JP2008186113A - PID control device and PID control method - Google Patents

Abstract

When controlling a control object by determining a PID parameter using a control law including a weighting coefficient for a difference in input to a PID control object based on a prediction model, the weight coefficient is appropriately and It is possible to easily set the desired control performance.
A trade-off curve relating to a variance of a control error and a variance of a difference of an input to a controlled object is drawn, and a position satisfying a predetermined condition set in advance is determined on the trade-off curve and the position is determined. A weighting coefficient and a PID parameter corresponding to are determined, and the PID parameter is determined as a PID parameter for controlling the control target.
[Selection] Figure 1

Description

  The present invention relates to a technical field related to a PID control apparatus and a PID control method for constructing a prediction model of a PID control target, determining a PID parameter based on the prediction model, and controlling the control target using the PID parameter. Belongs.

In recent years, in the process industry represented by chemical processes and petroleum refining processes, in response to the intensifying international competition, productivity improvement, energy saving / labor saving, quality improvement, and production cost reduction have been further promoted. ing. Under such circumstances, the role played by the control system is more important than ever. Especially in chemical processes and petroleum refining processes, the characteristics of the target system may change due to changes in operating conditions (changes in product brands, etc.), changes in raw materials and the environment, or nonlinearity of the system itself. Often exists. In order to obtain highly accurate controllability for such a system, it is originally desirable that the control system (PID parameter) is self-adjusted in accordance with the system characteristics. One approach is a self-tuning control method, and Non-Patent Document 1 discloses a self-tuning PID control method based on this concept. The self-tuning PID control method of Non-Patent Document 1 is a PID parameter adjustment method based on generalized minimum variance control (GMVC), and derives a control law (GMVC law) based on minimization of evaluation criteria. Then, based on the prediction model constructed based on the input to the PID control target and the output from the control target with respect to the input, the PID parameter is determined using the control law (GMVC law). At this time, since the above-mentioned control law includes a weighting factor for the difference in the input to the PID control target, it is necessary to set this weighting factor when determining the PID parameter.
Yamamoto, Kaneda, “A Design of Self-Tuning PID Controller Based on Generalized Minimum Dispersion Control Law”, Journal of System Control Information Society, 1998, Vol. 11, No. 1, p. 1-9

  By the way, the value of the weighting factor has a very important influence on the control performance. If the value is small, the control error (difference between the target value and the output from the control target) is reduced, and the target value followability (extension) is reduced. Product quality) can be improved, but the input to the controlled object is greatly shaken. On the other hand, if the value of the weighting factor is large, the input fluctuation (variation of input difference) is small and stable, but the target value follow-up property is lowered. For example, in a thermal process such as an injection molding machine or an extruder, the same process is repeated, and the speed of the process greatly affects the productivity. For this reason, quick response (target value followability) is required. On the other hand, in the petrochemical process and the oil refining process, it is a major premise that the transient state is stable, and the steady-state characteristic greatly affects the productivity. For this reason, steady-state characteristics are more important than quick response (however, product quality must be secured to some extent). It is necessary to determine the value of the weighting factor in consideration of such points.

  However, in the conventional PID parameter determination method, the weight coefficient is only appropriately determined, and it is difficult to reliably obtain the desired control performance. Especially in the chemical process, the fluctuation of input may become large, and problems in practical use have been pointed out.

  The present invention has been made in view of such a point, and the object of the present invention is to set a PID parameter using a control law including a weighting factor for a difference in input to a PID control target based on a prediction model. When determining and controlling the object to be controlled, the weighting factor can be set appropriately and easily to ensure that desired control performance is obtained.

  In order to achieve the above object, the present invention draws a trade-off curve regarding the variance of the control error and the variance of the difference of the input to the PID control object, and a predetermined condition set in advance on the trade-off curve. And a weighting coefficient and a PID parameter corresponding to the position are determined, and the PID parameter is determined as a PID parameter for controlling the controlled object.

  Specifically, in the invention of claim 1, a prediction model construction unit that constructs a prediction model of the control target based on an input to the PID control target and an output from the control target with respect to the input, and the prediction Based on the prediction model constructed by the model construction unit, a PID parameter determination unit that determines a PID parameter using a control law including a weighting factor for the input difference, and a PID parameter determined by the PID parameter determination unit And a PID control device including a control means for controlling the control target.

  The PID parameter determining means calculates the PID parameter for each weighting factor while changing the weighting factor, and distributes the control error corresponding to each weighting factor and the difference of the input difference at the time of the calculation. And the control error variance when the weighting factor is changed by plotting the calculated value on a biaxial graph of the variance of the control error and the variance of the input difference. And a trade-off curve related to the variance of the difference between the above inputs, a position satisfying a predetermined condition set in advance on the trade-off curve, and a weight coefficient and a PID parameter corresponding to the position are obtained. It is assumed that the PID parameter is determined as a PID parameter used by the control means.

