WO2018220690A1 - 制御系設計装置及び制御システム - Google Patents
制御系設計装置及び制御システム Download PDFInfo
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- WO2018220690A1 WO2018220690A1 PCT/JP2017/019974 JP2017019974W WO2018220690A1 WO 2018220690 A1 WO2018220690 A1 WO 2018220690A1 JP 2017019974 W JP2017019974 W JP 2017019974W WO 2018220690 A1 WO2018220690 A1 WO 2018220690A1
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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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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D23/00—Control of temperature
- G05D23/19—Control of temperature characterised by the use of electric means
Definitions
- the present invention relates to a control system design apparatus and a control system, and more particularly to a control system design apparatus and a control system that perform multipoint control.
- a temperature adjustment system in a system having interference that requires multipoint control with a plurality of sensors and a heat source (actuator) is known.
- a temperature control system is used in, for example, an air conditioning system and an injection molding machine.
- the temperature to be controlled may be the temperature of a hot plate measured by a sensor or the like, but may also be desired to control the temperature of an object to be heated (also called a workpiece) heated by the hot plate.
- Patent Document 1 a control method using predictive control is proposed in Patent Document 1, for example.
- a response waveform of the workpiece temperature when the target temperature (SetPoint, SP) of each channel of the hot plate is changed is obtained, and this response waveform and time series data of the workpiece temperature when the workpiece is mounted. Therefore, workpiece temperature prediction is realized with the amount of change in target temperature at the time of workpiece mounting as an unknown.
- the response waveform here is a step response waveform for a control target including a feedback loop by the PID controller.
- the target temperature change amount that minimizes the variation of the workpiece temperature in the transient state is genetically determined. This is realized by an algorithm (GA).
- Patent Document 2 proposes a method for minimizing the variation in the workpiece temperature in consideration of the saturation of the operation amount in the steady state.
- the target temperature (SetPoint, SP) of each channel of the hot plate is changed, and from the amount of change in the workpiece temperature (wafer temperature, WAF) and the manipulated variable (Manipulated Variable, MV) when stabilized, Work temperature prediction and operation amount prediction are realized with the amount of change in target temperature in the steady state as an unknown quantity.
- the target temperature that minimizes the workpiece temperature variation with the operation amount within the output range as a constraint (constraint)
- the amount of change is realized by a constrained optimization method.
- Patent Document 1 does not take into account the allowable operation amount.
- the operation amount to the heater may deviate from the output possible range such as exceeding the upper limit or lower limit of the output possible range. Therefore, in an actual system, the workpiece temperature as designed may not be realized, and the variation in workpiece temperature in a transient state cannot always be minimized.
- an object of the present invention is to provide a control system design device and a control system that reduce the difference or variation in the control amount at each point in a transient state while considering the saturation of the operation amount.
- a control system design apparatus controls (a) a control target according to a correction target value that is controlled according to a correction amount that is given a preset target value by controlling temperatures at multiple points in the control target.
- a control system design device that designs the correction amount of the target value for a multipoint control system that includes a correction amount calculation unit that calculates the correction amount of the target value.
- the correction amount calculation unit obtains time-series data of operation amounts with respect to changes in each input channel and time-series data of temperatures at multiple points in the control target when target values of a plurality of input channels are sequentially changed.
- the correction amount calculation unit acquires time series data of the manipulated variable and time series data of the multipoint temperature, and a known manipulated variable vector M ref in which the time series data of the manipulated variable is arranged, A known temperature vector T ref in which temperature series data is arranged is obtained.
- the correction amount calculation unit includes the evaluation function to be minimized as a function representing the variation of the predicted temperature of the multipoint to be controlled, and includes that the operation amount falls within a predetermined range in the constraint condition, A correction amount of the target value that minimizes the evaluation function under the constraint condition is calculated.
- control system design device and a control system that reduce the difference or variation in the control amount at each point in a transient state while considering the saturation of the operation amount.
- a configuration example is shown.
- a configuration example of the correction amount vector ⁇ when the number of pulses applied in the target temperature correction pattern is 50 and the number of input channels of the target temperature is 3 is shown.
