WO2021010086A1 - Procédé de conception de paramètres et procédé de commande à rétroaction - Google Patents

Procédé de conception de paramètres et procédé de commande à rétroaction Download PDF

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WO2021010086A1
WO2021010086A1 PCT/JP2020/023950 JP2020023950W WO2021010086A1 WO 2021010086 A1 WO2021010086 A1 WO 2021010086A1 JP 2020023950 W JP2020023950 W JP 2020023950W WO 2021010086 A1 WO2021010086 A1 WO 2021010086A1
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controller
control
parameters
pid control
control unit
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Japanese (ja)
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晃 村上
崇彦 杉原
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株式会社神戸製鋼所
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric

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  • the present invention relates to a method of designing parameters of a controller that performs feedback control, and a footback control method using a controller in which parameters designed using this method are set.
  • a practical feedback control system requires various performances. Specifically, stability, disturbance suppression, structural simplicity, adaptability, feasibility in hardware, ease of design, ease of maintenance, etc.
  • the control system includes PID control, robust control, adaptive control, model prediction control, etc., but each control system has advantages and disadvantages and is not universal.
  • PID control has a simple structure and can be given an adaptive function by table lookup or the like.
  • PID control is used not only for high-performance but difficult-to-maintain hardware (industrial personal computers, etc.), but also for general-purpose DCS (Distributed Control System), PLC (Programmable Logical Control), etc., which have limited performance but are easy to maintain. It can be easily realized with the hardware of.
  • PID control has few parameters, and it is possible to manually adjust the site while trying the control. On the other hand, PID control has a limited performance due to its simple structure.
  • phase lead compensation phase delay compensation
  • phase lead / delay compensation may be added.
  • these adjustment guidelines are not always clear quantitatively.
  • adjustment is performed while observing the actual response.
  • H ⁇ control which is one of the robust controls, can design a controller having robust stability and disturbance suppression specified in the frequency domain. If the model is accurate including uncertainty, it is possible to design a high-performance controller after reducing the number of trials and errors as compared with the PID control system.
  • the H ⁇ control has a complicated structure, becomes a controller with a high order, and may cause pole-zero cancellation in the controller. Then, H ⁇ control may require hardware capable of high-precision calculation.
  • H ⁇ control is difficult to adapt.
  • H ⁇ control is difficult to realize with general-purpose controller hardware.
  • Non-Patent Document 1 discloses a technique for H ⁇ control of the molten metal level of a slab continuous casting machine.
  • the design of robust control such as H ⁇ control is as follows.
  • the order is high.
  • Special special algorithms such as solving Ricatch inequalities and linear matrix inequalities are required. Since there is pole-zero cancellation, it tends to be numerically unstable and high-performance hardware is required (single-precision floating-point arithmetic is not sufficient, double-precision floating-point arithmetic is required, etc.). Difficult to adapt.
  • a high-order controller was calculated and obtained with dedicated software, and control was performed using high-performance control hardware.
  • a method of preparing a plurality of H ⁇ control controllers and switching the controllers during control was used.
  • the PID control system is mainly applied in the actual process, but it has the following problems.
  • PID control it is difficult to design in consideration of robustness.
  • the degree of freedom of control is small, and there are cases where the control capability is limited.
  • the limit of controllability is difficult to understand. That is, I did not know whether it was the limit of parameter adjustment or whether there was still an adjustment allowance.
  • An object of the present invention is a parameter design method capable of easily designing a feedback control system controller having robust stability and disturbance suppression characteristics, and a feedback control method using a controller in which parameters designed by this design method are set. Is to provide.
  • the parameter design method is a method of designing parameters of the controller in a controller including a PID control unit and a filter unit provided separately from the PID control unit and controlling the control target by feedback.
  • the mixed sensitivity problem which is determined based on the transfer function of the controlled object and the transfer function of the controller and includes robust stability and disturbance suppression characteristics, is obtained by decentralizing the frequency domain including the frequency to be controlled.
  • the PID control unit and the filter unit are respectively.
  • the present invention includes a determination step of determining the parameters of the controller composed of the parameters of the above.
  • FIG. 1 is a block diagram of the feedback control system 100 to which the feedback control method according to the embodiment is applied.
  • the feedback control system 100 includes a controller 1 and a control target 2.
  • the control amount (output) y of the control target 2 is negatively fed back, and the deviation e between the target value r and the control amount y is input to the controller 1.
  • the controller 1 calculates and outputs the operation amount u based on the deviation e.
  • the operation amount u is input to the control target 2.
  • a part of the manipulated variable u may be calculated based on the controlled variable y instead of the deviation e.