  With the above configuration, a prediction model is constructed by the prediction model construction means (system parameters are estimated), and the weight coefficient for the input difference to the PID control target is calculated by the PID parameter determination means based on the constructed prediction model. A PID parameter is determined using a control law including the control object, and the control object is controlled by the control means using the determined PID parameter. Here, the PID parameter determination means draws a trade-off curve regarding the variance of the control error and the variance of the input difference when determining the PID parameter. This trade-off curve is a curve in which the variance of the input difference increases as the variance of the control error decreases, and the position on the trade-off curve corresponds to the weighting factor, and the input difference increases as the weighting factor decreases. (The control error variance is reduced). When the weighting factor is determined, the PID parameter is determined. Therefore, the position on the trade-off curve corresponds to the weighting factor and the PID parameter.

  Here, the problem is which position on the trade-off curve the PID parameter obtained from is used. Therefore, conditions for setting the variance of the control error and the variance of the input difference are set in advance. For example, the condition that the variance of the input difference becomes the smallest while the variance of the control error is less than or equal to a predetermined value set in advance. Or the condition that the variance of the control error is the smallest while the variance of the input difference is less than or equal to a predetermined value set in advance (this is the same as the condition that the variance of the input difference becomes a predetermined value). Etc. are set in advance. Then, on the trade-off curve, a position satisfying the above condition is obtained, and a weighting coefficient and a PID parameter corresponding to the position are obtained. If the control object is controlled using this PID parameter, preset control performance (desired control performance that satisfies the above conditions) can be obtained, which is optimal for the process to be applied.

  According to a second aspect of the present invention, in the first aspect of the invention, the predetermined condition is a condition that the variance of the difference between the inputs is minimized while the variance of the control error is equal to or less than a predetermined value set in advance. It shall be.

  As a result, while ensuring product quality, dispersion of input differences (input fluctuations) is suppressed as much as possible, and optimum conditions for chemical processes and the like are obtained. In addition, since the dispersion of the input difference is suppressed, the actuator is not burdened greatly and the failure of the actuator is reduced accordingly.

  According to a third aspect of the present invention, in the first or second aspect of the present invention, the output when the prediction model constructed by the prediction model construction unit is used for the input to the controlled object, and the control for the input. The apparatus further comprises determination means for determining whether a modeling error that is a difference from the output from the target is larger than a preset reference value, and the prediction model construction means performs the modeling error by the determination means. Is determined to be larger than the reference value, the prediction model is reconstructed and updated to the reconstructed prediction model.

  As a result, since the prediction model is updated when the modeling error exceeds a preset reference value, the calculation cost can be reduced as compared with the case of sequentially updating the prediction model. Excellent in reliability. In other words, when the prediction error is updated even when the modeling error is within the above-mentioned reference value, an incorrect model is constructed due to the effect of noise added to the output and the control system becomes unstable. Is likely to be. Therefore, if the modeling error is within the reference value, the same prediction model is used as it is, and by updating the prediction model when the modeling error exceeds the reference value, the control reliability and Stability can be improved.

  According to a fourth aspect of the present invention, a prediction model construction step for constructing a prediction model of the control object based on an input to the PID control object and an output from the control object with respect to the input, and a construction of the prediction model construction step A PID parameter determining step for determining a PID parameter using a control law including a weighting factor for the input difference based on the predicted model, and the control using the PID parameter determined in the PID parameter determining step. It is invention of the PID control method provided with the control step which controls object.

  In the present invention, the PID parameter determination step calculates the PID parameter for each weighting factor while changing the weighting factor, and distributes the control error corresponding to each weighting factor and the input at the time of the calculation. When the weighting factor is changed by plotting the calculated value on a biaxial graph of the variance of the control error and the variance of the input difference, A trade-off curve regarding the variance of the control error and the variance of the difference between the inputs is drawn, and a position satisfying a predetermined condition set in advance is obtained on the trade-off curve, and a weighting factor and a PID corresponding to the position are obtained. It is assumed that the parameter is obtained and the PID parameter is determined as the PID parameter used in the control step.

  According to the present invention, the same effect as that attained by the 1st aspect can be attained.

  In the invention of claim 5, in the invention of claim 4, for the input to the controlled object, the output when using the prediction model constructed in the predictive model construction step, and the control object for the input A determination step for determining whether or not a modeling error, which is a difference from the output of, is greater than a preset reference value, and the determination step determines that the modeling error is greater than the reference value When this is done, the prediction model is reconstructed in the prediction model construction step and updated to the reconstructed prediction model.

  Thus, the same effect as that attained by the 3rd aspect can be attained.