- FIG. 5 is an explanatory diagram of a target temperature correction amount vector ⁇ * and a target temperature correction pattern SV correct (INi) (t). It is a flowchart of a target value response design process. The explanatory view of coefficient vector Kave_at90sec for average temperature calculation is shown. An example of a predicted temperature vector Tsteady of a workpiece after 15 seconds is shown. An example of a coefficient matrix Ksteady for calculating a predicted temperature vector after 15 seconds is shown. It is a figure which shows the effect of the control system in this embodiment.
- FIG. 1 is a block diagram of a control system in the present embodiment.
- the control system 1 includes a controlled object 10, a multipoint temperature controller 20, and a target temperature correction amount calculation unit (control system design device) 30.
- the multipoint temperature controller 20 and the target temperature correction amount calculation unit 30 may constitute a control device or a control system for the controlled object 10.
- the control object 10 includes, for example, a hot plate that generates heat according to the operation amount from the multi-point temperature controller 20 and a work heated by the hot plate.
- the heating plate is provided with a plurality of heaters (actuators) that generate heat according to the operation amount.
- measurement units such as sensors for detecting temperatures are provided at a plurality of positions on the hot plate.
- the temperature at multiple points of the hot plate may be controlled, or the temperature at multiple points of the workpiece may be controlled. It should be noted that the cooling is not limited to heat generation and heating.
- the multi-point temperature controller 20 controls the temperature at a predetermined point of the control target 10.
- the multipoint temperature controller 20 includes, for example, a PID controller 21 and an adder 22 for each channel.
- the multipoint temperature controller 20 further includes a correction pattern application unit 23.
- the PID controller 21 adjusts the operation amount output to an actuator such as a hot plate so that the control amount (PV) of the control target 10 becomes the target value (SV) for the corresponding channel.
- the control parameter of the PID controller 21 can be obtained by a known method. Here, it is assumed that the control parameter of the PID controller 21 has already been obtained and the control target 10 can be controlled by the PID controller 21.
- the adder 22 calculates the target temperature (corrected target temperature) corrected by adding the target value (SV) and the target temperature correction pattern input from the correction amount calculation unit 30 for the corresponding channel, and the PID controller 21. Output to.
- the correction pattern application unit 23 holds a correction amount vector of the target temperature for each channel, and outputs a correction pattern based on the correction amount vector to the adder 22 of each channel according to a predetermined condition.
- the predetermined condition includes, for example, detecting a disturbance, detecting a change in target temperature, and the like.
- a target temperature correction amount calculation unit (hereinafter referred to as a correction amount calculation unit) 30 calculates a target temperature correction amount vector for changing the target temperature of each channel.
- the target temperature correction amount vector defines how the target temperature is changed along the time axis, and includes, for example, the amplitude of a pulse as time series data as an element.
- the target temperature correction pattern is a waveform formed by a pulse train generated according to the target temperature correction amount vector. Details will be described later.
- the correction amount calculation unit 30 is either a target temperature correction amount vector for correcting the target temperature when a disturbance is detected and a target temperature correction amount vector for correcting the target temperature when changing the target temperature, or Both are calculated. Details of the calculation method will be described later.
- the correction amount calculation unit 30 may be a separate and independent device for the multipoint temperature controller 20.
- the correction amount calculation unit 30 can be configured with a personal computer. Further, the correction amount calculation unit 30 may be configured by a tablet terminal or a dedicated device in addition to the personal computer.
- the correction amount calculation unit 30 includes a processing unit such as a CPU, a storage unit that stores time-series data, and an interface unit that transmits and receives data to and from the multipoint temperature controller 20.
- the correction amount calculation unit 30 may be configured integrally with the multipoint temperature controller 20 in addition to the multipoint temperature controller 20 being configured as a separate and independent device.
- FIG. 2 is a flowchart of the disturbance response design process.
- the correction amount calculation unit 30 changes the target temperature to a predetermined shape for each channel, and response waveform data of the temperature of each channel and the operation amount of each channel. Is acquired (S11). For example, when the target temperature of an arbitrary input channel among a plurality of input channels is changed, the correction amount calculation unit 30 operates the time series data of the operation amount with respect to the change of the input channel and the multipoint temperatures in the control target. Get time-series data of.
- the correction amount calculation unit 30 sequentially changes input channels for changing the target temperature, and obtains time-series data of operation amounts and temperatures for all the input channels.
- the obtained time-series data is stored in the storage unit of the correction amount calculation unit 30. Note that step S11 is started in a stable state where the PID controller 21 controls the control target 10.