  • the control target 2 is, for example, the continuous casting machine 200.
  • FIG. 2 is a schematic view of the continuous casting machine 200.
  • the continuous casting machine 200 is an apparatus for producing a long slab by pouring molten steel into a mold 23 and pulling out molten steel whose side surfaces have solidified from the mold 23.
  • the continuous casting machine 200 includes a tundish 21, a nozzle 22, a mold 23, and a plurality of sets of rolls 24, and are arranged from the upstream side to the downstream side in this order.
  • the tundish 21 is a device in which molten steel flows from a ladle (not shown) and removes predetermined inclusions from the molten steel. Enclosures are removed by ascending and separating. A through hole is formed in the bottom wall of the tundish 21, and a nozzle 22 is attached to the through hole.
  • the mold 23 is a device in which molten steel flows from the tundish 21 through the nozzle 22 and cools the molten steel to form steel having a predetermined shape.
  • the mold 23 is water-cooled, and the molten steel in contact with the mold 23 is solidified from the outside to form a relatively thin solidified shell, and a steel having a predetermined shape is formed.
  • the roll 24 is a device that supports the steel while drawing the steel from the mold 23 at a predetermined speed.
  • the rolls 24 are a set of two arranged so as to be in contact with both sides of the steel, and a plurality of rolls 24 are arranged on the next stage of the mold 23 with a predetermined interval from the upstream side to the downstream side.
  • the plurality of sets of rolls 24 are arranged so that the casting direction (pulling direction) faces from the vertical direction to the horizontal direction.
  • the continuous casting machine 200 includes a slide valve 31, an actuator 32, and a vortex sensor 33, and controls the molten steel level in the mold 23.
  • the eddy current sensor 33 measures the molten steel level in the mold 23 (Level in the figure. For control, the value converted to a positive height with the vertical upward direction is used as the molten steel level). ..
  • the molten metal level measured by the vortex sensor 33 is output as a control amount y.
  • the deviation e between the control amount y and the target value r is input to the controller 1.
  • the controller 1 calculates the operation amount u and outputs it to the actuator 32.
  • the control amount y may be input to the controller 1.
  • the actuator 32 operates the slide valve 31 by the operating amount u. When the controller is a speed type, the actuator 32 operates the derivative or difference of the manipulated variable u.
  • FIG. 3 is a block diagram of the controller 1 shown in FIG.
  • the controller 1 includes a PID control unit 11 and a filter unit 12.
  • the filter unit 12 is provided separately from the PID control unit 11.
  • the deviation e is input to the PID control unit 11, and the output of the PID control unit 11 is input to the filter unit 12.
  • the output of the filter unit 12 becomes the operation amount u.
  • the control amount y may be input to the PID control unit 11.
  • the transfer function K PID (s) when the PID control unit 11 executes PID control is as follows.
  • the PID control unit that executes the equation (1) is originally one form of the "PID control unit", and should be described as "PID control unit that performs PID control of the structure of the equation (1)".
  • PID control unit since it is a long notation, it will be referred to as "PID control unit” hereafter.
  • the K PID (s) is a transfer function of the PID control unit 11, not a transfer function K (s) of the controller 1.
  • the transfer function K (s) of the controller 1 will be described later (Equation (15)).
  • K P proportional gain
  • T I integral time
  • T D derivative time
  • ⁇ is a coefficient for inexact differential and is often set to 0.1.
  • Constant gain proportional gain the gain of the integrator integral gain, if the gain of the differentiator and the differential gain, proportional gain is K P, the integral gain is K P / T I, the derivative gain K P ⁇ It becomes T D.
  • the filter unit 12 is a part that is added to the PID control unit 11 to form the controller 1.
  • PID control has a function of finely adjusting the gain and phase when sufficient control performance cannot be obtained.
  • vibration may be suppressed by adding the filter unit 12 and increasing the controller gain of a specific frequency, for example.
  • the filter unit 12 may be, for example, a phase lead compensator or a phase lag compensator.
  • control target 2 is represented by the transfer function P (s) in the embodiment. It may include wasted time.
  • the sensitivity function S (s) and the quasi-complementary sensitivity function R (s) are defined as follows. These functions are defined using K (s) and P (s) and are dealt with in the mixing sensitivity problem.
  • the transfer function P (s) of the controlled object 2 can be expressed as follows.
  • P 0 (s) is the nominal control target 2.
  • the mixing sensitivity problem will be described. Let the weighting functions be W 1H (s) and W 2H (s). The subscript H indicates that it is a weighting function for designing the high gain type controller 1.