  As described above, according to the PID control device and the PID control method of the present invention, a trade-off curve regarding the variance of the control error and the variance of the difference of the input to the PID control is drawn, and the preset value is set on the trade-off curve. A position satisfying the predetermined condition is obtained, a weighting factor and a PID parameter corresponding to the position are obtained, and the PID parameter is determined as a PID parameter for controlling the controlled object. It is possible to appropriately and easily set the weighting factor for the difference in the input to the controlled object, so that the desired control performance can be obtained with certainty.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Outline of control system>
FIG. 1 shows a PID control apparatus according to an embodiment of the present invention. This PID control apparatus includes an input u to a PID control target and an output y from the control target with respect to the input (specifically, a modeling error described later). η) based on the prediction model construction means 1 for constructing the prediction model of the control target, and based on the prediction model constructed by the prediction model construction section 1, A PID parameter determining unit 2 as a PID parameter determining unit that determines a PID parameter using a control law (equation (12) described later) including a weighting factor (λ described later), and the PID parameter determining unit 2 determines Using the PID parameter, the PID control unit 3 as a control means for controlling the controlled object and the prediction model constructed by the prediction model construction unit 1 for the input. Whether the modeling error (prediction error) η, which is the difference between the output y ^* when using the measurement model and the output y from the control target with respect to the input, is greater than a preset reference value γσ _ε And a parameter evaluation unit 4 as determination means for determining whether or not.

  The prediction model construction unit 1 constructs a prediction model by estimating system parameters (time constant T, system gain K, and dead time L) as will be described later so that the modeling error η is minimized. In the present embodiment, when the parameter evaluation unit 4 determines that the modeling error is larger than the reference value, the prediction model construction unit 1 reconstructs the prediction model (system parameter And re-estimate) to update to the reconstructed prediction model. That is, when the parameter evaluation unit 4 determines that the modeling error is larger than the reference value, the switch 10 of FIG. 1 is turned on and the prediction model construction unit 1 functions. Note that the switch 10 is automatically or manually turned on during the initial tuning of the PID parameters.

  When the prediction model is updated by the prediction model construction unit 1, the PID parameter determination unit 2 uses a control law including the weighting factor based on the updated prediction model (reestimated value of the system parameter). Then, the PID parameter is re-determined, and the PID control unit 3 controls the control target using the re-determined PID parameter.

As described in detail later, the PID parameter determination unit 2 obtains desired control performance (in this embodiment, control error variance σ _e ² ) when determining PID parameters (including re-determination). As described above, the PID parameter is determined based on the estimated values (T ^* , K ^*, and L ^* ) of the system parameters.

<Description of system>
In this embodiment, a process system such as a chemical process is the control target. Originally, chemical processes become higher-order lag systems when heat transfer, convection, radiation, etc. are considered, but as the number of system parameters increases, there will be more uncertainty and this will adversely affect control system design. Therefore, in the field where the process system is handled, the control target system is often described as a “first order delay + dead time” system, and also in this embodiment, the following expression (1) is expressed as a control target description model. (Detailed model). In equation (1), T is a time constant, K is a system gain, L is a dead time, and these are system parameters.

  Further, the dead time is approximated by a first-order paddy, and a second-order lag system (design model) such as the following equation (2) is considered.

  Next, a discrete time model represented by the following equation (3) corresponding to the equation (2) is considered.

In Expression (3), u (t) is an input to the controlled object at time t, y (t) is an output from the controlled object at time t, and χ (t) is at time t. This is a Gaussian white noise indicating a modeling error or the like. Z ⁻¹ is a time delay operator, which means z ⁻¹ y (t) = y (t−1). Δ represents a difference operator and is defined as Δ = 1−z ⁻¹ . Furthermore, A (z ⁻¹ ) and B (z ⁻¹ ) are polynomials represented by the following formula (4).

  Equation (4) is a CARIMA (Controlled Auto-Regressive and Integrated Moving Average) model, which is used for the process system for the purpose of removing step-like disturbances and steady terms around the target value point.

Given system parameters T, K and L (actually estimated values T ^* , K ^* and L ^* calculated as described below), the PID parameters (k _p , T _I and T _D ) are calculated.

<PID control law>
As the PID control law, in this embodiment, a PID (proportional / differential precedence type PID) control law given by the following equation (5) is used.

In the formula (5), _{k p} is proportional gain, _{T I} is the integral time, _{T D} is the derivative time, which are PID parameters. Further, T _S is the sampling interval, e (t) is a control error of at time t, is given by the following equation (6). Note that “: =” in formula (6), formula (8) described later, and the like means a definition formula.

  In Expression (6), r (t) is a target value at the time t (in this embodiment, constant regardless of the value of t).

  Here, in order to simplify the following consideration, the equation (5) is rewritten into the following equation (7).

In the formula (7), C (z ⁻¹ ) is represented by the following formula (8).

<PID parameter adjustment>
In the present embodiment, the PID parameter is adjusted using a PID parameter adjustment method (GMV-PID) based on generalized minimum dispersion control (GMVC).