- the correction amount calculation unit 30 first changes the target temperature of the input channel 1 using a pulse.
- FIG. 3 is an explanatory diagram of a specific example of changing the target temperature.
- the correction amount calculation unit 30 adds a pulse having a pulse width Ts of 1 second and a pulse amplitude Pulse of 1 ° C. to the integrator, and provides the output of the integrator to the adder 22.
- the integrator can be provided in the correction pattern application unit 22, for example. By the integration operation of the integrator, for example, with respect to the target temperature of 130 ° C., the output of the adder 22 rises to 131 ° C. over 1 second.
- the target temperature In addition to changing the target temperature in this way, it may be changed to a predetermined appropriate shape that does not saturate the operation amount that changes in accordance with the change in the target temperature.
- the shape in which the operation amount is not saturated may be, for example, a shape in which the change in the target temperature is not steep.
- temperature response data acquired when the target temperature of the input channel i is changed is Temp influence (OUTj, INi) (t), and operation amount response data (time series data).
- Temp influence OUTj, INi
- operation amount response data time series data
- MV influence OUTj, INi
- i is an input channel number to which a pulse is applied, and can be represented by a natural number, for example.
- j is an output channel number and can be expressed by a natural number, for example.
- step S12 the correction amount calculation unit 30 constructs an influence matrix from the response waveform data of temperature and manipulated variable (S12).
- the correction amount calculation unit 30 applies the temperature response waveform data Temp influence (OUTj, INi) (t) measured in step S11, the initial temperature Temp init (OUTj) before applying the pulse, Based on the pulse amplitude A Pulse , the temperature unit pulse response Temp pulse (OUTj, INi) (t) is calculated using the following equation.
- each symbol represents the following contents.
- M Number of input channels
- N Number of output channels
- kmax Number of pulses applied in the target temperature correction pattern
- ⁇ Time interval of predicted temperature
- lmax Number of temperature data to be predicted For example, prediction is performed from 0 second to ⁇ ⁇ (lmax ⁇ 1) seconds.
- FIG. 4 is an explanatory diagram of the temperature influence matrix C temp .
- the temperature influence matrix C temp is a real constant matrix of (lmax ⁇ N) rows (kmax ⁇ M) columns.
- unit pulse response time series data Temp pulse (OUT1, IN1) (t) obtained from the temperature response data corresponding to the output channel 1 when the target temperature of the input channel 1 is changed as in step S11.
- a column vector having the element as an element is arranged at a position indicated by a rectangular frame in FIG.
- the other input channels and output channels are similarly arranged.
- only one pulse is input in step S11, that is, the 0th pulse in FIG. 4.
- shifting the pulse in the time direction means a time series of the obtained unit pulse response.
- the data may be shifted by the correction pattern pulse period.
- each element of the column vector arranged at the position of influence from the 0th pulse input may be shifted to the position of influence from the first pulse input by the pulse period of the correction pattern.
- the pulse period is 1 second and the time interval of the predicted temperature is also 1 second
- each element of the column vector arranged at the position of influence from the 0th pulse input is shifted down by 1 and the 1st pulse What is necessary is just to arrange
- the correction amount calculation unit 30 receives the response MV influence (OUTj, INi) (t) of the operation amount measured in step S11, the initial operation amount MV init (OUTj) before applying the pulse, and the amplitude A Pulse of the applied pulse. Accordingly, the unit pulse response MV pulse (OUTj, INi) (t) of the manipulated variable is calculated using the following equation.
- FIG. 5 is an explanatory diagram of the influence matrix C mv of the operation amount.
- the manipulated variable influence matrix C mv is a real constant matrix of (lmax ⁇ M) rows (kmax ⁇ M) columns.
- the arrangement method of the time series data of the unit pulse response MV pulse (OUTj, INi) (t) is the same as the above-described temperature influence matrix.
- the obtained temperature influence matrix and manipulated variable influence matrix can be stored in the storage unit of the correction amount calculation unit 30.
- step S13 the correction amount calculation unit 30 obtains temperature time-series data Temp ref (OUTj) (t) and manipulated variable time-series data MV ref (OUTj) for each channel when a disturbance is applied (step S13 ).
- a disturbance for example, a work is placed on a hot plate, and the work and the hot plate are brought into contact with each other.
- the workpiece may be placed, for example, by an operator or may be automatically placed.