  • the mixed sensitivity problem of the formula (6) or (7) is referred to as a "general mixed sensitivity problem" in the embodiment to distinguish it from the 2-disk problem.
  • the constraint condition is one of the following.
  • the "mixing sensitivity problem” refers to a problem in which any of the equations (6) to (9) is included in the constraint condition.
  • the mixing sensitivity problem is solved using an optimization technique. This will be shown in a concrete example.
  • the control target 2 is a continuous casting machine 200.
  • T SC is the stepping cylinder time constant
  • L SC is the stepping cylinder waste time
  • K f is the flow coefficient
  • A is the mold.
  • T CD is the level clock time constant
  • L CD is the level clock waste time.
  • the stepping cylinder is the actuator 32
  • the mold cross-sectional area is the cross-sectional area of the mold 23
  • the level meter is the vortex sensor 33.
  • K f and A vary depending on the casting conditions, and the range is 0.6 ⁇ K f / A ⁇ 2.1. First, in this example, the following case is considered as the first high gain type controller 1.
  • the weight function is set as follows. As shown by the evaluation function described later, the variable K W1H of the weight function W 1H (s) is the value to be maximized.
  • the uncertainty ⁇ (s) is calculated assuming that the time constant and the dead time all change by ⁇ 20%.
  • the uncertainty ⁇ (s) constitutes equation (5).
  • the weights W 2H (s), W 2M (s), and W 2L (s) described later are set so as to cover ⁇ (s) in the high frequency region.
  • FIG. 4 is a Bode diagram of the H ⁇ controller obtained by solving a general mixing sensitivity problem and a graph showing the frequency shaping result. It can be seen that the H ⁇ controller has a large gain at low frequencies and a substantially constant gain near 0.1 [Hz] on the high frequency side, and is basically PI control. Furthermore, the gain decreases near 1.0 [Hz] on the high frequency side, and it can be interpreted that a filter is added.
  • the H ⁇ controller is obtained by the method of solving the equation (6), which is a general mixing sensitivity problem, as follows.
  • zH1 3 and pH1 4 is close to the pole-zero offset.
  • zH1 4 and pH1 5 is, close to the pole-zero offset.
  • pole-zero offset in the pole-zero offset, we can see that there are six pole-zero offsets (zH1 1,2 and pH1 2,3 , zH1 10,11 and pH1 11,12 , respectively. Extreme zero offset).
  • the 6th order controller can be excluded from the 13th order controller, and the 7th order controller can approximate the H ⁇ controller.
  • the remaining 7th order also contains poles and zeros that have a small effect, it is considered that the H ⁇ controller can be approximated by a lower order controller.
  • the structure of the controller 1 is fixed to the PID control unit 11 with the filter unit 12 added to achieve performance close to that of the H ⁇ controller.
  • the structure is fixed means that only the value of the variable parameter is different.
  • the transfer functions 1 / (2 ⁇ s + 1) and 1 / (3 ⁇ s + 1) have a fixed structure of 1 / (T ⁇ s + 1) with a variable parameter of T.
  • the transfer functions 1 / (2 ⁇ s + 1) and s / (3 ⁇ s + 1) have different molecules at 1 and s, and are not fixed.
  • there is also a method of lowering the dimension by realizing equilibrium but it is not necessarily adopted because a controller having a fixed structure like the PID control unit 11 cannot be obtained.
  • the parameter design method of the embodiment is a parameter design method of the controller 1 including the PID control unit 11 and the filter unit 12.
  • this design method there are the following Examples 1 to 3.
  • Example 1 Consider that the PID control unit + the secondary filter unit and the mixing sensitivity controller 1 are approximated by the PID control unit 11 + the secondary filter unit 12.
  • the phase lead / lag compensation is often a first-order rational expression ⁇ a first-order rational expression, but in the embodiment, it is a quadratic rational expression having a wider range. Even if it is a first-order rational expression, trial and error and readjustment are required to determine the parameters for phase lead / delay compensation, but in the embodiment, even if it is a second-order rational expression, it is based on the model. , Find the parameters by optimization without trial and error and readjustment.
  • the transfer function K (s) of the controller 1 of Example 1 is shown below.
  • the transfer function K (s) is composed of the transfer function K PID (s) of the PID control unit 1 shown in Equation 1 and the transfer function of the second-order filter unit 12.
  • Parameters of PID control unit 11 three K P, T I, T D) is a parameter of the filter unit 12 is four (a 1, a 2, b 1, b 2). It is necessary to determine these seven parameters as the parameters of the controller 1.