  One form of the GMVC evaluation criterion is given by the following equation (9).

In Formula (9), E [•] represents a spatial average. P (z ⁻¹ ) is a design polynomial and is designed by the following equation (10).

In the formula (10), p ₁ and p ₂ are represented by the following formula (11).

  In Equation (11), σ represents a parameter corresponding to the rise time, μ is a parameter related to the attenuation characteristic of the response, and is adjusted by δ. At this time, δ = 0 indicates a response shape corresponding to the binomial expansion model, and δ = 1.0 indicates a response shape corresponding to the Butterworth format model.

  In equation (9), λ is a weighting factor for the difference in the input to the controlled object. Here, σ, δ, and λ greatly affect the control performance (responsiveness, stability, steady characteristics, etc.). In order to improve the design prospects, σ is set to approximately 1/3 to 1/2 of the sum of the time constant and the dead time, and δ is set to 0 or more and 2.0 or less from a practical viewpoint. It is preferable. The setting of λ will be described in detail later.

  By minimizing the evaluation criterion of equation (9), a control law (GMVC law) according to the following equation (12) is given. This control law corresponds to a control law including the weight coefficient.

Here, F (z ⁻¹ ) is calculated based on the following diphantine equations (13) and (14).

  Then, consider the following equation (15) in which the second term coefficient polynomial of the above equation (12) is replaced with a stationary term.

  Here, υ is newly defined by the following equation (16).

  Thereby, Formula (15) becomes following Formula (17).

By comparing the above formula (7) and formula (17), formula (18) can be derived. From this, if C (z ⁻¹ ) is designed, the PID parameter based on GMVC can be calculated.

  That is, the PID parameter can be calculated by the following equation (19) from the equations (7) and (17).

  Note that the adjustment of the PID parameter is not limited to the above-described PID parameter adjustment method, and any method can be used as long as the method adjusts the PID parameter using a control law including a weighting factor for the input difference to the controlled object based on the prediction model. Such a method may be used.

<Adjustment of weighting factor λ (determination of PID parameter)>
Expression (19) includes υ (= B (1) + λ), that is, the weighting factor λ. If the weighting factor λ is not set appropriately, the PID parameter cannot be determined appropriately. Therefore, the PID parameter determination unit 2 adjusts the weight coefficient λ as follows to determine the PID parameter.

  First, the PID parameter is calculated from the equation (19) for each weight coefficient while changing the weight coefficient λ in a predetermined range within a predetermined range. The predetermined step may be fine enough to draw a trade-off curve described later, for example, 0.01. The predetermined range may be a range that includes a position that satisfies the conditions described later in the trade-off curve, and may be, for example, about 0 to 10.

Then, when calculating the PID parameter, the variance of the control error corresponding to each weighting factor λ and the variance of the difference of the input to the control target are calculated. In the present embodiment, the variance E [e ² (t)] of the control error and the variance E [(Δu (t)) ² ] of the input difference are calculated using the H ₂ norm. Details of this calculation will be described later.

Next, as shown in FIG. 2, a biaxial graph of the variance E [e ² (t)] of the control error and the variance E [(Δu (t)) ² ] of the input difference (in this embodiment, , Plotting the calculated values of both variances on a graph with the control error variance on the vertical axis and the variance of the input difference on the horizontal axis), the control error when the weighting factor is changed Draw a trade-off curve for the variance and the variance of the difference between the inputs. This trade-off curve is a curve in which the variance of the input difference increases as the variance of the control error decreases, and the position on the trade-off curve corresponds to the weighting factor, and the input difference increases as the weighting factor decreases. (The control error variance is reduced). When the weighting factor is determined, the PID parameter is determined. Therefore, the position on the trade-off curve corresponds to the weighting factor and the PID parameter. A trade-off curve may be drawn on a graph with the variance of the control error as the horizontal axis and the variance of the input difference as the vertical axis.

  Here, when the parameter evaluation unit 4 determines that the modeling error is larger than the reference value, the variance of the control error and the difference between the inputs are calculated based on the past input / output data to the control target. When the variance is calculated and the calculated value is plotted on the graph, the plotted position is located in the upper right region with respect to the trade-off curve. Therefore, if the control target is controlled using the PID parameter corresponding to the position on the trade-off curve, at least one of the variance of the control error and the variance of the input difference can be improved.

Which position on the trade-off curve to use the PID parameter is determined in consideration of the required control performance. That is, the conditions for setting the variance of the control error and the variance of the input difference are set in advance. For example, the condition that the variance of the input difference becomes the smallest while the variance of the control error is less than or equal to a predetermined value set in advance. Or the condition that the variance of the control error is the smallest while the variance of the input difference is less than or equal to a predetermined value set in advance (this is the same as the condition that the variance of the input difference becomes a predetermined value). Etc. are set in advance. In the present embodiment, the condition that the variance of the input difference is the smallest while the variance of the control error is equal to or less than a predetermined value σ _e ² is set so as to be optimal for a chemical process or the like. The predetermined value σ _e ² may be set in consideration of product quality, and a position satisfying this condition is obtained on the trade-off curve. For example, when the predetermined value σ _e ^{2 is set} to 1.0, the position of the + mark on the trade-off curve in FIG.