- the time series data of the temperature and the time series data of the manipulated variable when the disturbance is applied can be stored in the storage unit of the correction amount calculation unit 30.
- the target temperature when the disturbance is applied, the target temperature may be once reduced and then the disturbance may be applied.
- the output can be prevented from being saturated when a disturbance is applied, and the time-series data of the temperature and the time-series data of the manipulated variable can be obtained without the output being saturated.
- the target temperature may be increased thereafter and returned to the original target temperature. In other words, after the target temperature is once reduced, it may be changed in a predetermined pattern that gradually increases.
- step S ⁇ b> 14 the correction amount calculation unit 30 determines the correction amount ⁇ SV (correction amount vector) of the target temperature (SV) at each time / each channel from when the work is placed on the hot plate until the control amount becomes stable. Based on the time-series data acquired in steps S11 and S13, a prediction formula for the temperature and the manipulated variable in the transient state is constructed (S14).
- the correction amount calculation unit 30 obtains a known temperature vector T ref in which time-series data Temp ref (OUTj) (t) at multiple points when a disturbance is applied is arranged. Further, the correction amount calculation unit 30 obtains a known operation amount vector M ref in which data of operation amount time-series data MV ref (OUTj) (t) when a disturbance is applied is arranged.
- FIG. 6 shows the known temperature vector T ref and the known manipulated variable when the number of temperature output channels is 5, the number of manipulated variable output channels is 3, and the number of predicted temperatures is 91 (predicted from 0 to 90 seconds). The structural example of vector Mref is shown.
- the known temperature vector T ref is a column vector composed of real constants having a length of the number of predicted temperatures: 91 ⁇ the number of temperature output channels: 5.
- the known manipulated variable vector M ref is a column vector composed of real constants having a length of the number of predicted temperatures: 91 ⁇ number of manipulated variable output channels: 3.
- the correction amount calculation unit 30 defines a correction amount vector (design parameter vector) having time series data of the target temperature correction amount for each input channel as an element.
- FIG. 7 shows a configuration example of the correction amount vector ⁇ when the number of pulses applied in the target temperature correction pattern is 50 and the number of target temperature input channels is 3.
- the predicted temperature vector T forecast and the predicted manipulated variable vector M forecast can be defined as follows.
- the predicted value of the temperature fluctuation amount is obtained by multiplying the temperature influence matrix C temp by the target temperature correction amount ⁇ .
- the predicted temperature T forwardcast is obtained by adding the predicted value of the temperature fluctuation amount and the temperature at the time of the disturbance response as a reference. The same applies to the operation amount.
- the predicted temperature vector T forwardcast is a column vector having a length of the number of predicted temperatures: 91 ⁇ the number of output channels of temperature: 5, and ⁇ as a variable.
- the predicted manipulated variable vector M forwardcast is a column vector having a length of the number of predicted temperatures: 91 ⁇ the number of output channels of manipulated variables: 3, and ⁇ as a variable.
- step S15 the correction amount calculation unit 30 sets, for example, the predicted value of the operation amount in the transient state within a range in which the operation amount can be output as a constraint condition (constraint condition), and calculates the total variance of the transient temperature.
- the optimization calculation with the restriction to be minimized is performed, and the correction amount ⁇ SV (correction amount vector ⁇ ) of the target temperature is calculated (S15).
- the output range of the manipulated variable can be determined in advance according to the performance of an actuator such as a heater.
- the dispersion the dispersion of the predicted temperatures of multiple points with respect to the average temperature can be used.
- the predicted average temperature vector T ave is a column vector having a length of the number of predicted temperatures: 91 ⁇ the number of temperature output channels: 5.
- the predicted average temperature vector T ave can be expressed by the following equation. K ave indicates an example in which the number of predicted temperatures is 91 and the number of temperature output channels is five.
- the evaluation function F ( ⁇ ) can be expanded as follows.
- evaluation function F ( ⁇ ) can be expressed as follows.
- the operation amount is always 0% to 100% of the output range.
- the constraint condition can be expressed as follows using the predicted manipulated variable vector M forwardcast .