  • the controller 1 is not linear. It is difficult to determine these parameters because it is necessary to balance robust stability and disturbance inhibition. Even if the filter unit 12 of the primary, it is necessary to determine five parameters (K P, T I, T D, a 1, b 1) a. At the same time, it is necessary to meet the needs of maintaining stability, increasing the disturbance suppression band as much as possible, reducing the fluctuation of the molten metal level, and improving the quality of slabs.
  • the evaluation function to be minimized is set as follows.
  • the gain of the weighting function is made as large as possible to maximize the frequency band of disturbance suppression.
  • the variable K W1H is described by the equation (12).
  • ⁇ () indicates the maximum singular value.
  • K p> 0, T I > 0, T D ⁇ 0 is essential constraints. Furthermore, since this optimization problem is non-convex and may fall into a local solution, the following constraints are set for each variable in order to facilitate convergence. Incidentally, K p> 0, T I > 0, essential non constraint constraint T D ⁇ 0, which has provided for convenience to avoid the case where Recessed a local solution, not essential. For example, in the multi-start local search method of this example, the optimum solution can be obtained without any convenient restrictions by increasing the number of initial values to be tried at the time of optimization.
  • the last two equations limit the attenuation coefficient of the filter unit 12. That is, the last two equations are provided to search for the optimum value in a region where the zeros and poles are less likely to vibrate and are less likely to approach the imaginary axis.
  • the multi-start local search method is used for the optimization method, and for the initial value, the initial value is tried at multiple points, and the optimization result from the next initial value so as not to fall into a local solution. It was adopted.
  • the optimization problem is in the form of finding the minimum value of the evaluation function of equation (16) under the constraints of equations (18) and (19).
  • the setting of constraint conditions excluding the constraint of the mixed sensitivity problem and the constraint of the PID parameter may be included in the global optimization or may not be necessary.
  • the reason is that, in the embodiment, a kind of multi-start local search method is used, and the constraints excluding the constraint of the mixed sensitivity problem and the constraint of the PID parameter are convenient so that the convergence in the local search is easy. This is because it is provided in.
  • FIG. 5 is a Bode diagram and a graph showing the frequency shaping result of the controller 1 in which the parameters obtained by solving the general mixing sensitivity problem in the controller 1 including the PID control unit 11 and the secondary filter unit 12 are set. Is.
  • the parameters here are the parameters shown in the equation (21). Since the filter is PI control + 2nd order, the order is 3rd order, but it can be seen that controller 1 having almost the same performance as the H ⁇ controller is obtained.
  • the controller 1 fixed to the structure of the PID control unit 11 + secondary filter unit 12 can be obtained by calculation instead of adjustment using a model.
  • FIG. 6 is a flowchart of the design method of the controller 1 according to the embodiment.
  • the designer sets the transfer function P (s) of the controlled object 2 (P 0 (s) is used as P (s) as described above) (S1).
  • the designer determines the structures of the PID control unit 11 and the filter unit 12 (S2).
  • the designer sets the evaluation function (S3).
  • the designer sets the constraint condition (S4).
  • the designer uses a computer to solve the global optimization problem (S5).
  • the parameter of the controller 1 is determined by the process S5.
  • Example 2 PID control unit + 1st-order filter unit, mixing sensitivity
  • K P> 0, T I > 0, T D ⁇ 0 is essential constraints.
  • the optimization problem is non-convex and may fall into a local solution, the following constraints are set for each variable in order to facilitate convergence.
  • the optimization calculation is performed with a constraint that the value is set to 0.
  • K P> 0, T I > 0, T D ⁇ 0 is indispensable except constraint constraints, which has provided for convenience to avoid the case of falling into a local solution, not essential.
  • the optimum solution can be obtained without any convenient restrictions by increasing the number of initial values to be tried at the time of optimization.
  • FIG. 7 is a Bode diagram and a graph showing the frequency shaping result of the controller 1 in which the parameters obtained by solving the general mixing sensitivity problem in the controller 1 including the PID control unit 11 and the primary filter unit 12 are set.
  • the parameters here are the parameters shown in the equation (24).
  • the order is quadratic because of the PI control + 1st order filter.
  • the sensitivity function S is on the low frequency side as compared with FIG. 5 (the controller 1 that executes the PI control + the second-order filter). From this, it can be seen that the disturbance suppression performance is lower than that of the controller 1 that executes the PI control + secondary filter and the H ⁇ controller. This is probably because the degree of freedom in design is not sufficient.
  • Example 3 PID control unit + secondary filter unit, 2-disk
  • the constraint of the mixing sensitivity problem is further relaxed, so that the disturbance suppression band is widened.