Then, a weighting factor and a PID parameter corresponding to the position are obtained, and the PID parameter is determined as a PID parameter used by the PID control unit 3. The PID control unit 3 controls the control target using the determined PID parameter, so that the preset control performance (in this embodiment, the variance of the control error is equal to or less than a predetermined value σ _e ^2). As a result, the desired control performance that satisfies the condition that the variance of the input difference becomes the smallest is obtained.

<Construction of prediction model (estimation of system parameters)>
In the present embodiment, the system parameter is estimated by applying a sequential least square method to past input / output data to the control target (in this embodiment, N-step input / output data traced back from the current time). Do it.

  First, a discrete time model represented by the following equation (20) corresponding to the detailed model of the above equation (1) is considered.

In Expression (21), ξ (t) represents a modeling error at time t, and is Gaussian white noise having an average of 0 and a variance of σ _ξ ² . Further, d is a dead time, usually, it is difficult to accurately determine the dead time in the process system, within the range which is assumed the dead time _{d (d = d m, d} m + 1, ..., d M) Then, d that minimizes the estimation error ε (t) at time t (see the following equation (24)) is determined as an estimated value d ^* (t) of the dead time. Furthermore, α (z ⁻¹ ) and β (z ⁻¹ ) are represented by the following formula (21).

Α ₁ , β ₀ and β _{1 in} equation (21) are estimated by the sequential least square method of equations (22) to (26) below.

In equations (25) and (26), [•, •, •] ^T means transposing a row vector to a column vector.

Subsequently, the estimated values (T ^* , K ^*, and L ^* ) of the system parameters are calculated by the following equations (27) to (29).

<Control algorithm>
As shown in FIG. 3, in the first step S1, the prediction model construction unit 1 estimates the system parameters by applying the sequential least squares method to the past input / output data to the controlled object as described above. At the same time, the standard deviation σ _ε of the estimation error ε (t) is calculated.

In the next step S2, the PID parameter determination unit 2 uses the estimated system parameter (estimated value of the system parameter) to change the weighting factor λ in predetermined increments as described above for each weighting factor. The PID parameter is calculated, and at the time of the calculation, the variance E [e ² (t)] of the control error corresponding to each weighting factor λ and the variance E [(Δu (t)) ² ] of the input difference to the controlled object And draw a trade-off curve.

  The specific calculation of the both variances is performed as follows. That is, first, the following formulas (30) and (31) are obtained in a steady state.

T (z ⁻¹ ) in formula (30) and formula (31) is defined by the following formula (32).

Then, the variance E [e ² (t)] of the control error e (t) and the variance E [(Δu (t)) ² ] of the input difference Δu (t) are obtained using the H ₂ norm ‖ · ‖ _2. , And can be calculated by the following equations (33) and (34), respectively.

The H ₂ norm is calculated using the estimated value of the system parameter and the PID parameter calculated based on the estimated value. Actually, since σ _ξ is unknown, both variances are calculated by replacing σ _ξ with the standard deviation σ _ε of the estimation error ε (t) calculated in step S1.

In the next step S3, the condition that the PID parameter determination unit 2 minimizes the variance of the input difference while the variance of the control error is not more than a predetermined value σ _e ² on the trade-off curve. (That is, a position where the variance of the control error is a predetermined value σ _e ² ) is obtained, and a weighting coefficient and a PID parameter corresponding to this position are obtained. This PID parameter is determined as a PID parameter used by the PID control unit 3.

  In the next step S4, the PID control unit 3 controls the controlled object using the PID parameter determined in step S3.

  In the next step S5, t is set to t + 1, and the process proceeds to step S6. In step S6, the parameter evaluation unit 4 uses the system parameter (estimated value) calculated in step S1 to calculate the modeling error (prediction error) η (t) at time t according to equation (35). calculate.

It should be noted that θ ^* (t) and Ψ (t−1) in Expression (35) are given in the same form as Expression (25) and Expression (26), respectively.

In the next step S7, the parameter evaluation unit 4 determines whether or not Expression (36) is satisfied, that is, whether or not the absolute value of the modeling error η (t) is larger than the reference value γσ _ε .

In the present embodiment, the reference value is set to γ times the standard deviation σ _ε calculated in step S1 on the assumption that the modeling error is approximately normally distributed due to the property of the least square method. The value of γ is preferably 3.0 or more and 5.0 or less from a statistical viewpoint.