- the correction amount calculation unit 30 calculates the parameters Q, p, and r of the evaluation function from the temperature influence matrix C temp and the known temperature vector T ref . More specifically, the correction amount calculation unit 30 uses the temperature influence matrix C temp and the known temperature vector T as parameters Q, p, and r when the evaluation function F ( ⁇ ) is expressed by the above equation (1). From ref , the above equation (2) is used. Further, the correction amount calculation unit 30 obtains the parameters A in and A ub when the constraint condition is expressed by the above equation (3) from the operation amount influence matrix C mv and the known operation amount vector M ref from the above equation (4). ). Then, the correction amount calculation unit 30 solves the conditional optimization problem that minimizes the evaluation function under the above constraint conditions. This conditional optimization problem is a convex quadratic programming problem and can be solved by using a known method such as a quadratic programming method. Thereby, the correction amount calculation unit 30 can obtain the optimum target temperature correction amount ⁇ * .
- step S16 the correction amount calculation unit 30 outputs the target temperature correction amount vector ⁇ * to, for example, the correction pattern application unit 23 of the multipoint temperature controller 20 (S16).
- the correction pattern application unit 23 stores a correction amount vector ⁇ * of the target temperature.
- the obtained target temperature correction amount vector ⁇ * represents the amplitude of the pulse train input to the integrator for each input channel.
- Each pulse is added by the integrator, and a correction pattern of the target temperature is output from the integrator.
- the correction pattern (waveform) output from the integrator is added to the target temperature (SV) by the adder 22 and output to the PID controller 21.
- FIG. 8 is an explanatory diagram of the target temperature correction amount vector ⁇ * and the target temperature correction pattern SV correct (INi) (t).
- the input channel 1 will be described. 50 pulses having amplitudes h 1 (0) * to h 1 (49) * are output to the integrator corresponding to the input channel 1.
- the pulse width of each pulse is 1 second, and the interval at which each pulse rises is also 1 second. That is, it outputs without leaving a gap between the immediately preceding pulse and the immediately following pulse.
- the integrator a waveform whose amplitude is increased or decreased by the amplitude of the pulse is obtained. The same applies to other input channels.
- the pulse train is output to the integrator, and a correction pattern of the target temperature is output from the integrator to the adder 22.
- the control target 10 can be controlled by applying the target temperature correction pattern.
- the detection of disturbance may be detected by the correction pattern application unit 23, or another block may be detected and notified to the correction pattern application unit 23.
- Target value response design 1 Next, the design and control of the target value response will be described. In this embodiment, target value response design can be performed instead of the above-described disturbance response design.
- FIG. 9 is a flowchart of the target value response design process. Steps S21 to S24 are the same as or similar to the processing in the above-described disturbance response design.
- step S21 the correction amount calculation unit 30 (for example, a processing unit, the same applies hereinafter) changes the target temperature to a predetermined shape for each channel, and acquires response waveform data of the temperature of each channel and the operation amount of each channel. (S21).
- step S22 the correction amount calculation unit 30 constructs an influence matrix from the response waveform data of temperature and manipulated variable (S22). Steps S21 and S22 are the same as steps S11 and S12 of the disturbance response design, and thus detailed description thereof is omitted.
- step S23 the correction amount calculation unit 30 uses the temperature time-series data Temp ref (OUTj) (t) and the manipulated variable time-series data MV ref (OUTj) when the temperature is stabilized before the target temperature is changed. Obtained for each channel (S23).
- Step S23 is the same as step S13 in the disturbance response design, except for the difference between the state in which the disturbance is applied and the state in which the temperature is stabilized before the target temperature is changed.
- step S24 the correction amount calculation unit 30 sets the correction amount ⁇ SV of the target temperature (SV) at each time / each channel from when the target temperature is changed to when the control amount becomes stable as an unknown, and is acquired at steps S21 and S23. Based on the time-series data, a prediction formula for the temperature and manipulated variable in the transient state is constructed (S24).
- the correction amount calculation unit 30 obtains a known temperature vector T ref in which time-series data Temp ref (OUTj) (t) at multiple points when the temperature is stabilized before the target temperature is changed is arranged. Ask. Further, the correction amount calculation unit 30 obtains a known operation amount vector M ref in which data of operation amount time-series data MV ref (OUTj) (t) is arranged when the temperature is stabilized before the target temperature is changed.
- the correction amount calculation unit 30 defines a correction amount vector (design parameter vector) having the target temperature correction amount as an element.
- the method for obtaining each vector is the same as in the disturbance response design.
- the predicted temperature vector T forward and the predicted manipulated variable vector M forward can also be defined in the same manner as the disturbance response design.