  • the controller 1 is approximated by the PID control unit 11 + the second-order filter unit 12.
  • the evaluation function is the same as in the above case.
  • K P> 0, T I > 0, T D ⁇ 0 is essential constraints. Furthermore, since this optimization problem is non-convex and may fall into a local solution, the following constraints are set for each variable in order to facilitate convergence. Incidentally, K P> 0, T I > 0, T D ⁇ 0 is indispensable except constraint constraints, which has provided for convenience to avoid the case of falling into a local solution, not essential. By increasing the number of initial values to be tried at the time of optimization, the optimum solution can be obtained without any convenience restrictions.
  • the optimization problem is in the form of finding the minimum value of the evaluation function of equation (16) under the constraints of equations (26) and (27).
  • the local search part was optimized using a publicly available nonlinear optimization method (the fmincon function of "Optimization Toolbox” (registered trademark) of The MathWorks, Inc.), and the following results were obtained.
  • FIG. 8 is a Bode diagram and a graph showing the frequency shaping result of the controller 1 in which the parameters obtained by solving the 2-Disc mixing sensitivity problem in the controller 1 including the PID control unit 11 and the secondary filter unit 12 are set. Is.
  • the parameters here are the parameters shown in the equation (29). Although it is difficult to understand in FIG. 8 (it can be seen by enlarging FIG. 8), it can be seen that the sensitivity function S is on the high frequency side and the disturbance suppression performance is high as compared with FIG.
  • Example 4 Consider that the controller 1 (PID control unit 11 + secondary filter unit 12) of the application example 1 is made to correspond to a change of the control target 2 (continuous casting machine 200). Since the structure is fixed, the control characteristics of the controller 1 can be continuously changed as described later.
  • K f / A is designed from 0.6 to 2.1 in increments of 0.1.
  • the high gain type controller 1 is designed, but the middle gain type and low gain type controllers 1 which are lower gain types are also designed. Therefore, there are three types of gain to design. Therefore, the number of controllers 1 to be designed is 48. This is shown in the table below. The high gain type is indicated by “H”, the middle gain type is indicated by “M”, and the low gain type is indicated by "L”.
  • the PID parameter may be written in the table and the PID parameter may be changed according to the control target 2 or the change of the disturbance. This time, it is considered that the parameters of the controller 1 are tabulated and the parameters are continuously changed according to the change of the control target 2 and the disturbance. By continuously changing the parameters, the control characteristics of the controller 1 are continuously changed.
  • K f / A is designed from 0.6 to 2.1 in increments of 0.1 in the same manner as in Example 1 (in the case of 0.6, it has already been designed in Example 1).
  • H2 to H16 can be calculated in the same manner as in Example 1 by changing K f / A in the equation (10) to obtain the controller 1 of Example 1.
  • the weighting function and the evaluation function are set as follows to perform optimization.
  • the variable T W1M of the weighting function W 1M (s) is the value to be minimized.
  • W 2M (s) is the same as W 2H (s).
  • the evaluation function to be minimized for the middle gain type is set as follows.
  • the evaluation function maximizes the frequency band of disturbance suppression by making T W1M as small as possible and, as a result, increasing the gain of the weighting function W 1M (s).
  • the weighting function and the evaluation function to be minimized are set as follows to perform optimization. As shown by the evaluation function described later, the variable T W1L of the weighting function W 1L (s) is the value to be minimized.
  • the evaluation function of the low gain type was set as follows. As small as possible T W1L, as a result, by increasing the gain of the weighting function W 1L (s), is an evaluation function that maximizes the frequency band of the disturbance suppression.
  • the parameters of each of the 48 controllers 1 shown in the above table are obtained.
  • the 48 controllers 1 have the same structure, but have different parameters and different control characteristics.
  • the control characteristics here are determined by the combination of the K f / A value and the gain type (H, M, L).
  • This table is stored in advance in the storage unit of the controller 1.
  • the 48 controllers 1 shown in the above table have a common structure, and these controllers 1 are realized by changing the parameters. This will be described in detail.
  • the gain type H, and the parameters K f / A is identified by 0.6 (K P, T I, a 1, a 2, b 1, b 2) is selected by the interpolation in the controller 1 (Set to controller 1), controller 1 with controller number H1 is realized.
  • the controller 1 of Example 4 continuously changes its control characteristics (combination of K f / A value and gain type).
  • the gain type is 1, H is 1, M is 2, and L is 3. That is, the gain type 1.4 is between H and M at a ratio of 0.4: 0.6.
  • TMP1 is taken at the point where H2 and M2 are internally divided into 0.4: 0.6.