  When the determination in step S7 is YES, the process returns to step S1, while when the determination in step S7 is NO, the process returns to step S5. That is, when the parameter evaluation unit 4 determines that the modeling error is larger than the reference value, the prediction model is reconstructed (by re-estimating the system parameters) and the reconstructed prediction model Update to When the prediction model is updated in this way, the PID parameter determination unit 2 re-determines the PID parameter as described above (updates the PID parameter) based on the updated prediction model (system parameter re-estimated value). The PID control unit 3 controls the controlled object using the re-determined PID parameter. On the other hand, if the modeling error is equal to or less than the reference value, the prediction model is not updated. As a result, the PID parameter is not updated, and the PID control unit 3 uses the same PID parameter as the previous time to determine the control target. Control.

Therefore, in this embodiment, a trade-off curve regarding the variance of the control error and the variance of the difference in the input to the PID control target is drawn, and a predetermined condition (the variance of the control error is set on the trade-off curve). A position satisfying the condition that the variance of the input difference is the smallest within a predetermined value σ _e ² or less that is set in advance, and a weighting factor λ and a PID parameter corresponding to the position are obtained, and the PID Since the parameter is determined as a PID parameter for controlling the controlled object, the control object is controlled using the determined PID parameter, thereby suppressing the variance of the control error to a desired value σ _e ² . In addition, it is possible to suppress variance in input differences (input fluctuations). Therefore, the weighting factor λ can be set appropriately and easily, and the desired control performance can be obtained with certainty.

  In the present embodiment, when the modeling error is determined to be larger than the reference value, the prediction model is updated. Therefore, when the prediction model is sequentially updated (in the flowchart of FIG. 3, Compared with the case of returning to step S1 immediately after step S5), the calculation cost can be reduced. In addition, when the prediction model is updated sequentially, the prediction model is updated even when the modeling error is within the reference value and is stable, and at this time, an incorrect model is added due to the influence of noise added to the output. If constructed, the control system is more likely to become unstable. However, in this embodiment, since the modeling error becomes larger than the reference value and the prediction model needs to be updated, the updating is performed, so that the reliability and stability of the control can be improved. However, this is not always necessary, and the prediction model may be updated sequentially.

  Further, in the initial tuning of the PID parameter, steps S1 to S4 in the flowchart of FIG. 3 may be executed only once.

  Here, the effectiveness of the PID control method of the present invention is quantitatively evaluated by numerical examples.

(Numerical example 1)
First, assuming the application of the PID control method of the present invention during initial tuning of PID parameters, consider the following numerical example.

  That is, it is assumed that the description model to be controlled is given by Expression (37).

Consider a model in which Equation (37) is discretized at a sampling interval T _S = 10.0 s and Gaussian white noise having a mean of 0 and a variance of 0.001 is added as a modeling error.

  FIG. 4 shows a control result when the PID control method of the present invention is applied to this control target. However, in the first 1000 steps (t = 0 to 999), control is performed using the following PID parameters.

k _p = 3.56
T _I = 100.0
T _D = 49.5
Further, it is assumed that steps S1 to S4 in the flowchart of FIG. 3 are executed at the time of t = 1000 using the input / output data between the above 1000 steps. Note that d _m = 4, d _M = 8, σ _e ² = 0.09, p ₁ = −1.53, and p ₂ = 0.59, and in step S4, λ is 0.0 to 10. The period up to 0 was changed in increments of 0.01.

The trade-off curve at t = 1000 is shown in FIG. The position of the mark ● on the graph in FIG. 5 is calculated based on the past 1000 steps of input / output data, and the variance of the control error and the variance of the input difference are calculated and the calculated values are plotted on the graph. It is the position and shows the control performance (variance of control error and variance of input difference) in the first 1000 steps. Further, the position of the + mark on the graph shows that the variance of the input difference is the largest on the trade-off curve while the variance of the control error is not more than a predetermined value σ _e ² (= 0.09). It is a position that satisfies the condition of becoming smaller. The value of the weighting factor λ corresponding to this position was λ = 0.05. When λ = 0.0 to 0.03, the control system becomes unstable and the control performance cannot be calculated. When λ = 0.04, the response is close to the stability limit, and it can be seen that the variance of the control error is large.

4 and 5 that the control error and the input difference are effectively suppressed at the time point t = 1000. Note that by estimating the system parameters at t = 1000,
T ^* = 99.22
K ^* = 0.500
L ^* = 50.00
And σ _ε = 0.0314 was obtained by calculating the standard deviation of the estimation error.

When the PID parameter was calculated from the estimated value of the system parameter and λ = 0.05,
k _p = 5.80
T _I = 69.68
T _D = 15.88
It became.