- step S25 for example, the correction amount calculation unit 30 sets the predicted value of the manipulated variable in the transient state within the allowable output range of the manipulated variable and the like, and minimizes the total dispersion of the transient temperature.
- the target temperature change amount ⁇ SV (correction amount vector ⁇ ) is calculated (S25).
- the output range of the manipulated variable can be determined in advance according to the performance of an actuator such as a heater.
- the dispersion the dispersion of the predicted temperatures of multiple points with respect to the average temperature can be used.
- a constraint condition a first constraint condition regarding the saturation of the manipulated variable, a second constraint condition regarding the final temperature, and a third constraint condition regarding the settling time can be defined.
- the third constraint on the settling time may be excluded.
- the first constraint condition it is defined that the manipulated variable falls within a possible output range.
- the second constraint condition it is defined that the average temperature at multiple points in a predetermined time becomes a target value or a corrected target value.
- a third constraint It is defined that the average temperature of multiple points becomes a target value or a corrected target value at a desired settling time.
- the first constraint condition regarding the operation amount is the same as the constraint condition in the above-described disturbance response design.
- the second constraint on the final temperature is a condition for stabilizing the temperature at each point to be controlled at the target temperature after the change. For example, the case where the target temperature after the change is 120 ° C. and prediction is made from 0 to 90 seconds as described above will be described as an example. For example, the average temperature of each point at the time of 90 seconds is set to the target temperature 120 ° C. after the change.
- the second constraint condition can be expressed as follows using the predicted temperature vector T forwardcast .
- K ave — at 90 sec is a coefficient vector for extracting an element at the time of 90 seconds from the predicted temperature vector T forecast .
- FIG. 10 is an explanatory diagram of the coefficient vector K ave_at 90 sec for calculating the average temperature.
- the second constraint condition can be expressed as follows.
- the target temperature after the change is an example of the target temperature after the change, and can be appropriately set as the final target value or the corrected target value SV last after the target temperature change.
- an appropriate time point t3 that is assumed to be a stable state may be used, and the coefficient vector for calculating the average temperature is appropriately set so as to extract an element at a desired time point from the predicted temperature vector T forecast. can do.
- an appropriate time point assumed to be a stable state for example, an arbitrary time point after the settling time to be designed can be set.
- the third constraint on the settling time is a condition for the temperature at each point to be controlled to stabilize at the target temperature for the specified settling time.
- the target temperature after the change is 120 ° C
- the target time until stabilization (design value of settling time) is 15 seconds
- the condition for judging the stability is that the temperature of each point is within 120 ° C error from 120 ° C
- the time until stabilization (settling time) and the conditions for determining stability can be set as appropriate depending on the device to be applied and the controlled object.
- the predicted temperature of each point (for example, each point on the workpiece) after 15 seconds should be within an error of 0.1 ° C. from 120 ° C., so the predicted temperature vector T steady of the workpiece after 15 seconds is required. Is extracted from the predicted temperature vector T forwardcast .
- FIG. 11 shows an example of the predicted temperature vector Tsteady of the work after 15 seconds.
- FIG. 12 shows an example of a coefficient matrix Ksteady for calculating a predicted temperature vector after 15 seconds.
- the coefficient matrix K steady is a matrix of real number constants of (76 ⁇ 5) rows (91 ⁇ 5) columns.
- a zero matrix 0 (m, n) in the figure is an m-by-n matrix in which all elements are zero.
- the third constraint condition can be expressed as follows using the predicted temperature vector T steady of the workpiece after 15 seconds.
- the first to third constraints are as follows.
- the correction amount calculation unit 30 calculates the parameters Q, p, and r of the evaluation function from the temperature influence matrix C temp and the known temperature vector T ref . More specifically, the correction amount calculation unit 30 sets the parameters Q, p, and r when the evaluation function F ( ⁇ ) is expressed by the above equation (1) shown in the description of the disturbance response design as the influence of temperature. It is calculated from the degree matrix C temp and the known temperature vector T ref by the above equation (2) shown in the description of the disturbance response design. Further, the correction amount calculation unit 30 sets the parameters A in , A ub , A eq and b eq when the constraint condition is expressed by the above equation (5), the manipulated variable influence matrix C mv, and the temperature influence degree. The matrix C temp , the known manipulated variable vector M ref, and the known temperature vector T ref are calculated by the above equation (6).
