | assembled within parameter determination apparatus 1 '. Further, it is not necessary to provide a separate device for constructing the neural network.

  Next, the flow of the PID parameter determination method in the parameter determination apparatus 1 ′ will be described with reference to FIG.

  First, the local linear model construction unit 10 constructs a plurality of local linear models for a system having nonlinear characteristics (S11). After S11, the first parameter calculation unit 11 calculates a PID parameter corresponding to the local linear model for each local linear model (S12). After S12, the neural network construction unit 13 uses the PID parameter of each local linear model calculated by the first parameter calculation unit 11 as a teacher signal and inputs it to the nonlinear system corresponding to each local linear model. A neural network is constructed using the output from the non-linear system for the input as learning data (S13). After S13, the second parameter calculation unit 12 ′ calculates PID parameters for PID control using the neural network (S14).

  Through such steps (S11 to S14), an optimum PID parameter can be determined.

  Next, the effect in the case of using the optimum PID parameter obtained by the parameter determination device 1 ′ was confirmed. Here, as in the first embodiment, the Hammerstein model represented by Equation 27 is used as the nonlinear system.

As in the first embodiment, the local linear model construction unit 10 divides the nonlinear system represented by Expression 27 into four. Then, the local linear model construction unit 10 applied the collective least square method to the linear model of Expression 28 to create four local linear models (y _i (t)). The control input (u (t)) used the same white noise as in the first embodiment. And the 1st parameter calculation part 11 calculated the PID parameter corresponding to the created four local linear models for every local linear model. The process up to this point is the same as in the first embodiment.

  Next, the PID parameter of PID control was calculated by the second parameter calculation unit 12 ′ using the neural network constructed by the neural network construction unit 13. At the time of constructing the neural network, the variance of the input to the system as learning data was set to 0.4.

Here, control results y (t) and u (t) in the control apparatus using the optimum PID parameter are shown in FIGS. 12 (a) and 12 (b), respectively. FIGS. 13A, 13B, and 13C show the calculation results (k _c , T _I , T _D ) of the PID gain at this time.

  As shown in the first embodiment, when using a fixed parameter as a comparative control, as shown in FIGS. 5A and 5B, the control result increases as the target value increases due to the nonlinearity of the system. Has deteriorated. On the other hand, when the control device is used, as shown in FIGS. 12 (a) and 12 (b), the control result does not deteriorate even when the target value increases, and FIGS. ) As shown in (c), it can be seen that the PID gain is appropriately adjusted with respect to the nonlinearity of the system.

  As a result, by using the control device, it is possible to perform control with higher accuracy than in the past.

  The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope shown in the claims, and embodiments obtained by appropriately combining technical means disclosed in different embodiments. Is also included in the technical scope of the present invention.

  Note that each unit and each processing step of the parameter determination device of the above embodiment and the control device provided with this device has a program stored in a storage unit such as a ROM (Read Only Memory) or RAM by a calculation unit such as a CPU. This can be realized by controlling input means such as a keyboard, output means such as a display, or communication means such as an interface circuit. Therefore, the computer having these means simply reads the recording medium in which the program is recorded, and executes the program, thereby performing the various functions and various processes of the parameter determination device of the present embodiment and the control device including the device. Can be realized. In addition, by recording the program on a removable recording medium, the various functions and various processes described above can be realized on an arbitrary computer.

  As this recording medium, a program medium such as a memory (not shown) such as a ROM may be used for processing by the microcomputer, or a program reader is provided as an external storage device (not shown). It may be a program medium that can be read by inserting a recording medium therein.

  In any case, the stored program is preferably configured to be accessed and executed by the microprocessor. Furthermore, it is preferable that the program is read out, and the read program is downloaded to a program storage area of the microcomputer and the program is executed. It is assumed that this download program is stored in advance in the main unit.

  The program medium is a recording medium configured to be separable from the main body, such as a tape system such as a magnetic tape or a cassette tape, a magnetic disk such as a flexible disk or a hard disk, or a disk such as a CD / MO / MD / DVD. Fixed disk system, card system such as IC card (including memory card), or semiconductor memory such as mask ROM, EPROM (Erasable Programmable Read Only Memory), EEPROM (Electrically Erasable Programmable Read Only Memory), flash ROM, etc. In particular, there are recording media that carry programs.

  Further, if the system configuration is capable of connecting to a communication network including the Internet, the recording medium is preferably a recording medium that fluidly carries the program so as to download the program from the communication network.

  Further, when the program is downloaded from the communication network as described above, it is preferable that the download program is stored in the main device in advance or installed from another recording medium.

  Since an optimal control parameter can be determined even for a controlled object having a non-linear characteristic, it can be applied to various controlled objects including a controlled object whose structure is unknown.