The variance of the control error at t = 1500 to 2000 is 0.1054, which exceeds the preset predetermined value σ _e ² (= 0.09), but is almost close to the predetermined value, and a desired control performance is obtained. You can see that In other words, the control performance has moved from the position of the mark ● on the graph to the position of the mark + (in fact, the position in the vicinity thereof).

Subsequently, FIG. 6 shows the result of performing the same simulation with σ _e ² = 0.25. As described above, when the predetermined value σ _e ² set in advance is increased, the variance of the control error increases, but the variance of the input difference is suppressed.

The PID parameter in this case is
k _p = 2.44
T _I = 69.13
T _D = 15.84
Met.

The value of T _I and T _D are a substantially same value as a result earlier, K _p is different. This is because the values of λ are different, and the relationship between λ and the PID parameter is clear from the equations (16) and (19).

  The variance of the control error at t = 1500 to 2000 is 0.2543, indicating that the desired control performance can be obtained.

  As described above, the effectiveness of the PID control method of the present invention in the initial tuning of PID parameters was confirmed.

(Numerical example 2)
Next, assuming the case where the system characteristics fluctuate, consider the following numerical examples.

  That is, it is assumed that the description model to be controlled is given by the equation (38).

  However, up to the first 2500 steps, the characteristics are the same as those in Numerical Example 1 above, and at t = 2501 to 5000, the time constant K and the system gain K change as shown in the following equation (39), and there is no dead time. Shall.

Eventually, the time constant is halved and the system gain is 6 times. Here, as in Numerical Example 1, Equation (38) is discretized at the sampling interval T _S = 10.0 s, and a model added with Gaussian white noise having a mean of 0 and a variance of 0.0001 is added as a modeling error. Think.

  The PID control method of the present invention is applied to this controlled object. However, in the first 1000 steps, as in Numerical Example 1, it is assumed that control is performed using the following PID parameters.

k _p = 3.56
T _I = 100.0
T _D = 49.5
Then, it is assumed that steps S1 to S7 in the flowchart of FIG. 3 are executed from t = 1000. Note that d _m = 4, d _M = 8, σ _e ² = 0.04, p ₁ = −1.53, and p ₂ = 0.59, and in step S4, λ is 0.0 to 10. The period up to 0 was changed in increments of 0.01. The value of γ in step S7 is γ = 3.0. Further, the number N of data used for system parameter estimation is set to N = 200.

The control result at this time is shown in FIG. 7, and the change of the PID parameter is shown in FIG. As can be seen from FIG. 8, the PID parameter was changed four times (t = 1000, 3243, 4657, 4814) including the change at t = 1000. Λ at the time of this change was calculated as 0.22 (t = 1000), 0.58 (t = 3243), 1.03 (t = 4657), and 1.38 (t = 4814). The variance of the control error after t = 1000 is 0.0348, which is less than a predetermined value σ _e ² (= 0.04) set in advance, and the difference in input is suppressed, so that the desired control performance is achieved. You can see that From this, it can be seen that the PID parameter is appropriately determined with respect to the system fluctuation, and a good control result is obtained.

  Subsequently, FIG. 9 shows a control result when the value of γ is γ = 5.0, and FIG. 10 shows a change in the PID parameter at that time. By increasing the value of γ, the number of times that the modeling error was determined to be larger than the reference value was reduced, and the PID parameter was changed only twice, t = 1000 and t = 3636. Λ at this change was 0.22 (t = 1000) and 1.35 (t = 3636). The variance of the control error after t = 1000 is 0.0419, and the desired control performance is obtained although the performance is slightly inferior to the case where γ = 3.0.

  By changing the value of γ in this way, the sensitivity to system fluctuations or modeling errors can be adjusted. That is, if the value of γ is decreased, the sensitivity is increased and the frequency of changing the PID parameter is increased. On the other hand, if the value of γ is increased, the sensitivity is decreased and the frequency of changing the PID parameter is decreased.

FIG. 11 shows the control result when γ = 5.0 and t = 1000 or later without changing the PID parameter. The PID parameter after t = 1000 is
k _p = 1.9458
T _I = 67.6249
T _D = 16.4162
Met.

  In this case, the control system is unstable at the end because the PID parameter is not changed with respect to the system fluctuation. This confirms the effectiveness of changing the PID parameter when the modeling error is greater than the reference value.

  The present invention is useful for a PID control device and a PID control method for constructing a prediction model of a PID control target, determining a PID parameter based on the prediction model, and controlling the control target using the PID parameter. In particular, it is useful when determining a PID parameter using a control law including a weighting factor for a difference in input to a PID control target based on the prediction model.