  • TMP2 is taken at the point where H3 and M3 are internally divided into 0.4: 0.6.
  • RESULT is set at the point where TMP1 and TMP2 are internally divided into 0.2: 0.8.
  • the value of this RESULT becomes the value of K p obtained by interpolation.
  • FIG 10A is a diagram in which the numerical values in the graph of the table of each parameter (K P, T I, a 1, a 2, b 1, b 2) shown in Figure 9A.
  • K P, T I, a 1, a 2, b 1, b 2 shown in Figure 9A.
  • Each graph is shown in three dimensions, the first axis shows K f / A, the second axis shows the gain type (H, M, L), and the third axis shows the parameters.
  • the gain type remains H, and the K f / A of the control target 2 is continuously reduced from 2.1 to 0.6.
  • the gain type is continuously changed from H to M to L. This applies, for example, to reducing the casting speed and then changing the gain type, for example, to reduce the controller gain.
  • the controller 1 continuously changes from H16, H15, H14, ..., H2, and H1 according to the value of K f / A. It is a parameter of the controller 1 K P, T I, T D, a 1, a 2, b 1, b 2 reads from the above table is calculated by interpolation.
  • K f / A is 0.6.
  • K P, T I, T D , a 1, a 2, b 1, b 2 are parameters of the controller 1, similarly, read from the above table is calculated by interpolation.
  • the operation of the controller 1 described above is provided with the following storage process and change process.
  • the parameters for example, FIG. 9A
  • the controller 1 is changed by determining the parameter from each of the parameters of the 48 controllers stored in the storage process by interpolation and setting the control target 2 as the parameter of the controller 1 for feedback control. To do.
  • the controller 1 is changed so that the control characteristics of the controller 1 change continuously.
  • the controller 1 continuously changes the control characteristics based on the value of K f / A and the value of the gain type (real number) during the feedback control of the continuous casting machine 200.
  • K f / A for each sampling cycle and adopt the controller number (real number) corresponding to K f / A.
  • the gain type real number
  • These are performed by the upper system of the control system of PID control + filter (note that it means higher in software, and the actual calculation may be performed inside the same DCS or PLC as the PID control unit + filter unit).
  • the method of determining the controller number and the gain type is performed in the upper system, but in this embodiment, the controller number is changed based on the calculated K f / A, and the gain type is given. It is supposed to be.
  • the formula (6) described in the following document may be used.
  • FIG. 10B shows an outline of the adaptation simulator.
  • change K f / A is specified as the simulation condition.
  • K f / A is input to the parameter table of FIG. 9A, assuming that it can be calculated accurately in the upper system.
  • the gain type is specified as being set in the upper system.
  • a level disturbance is applied.
  • This simulator is a linearized deviation system.
  • the dynamic characteristics of the continuous casting machine, which is originally a non-linear control target, are linearized around the operating point, and the molten metal level fluctuation caused by changes in the casting speed, TD weight, and mold width is fed by the method of Patent No. 6108923. It is assumed that it is compensated by forward. A simulation is performed using this simulator.
  • FIG. 11A is a graph showing setting conditions 1 to 3 and results 1 to 2 when adaptation simulation is performed for the controller 1 of Example 4.
  • FIG. 11B is a graph showing the results 3 to 8 when the adaptation simulation is performed for the controller 1 of Example 4.
  • the location in the table is changed as shown by the broken line arrow.
  • FIG. 11C shows an example at the time of testing with another control system.
  • the controller number integer
  • gain type integer
  • molten metal level which is the control amount
  • slide valve opening has a difference between the primary delay of the actuator and the dead time, but in the low frequency region, the operation is almost the same as the operation amount.
  • this simulation is performed under setting conditions 1 to 3.
  • the horizontal axis shows the time t and the vertical axis shows K f / A.
  • K f / A is continuously reduced from 2.1 to 0.6.
  • Decrease in K f / A is decreased TD weight (weight of the molten steel in the tundish 21), which corresponds to the deceleration or the like of the casting speed V C.
  • the horizontal axis shows the time t and the vertical axis shows the gain type (H, M, L).
  • the controller 1 is continuously changed into a high gain type, a middle gain type, and a low gain type.
  • the horizontal axis shows the time t
  • the vertical axis shows the disturbance with respect to the molten metal level.
  • This disturbance is a sine wave with a period of 4 seconds and an amplitude of 10 mm.
  • the level fluctuation is set to be large with a 4-second cycle, which is the most difficult to control. The reason is that in the case of the conventional switching control, when the level fluctuation is large at the moment of switching, a temporary level fluctuation is likely to occur.