It is a functional block diagram of the parameter determination apparatus which concerns on embodiment of this invention. It is the block diagram which showed the structure of the PID control system. It is a figure for demonstrating calculation of an estimation error. It is the flowchart which showed the flow of the determination method of the PID parameter in the said parameter determination apparatus. It is the graph which showed the static characteristic of the nonlinear system, and the static characteristic of the said linear nominal model. (A) is a graph showing a control result y (t) using a fixed parameter of the linear nominal model, and (b) is a graph showing a control result u (t) using a fixed parameter. (A) is a graph showing a control result y (t) when using the PID parameter determined by the parameter determination device, and (b) is a control result u (when using the PID parameter. It is the graph which showed t). (A) is, in the case of using the PID parameter is a graph showing the results of a gain for the k _c, (b) is, in the above case, a graph showing the results of a gain for T _I Yes, (c) is, in the above case is a graph showing the results of a gain of about T _D. It is a functional block diagram of the parameter determination apparatus which concerns on other embodiment of this invention. It is the figure which showed the structure of the RBF network. 10 is a flowchart showing a flow of a PID parameter determination method in the parameter determination apparatus of FIG. (A) is the graph which showed the control result y (t) at the time of using the PID parameter determined with the parameter determination apparatus of FIG. 9, (b) is the control result at the time of using the said PID parameter. It is the graph which showed u (t). (A) is, in the case of using the PID parameters determined by the parameter determination device of FIG. 9 is a graph showing the results of a gain for the k _c, (b) is, in the case of the above, the T _I a graph showing the results of a gain, (c) is, in the above case is a graph showing the results of a gain of about T _D. It is a figure for demonstrating the conventional parameter determination method.

Explanation of symbols

1.1 'Parameter Determination Device 10 Local Linear Model Building Unit (Local Linear Model Building Means)
11 First parameter calculation unit (first parameter calculation means)
12.12 '2nd parameter calculation part (2nd parameter calculation means)
13 Neural network construction part (Neural network construction means)

Claims (11)

A parameter determination device for determining a control parameter for PID control,
A local linear model construction means for constructing a plurality of local linear models for a controlled object having nonlinear characteristics,
First parameter calculation means for calculating a control parameter corresponding to the local linear model for each local linear model;
An output value output from the control object in response to an input to the control object, and an output value in each local linear model for the input when each control parameter calculated by the first parameter calculation unit is used; Based on the magnitude of each difference, the control parameters calculated by the first parameter calculation means are weighted corresponding to the differences, and the control parameters for PID control are calculated from the weighted control parameters. And a second parameter calculating means.   The control device according to claim 1, wherein the first parameter calculation unit calculates each control parameter using a parameter included in each local linear model. A parameter determination device for determining a control parameter for PID control,
A local linear model construction means for constructing a plurality of local linear models for a controlled object having nonlinear characteristics,
First parameter calculating means for calculating a control parameter corresponding to the local linear model for each local linear model;
The control parameter of each local linear model calculated by the first parameter calculation means is used as a teacher signal, and the input to the control target corresponding to each local linear model and the output from the control target corresponding to the input are learned A parameter determination device comprising: second parameter calculation means for calculating a control parameter for PID control using a neural network constructed as data. The local linear model is constructed by dividing the range of the input to the controlled object into a plurality of ranges, and the input to the controlled object in each range and the output from the controlled object to the input Built on the basis of
4. The parameter determination apparatus according to claim 3, wherein an input to the control object used when constructing a local linear model is used as an input to the control object as the learning data in each range.   5. The parameter determining apparatus according to claim 3, further comprising neural network construction means for constructing the neural network.   A control comprising the parameter determination device according to any one of claims 1 to 5, wherein the control target is controlled using a control parameter for PID control calculated by the second parameter calculation means. apparatus. A parameter determination method for determining a control parameter for PID control,
A local linear model construction step for constructing a plurality of local linear models for a controlled object having nonlinear characteristics;
A first parameter calculation step of calculating a control parameter corresponding to the local linear model for each local linear model;
An output value output from the control object in response to an input to the control object, and an output value in each local linear model for the input when using each control parameter calculated in the first parameter calculation step; Based on the magnitude of each difference, the control parameters calculated in the first parameter calculating step are weighted corresponding to the differences, and the control parameters for PID control are calculated from the weighted control parameters. A parameter determining method comprising: a second parameter calculating step. A parameter determination method for determining a control parameter for PID control,
A local linear model construction step for constructing a plurality of local linear models for a controlled object having nonlinear characteristics;
A first parameter calculation step of calculating a control parameter corresponding to the local linear model for each local linear model;
The control parameter of each local linear model calculated in the first parameter calculating step is used as a teacher signal, and the input to the control target corresponding to each local linear model and the output from the control target corresponding to the input are learned. A parameter determination method comprising: a second parameter calculation step of calculating a control parameter for PID control using a neural network constructed as data.   The program for functioning a computer as each means of the parameter determination apparatus of any one of Claim 1 to 5.   The program for making a computer perform the parameter determination method of Claim 7 or 8.   A recording medium on which the program according to claim 9 is recorded.

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