It is a block diagram which shows the PID control apparatus which concerns on embodiment of this invention. It is a biaxial graph of the dispersion | variation of a control error, and the difference of the input to a control object which shows the trade-off curve regarding dispersion | distribution of a control error and the dispersion | variation of the difference of the input to a control object. It is a flowchart which shows the control algorithm in a PID control apparatus. It is a control result in Numerical Example 1 (σ _e ² = 0.09), (a) shows the temporal transition of the output from the controlled object, and (b) shows the temporal transition of the difference of the input to the controlled object. It is a graph shown, respectively. It is a biaxial graph of the variance of control error and the difference of the input to a controlled object, showing the trade-off curve in Numerical Example 1 (σ _e ² = 0.09). It is a control result in Numerical Example 1 (σ _e ² = 0.25), (a) shows the temporal transition of the output from the controlled object, and (b) shows the temporal transition of the difference of the input to the controlled object. It is a graph shown, respectively. It is a control result in Numerical Example 2 (γ = 3.0), (a) shows the temporal transition of the output from the controlled object, and (b) shows the temporal transition of the difference of the input to the controlled object. It is a graph. It is a control result in Numerical Example 2 (γ = 3.0), (a) shows the time transition of the proportional gain, (b) shows the time transition of the integration time, and (c) shows the time of the derivative time. It is a graph which shows transition, respectively. It is a control result in Numerical Example 2 (γ = 5.0), (a) shows the temporal transition of the output from the controlled object, and (b) shows the temporal transition of the difference of the input to the controlled object. It is a graph. It is a control result in Numerical Example 2 (γ = 5.0), (a) shows the time transition of the proportional gain, (b) shows the time transition of the integration time, and (c) shows the time of the derivative time. It is a graph which shows transition, respectively. It is a control result when the PID parameter is not changed after t = 1000 with respect to Numerical Example 2 (γ = 5.0), (a) shows the temporal transition of the output from the control target, (b ) Are graphs showing temporal transitions of differences in the input to the controlled object.

Explanation of symbols

1 Prediction model construction part (prediction model construction means)
2 PID parameter determination unit (PID parameter determination means)
3 PID control unit (control means)
4 Parameter evaluation unit (determination means)

Claims (5)

Based on the input to the PID control target and the output from the control target with respect to the input, based on the prediction model construction means for constructing the prediction model of the control target, and the prediction model constructed by the prediction model construction means PID parameter determining means for determining a PID parameter using a control law including a weighting factor for the input difference; and control means for controlling the control object using the PID parameter determined by the PID parameter determining means; A PID control device comprising:
The PID parameter determining means calculates the PID parameter for each weighting factor while changing the weighting factor, and calculates the variance of the control error corresponding to each weighting factor and the variance of the input difference at the time of the calculation. By calculating and plotting the calculated values on a biaxial graph of the variance of the control error and the variance of the input difference, the variance of the control error and the above when the weighting factor is changed Draw a trade-off curve regarding the variance of the input difference, find a position that satisfies a predetermined condition set in advance on the trade-off curve, and obtain a weighting factor and a PID parameter corresponding to the position, A PID control device configured to determine a PID parameter as a PID parameter used by the control means. The PID control device according to claim 1,
The PID control apparatus according to claim 1, wherein the predetermined condition is a condition that the variance of the difference of the input is minimized while the variance of the control error is equal to or less than a predetermined value set in advance. In the PID control device according to claim 1 or 2,
A modeling error that is a difference between an output when the prediction model constructed by the prediction model construction unit is used and an output from the control object with respect to the input is set in advance for the input to the control object. Determination means for determining whether or not the reference value is greater than the determined reference value;
The prediction model construction means is configured to reconstruct a prediction model and update to the reconstructed prediction model when the determination means determines that the modeling error is larger than the reference value. A PID control device. Based on the input to the PID control target and the output from the control target with respect to the input, based on the prediction model construction step for constructing the prediction model of the control target, and the prediction model constructed in the prediction model construction step A PID parameter determining step for determining a PID parameter using a control law including a weighting factor for the input difference, and a control step for controlling the control object using the PID parameter determined in the PID parameter determining step; A PID control method comprising:
The PID parameter determination step calculates the PID parameter for each weighting factor while changing the weighting factor, and calculates the variance of the control error corresponding to each weighting factor and the variance of the input difference at the time of the calculation. By calculating and plotting the calculated values on a biaxial graph of the variance of the control error and the variance of the input difference, the variance of the control error and the above when the weighting factor is changed Draw a trade-off curve regarding the variance of the input difference, find a position that satisfies a predetermined condition set in advance on the trade-off curve, and obtain a weighting factor and a PID parameter corresponding to the position, A PID control method, comprising: determining a PID parameter as a PID parameter used in the control step. The PID control method according to claim 4, wherein
A modeling error that is a difference between an output when the prediction model constructed in the prediction model construction step is used and an output from the control object with respect to the input is set in advance for the input to the control object. A determination step of determining whether or not the reference value is greater than the determined reference value;
A PID characterized in that when the modeling error is determined to be larger than the reference value in the determination step, the prediction model is reconstructed in the prediction model construction step and updated to the reconstructed prediction model. Control method.

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