  • results of the simulation are shown in Result 1 and Result 2.
  • the horizontal axis shows the time t
  • the vertical axis shows the molten metal level of the controlled amount.
  • FIG. 11E and FIG. 11F show another simulation result executed under different conditions when the controller 1 is changed as shown in FIG. 11D.
  • a parameter K P, T I, T D is a 1, a 2, b 1 , b 2, continuously changed, stable, rapid melt-surface level and the operation amount varies It can be confirmed that there is no control.
  • the structure of the controller 1 is fixed, and the control characteristics of the controller 1 change continuously when the controller 1 reads the parameters from the table, so that the adaptation is easy.
  • the control characteristics of the controller 1 change continuously when the controller 1 reads the parameters from the table, so that the adaptation is easy.
  • there are few parameters compared to the case of H ⁇ control, there are few parameters, and there is no part that tends to be unstable in numerical calculation such as pole-zero cancellation, which is considered to be one of the reasons why stable adaptation can be achieved.
  • pole-zero cancellation which is considered to be one of the reasons why stable adaptation can be achieved.
  • control amount y and the operation amount u may temporarily increase when the controller 1 is switched, as in the case where the controller is switched. It has not occurred.
  • FIG. 12 is a flowchart showing this. This flowchart shows one sampling cycle and is repeated for each sampling cycle. If the output of the operation amount u is a speed type, bump press switching with manual operation or the like is possible.
  • the controller 1 reads information for determining the controller 1 (S11).
  • the information is the value of K f / A and the gain type (real numbers 1 or more and 3 or less). "1" corresponds to the gain type H, "2" corresponds to the gain type M, and "3" corresponds to the gain type L.
  • the parameter determined in the process S12 is set in the controller 1, and the deviation e between the control amount y and the target value r is input (S13). Then, the controller 1 calculates the operation amount u based on the deviation e (S14) and outputs it to the control target 2 (S15). In addition to the deviation e as described above, the control amount y may be used.
  • the PID control unit 11 + the filter unit 12 are discretized by a known method.
  • a difference may be used, or a bilinear transform may be used.
  • a kind of multi-start local search method is used as a local nonlinear optimization method (sequential quadratic design method, etc.), but the optimization method is a genetic algorithm (GA) or a particle swarm optimization method (). Other global optimization methods such as PSO) and Simulated Annealing (SA) may be used.
  • G genetic algorithm
  • SA Simulated Annealing
  • the filter unit 12 shows an example of secondary (including the case of primary), it may be tertiary or higher.
  • the transfer function of the PID control unit 11 is not limited to the equation (1). As another example of the transfer function of the PID control unit 11, for example, there are the following three.
  • the parameter design method is a method of designing parameters of the controller in a controller including a PID control unit and a filter unit provided separately from the PID control unit and feedback-controlling the control target.
  • the mixed sensitivity problem which is determined based on the transfer function of the controlled object and the transfer function of the controller and includes robust stability and disturbance suppression characteristics, is obtained by decentralizing the frequency domain including the frequency to be controlled.
  • the PID control unit and the filter unit are respectively.
  • the present invention includes a determination step of determining the parameters of the controller composed of the parameters of the above.
  • the PID control unit is a part that executes PID control.
  • the control executed by the PID control unit is a control including at least P control. That is, control without I control or D control (including control in which the gain of I control or D control is 0 and there is substantially no I control or D control) may be used.
  • control without I control or D control including control in which the gain of I control or D control is 0 and there is substantially no I control or D control
  • P control, PI control, PD control, or PID control may be used.
  • the PID control unit may be a proportional leading type, a differential leading type, or the like.
  • the PID control unit may include an inexact differential or a filter for removing noise.
  • the frequency to be controlled is, for example, from frequency 0 to the Nyquist frequency in digital control.
  • the filter unit has a function of adjusting the gain and the phase.
  • a quadratic filter unit (a filter unit composed of a quadratic rational expression) can be mentioned.
  • Solving the mixed sensitivity problem by an optimization method means, for example, an evaluation function (for example, an equation) represented by a predetermined variable (variable K W1H ) included in a weighting function (for example, equation (12)) constituting the mixed sensitivity problem.
  • the minimum value of (16)) is obtained under constraints such as a mixing sensitivity problem (for example, equations (18) and (19)).
  • the parameter design method according to one aspect of the embodiment has the following advantages.
  • Parameters can be mounted on a device (for example, DCS, PLC) on which the PID control unit and the filter unit can be mounted, eliminating the need for special hardware.
  • a device for example, DCS, PLC
  • H ⁇ control requires dedicated software such as a solver for Ricatch equations and linear matrix inequalities, but the parameter design method according to the first aspect of the present invention does not require dedicated software and is general-purpose nonlinear. Optimization software can be used.
  • the control performance may not be sufficient (for example, the control target is a vibration system).
  • the control target is a vibration system.
  • control target is a continuous casting machine
  • control amount is the molten metal level
  • control target is not limited to this, and may be, for example, a vibration system.
  • the feedback control method according to the other aspect of the embodiment is stored in the storage step of storing the respective parameters of the plurality of controllers designed by the parameter design method according to the one aspect of the embodiment in advance, and the storage step.
  • a change step of changing the controller by determining a parameter from each of the parameters of the plurality of controllers by interpolation and setting the control target to the parameter of the controller for feedback control is provided.
  • the controller is changed so that the control characteristics of the controller are continuously changed.
  • determined by interpolation means that the parameters are stored as table values and obtained by interpolation such as linear interpolation. Further, it includes equivalent processing such as function-approximate of parameters like a response surface and determination using the function. That is, it suffices that the controller can continuously change the parameters and can determine the continuous values of the parameters.
  • the feedback control method according to another aspect of the embodiment is based on the respective parameters of the plurality of controllers designed by the parameter design method according to one aspect of the embodiment.
  • one controller may not be sufficient. Therefore, in consideration of the state of the controlled object and the state of disturbance, a plurality of controllers having different control characteristics are prepared, and the controllers are changed according to the situation.
  • the parameters of a plurality of controllers having a fixed structure can be stored in a table, and the controllers can be continuously changed by a simple method of table lookup and interpolation. Therefore, robust stable and adaptive feedback control can be realized by general-purpose control (PID control and filter), and can be realized by general-purpose hardware such as DCS and PLC.
  • the feedback control method according to another aspect of the embodiment can be applied to the molten metal level control of the continuous casting machine. It can also be applied to other equipment that can be modeled other than continuous casting machines.
  • the controller is changed so that the control characteristics of the controller change continuously, so that the control amount and the operation amount do not fluctuate. it can.
  • the control target is a continuous casting machine and the control amount is the molten metal level
  • the surface scratches on the cast slab are reduced, so that the surface grinding operation Decreases.
  • the entrainment of powder is reduced, the quality of the final product such as a steel plate is improved.

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Abstract

Procédé de conception de paramètres destiné à la conception des paramètres d'un dispositif de commande par un dispositif de commande (1), le dispositif de commande comprenant une unité de commande PID (11) et un élément de filtre (12) installé séparément de l'unité de commande PID, et le dispositif de commande mettant en œuvre une commande à rétroaction pour un objet à commander (2). Ce procédé comprend : une étape de paramétrage pour paramétrer une condition de contrainte pour un problème de sensibilité mixte pour chacune d'une pluralité de fréquences obtenues par discrétisation d'une région de fréquences comprenant une fréquence sur laquelle une commande est effectuée, le problème de sensibilité mixte étant défini sur la base d'une fonction de transfert de l'objet à commander et d'une fonction de transfert d'un dispositif de commande, et le problème de sensibilité mixte présentant une stabilité robuste et une caractéristique de suppression des perturbations ; et une étape de détermination dans laquelle un procédé d'optimisation est utilisé pour résoudre le problème de sensibilité mixte, avec une telle condition de contrainte, afin de déterminer les paramètres du dispositif de commande configuré au moyen des paramètres respectifs de l'unité de commande PID et de l'élément de filtre.
PCT/JP2020/023950 2019-07-12 2020-06-18 Procédé de conception de paramètres et procédé de commande à rétroaction WO2021010086A1 (fr)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH09146608A (ja) * 1995-11-17 1997-06-06 Nkk Corp 連続鋳造機モールド内湯面レベル制御方法
JP2000322106A (ja) * 1999-05-13 2000-11-24 Nkk Corp 連続鋳造機モールド内湯面レベル制御方法
JP2001129647A (ja) * 1999-08-25 2001-05-15 Sumitomo Metal Ind Ltd 連続鋳造機の湯面レベル制御方法及び湯面レベル制御装置

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH09146608A (ja) * 1995-11-17 1997-06-06 Nkk Corp 連続鋳造機モールド内湯面レベル制御方法
JP2000322106A (ja) * 1999-05-13 2000-11-24 Nkk Corp 連続鋳造機モールド内湯面レベル制御方法
JP2001129647A (ja) * 1999-08-25 2001-05-15 Sumitomo Metal Ind Ltd 連続鋳造機の湯面レベル制御方法及び湯面レベル制御装置

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