- the correction amount calculation unit 30 solves the conditional optimization problem that minimizes the evaluation function under the above constraint conditions.
- This conditional optimization problem is a convex quadratic programming problem and can be solved by using a known method such as a quadratic programming method. Thereby, the correction amount calculation unit 30 can obtain the optimum target temperature correction amount ⁇ * .
- step S26 the correction amount calculation unit 30 outputs the calculated correction amount vector ⁇ * to, for example, the correction pattern application unit 23 of the multipoint temperature controller 20 (S26).
- the correction pattern application unit 23 when the target temperature is changed (or when the change of the target temperature is detected), the correction pattern application unit 23 outputs a pulse having the amplitude of each element of the calculated correction amount vector ⁇ * to the integrator, The target temperature correction pattern is output from the integrator to the adder.
- the configuration of the target temperature correction pattern based on the calculated correction amount vector ⁇ * is the same as in the above-described disturbance response design.
- PID control is performed at the target temperature adjusted by the correction pattern, and it is possible to realize the control that reduces the variation in temperature while keeping the operation amount in the transient state within the output possible range.
- Target value response design 2 Next, another example of target value response design will be described.
- the evaluation function and constraint conditions of the target value response design 1 described above may be as follows. Other processes are the same as those in the target value response design 1 described above.
- the maximum temperature difference d from the average temperature at the temperature of each point controlled as the evaluation function is set to be minimized.
- the maximum difference temperature range from the average temperature is the maximum value of the difference width (absolute value of the difference) between each of the predicted temperatures of the multiple points to be controlled and the average temperature of the multiple points. In other words, the temperature variation at each point with respect to the average temperature is minimized.
- the constraint condition in addition to the first constraint condition regarding the saturation of the manipulated variable, the second constraint condition regarding the final temperature, and the third constraint condition regarding the settling time, the fourth constraint condition regarding the temperature difference from the average temperature is defined. be able to. Note that the third constraint on the settling time may be excluded. For example, the first to third constraint conditions are the same as those in the target value response design 1.
- Differential temperature E n from the mean temperature of each point of controlling defines that is within ⁇ d ° C..
- the maximum temperature difference from the average temperature of each point to be controlled is set to d ° C. (d is 0 or more).
- the design parameter is a vector ⁇ composed of a correction amount vector ⁇ and a maximum temperature difference d, and the evaluation function is expressed as follows.
- Prediction difference temperature vector E n from the mean temperature of each point control is a column vector having the length of the data number 91 ⁇ Number of output channels 5 to predict, it can be expressed as follows.
- K ave is the same as that described in the disturbance response design.
- the fourth constraint differential temperature E n from the mean temperature of each point of control is within ⁇ d ° C. can be expressed as follows.
- the correction amount calculation unit 30 includes parameters A in , A ub , A eq, and b eq when the constraint condition is expressed by the above equation (7), the manipulated variable influence matrix C mv, and the temperature influence matrix C. It is calculated by the above equation (8) from temp , known manipulated variable vector M ref , and known temperature vector T ref . Thereafter, the correction amount calculation unit 30 can obtain the optimum target temperature correction amount ⁇ * by solving the optimization problem.
- This optimization problem is a linear programming problem and can be solved by using a known method.
- FIG. 13 is a diagram illustrating an effect of the control system (at the time of disturbance response design) in the present embodiment.
- FIG. 13 (a) shows response waveforms (w11 to w15) before application of the correction pattern
- FIG. 13 (b) shows response waveforms (w21 to w25) when the correction pattern is applied.
- FIG. 13C shows changes in the operation amount (ch1 to ch3) when the correction pattern is applied.
- the vertical axis indicates the temperature difference between the temperature average value of each point of the work and each point (° C.)
- the horizontal axis indicates the work placed on the hot platen. Indicates the elapsed time (seconds) since In FIG. 13C, the vertical axis indicates the ratio (%) where the maximum output of the operation amount of each channel is 100, and the horizontal axis indicates the elapsed time after the work is placed on the hot plate.
- FIG. 13A corresponds to, for example, the waveform obtained in step S13 described above, and FIG. 13B illustrates the case where a correction pattern based on the target temperature correction amount vector obtained in step S15 is applied. Corresponds to the waveform.
- the disturbance response design and the target value response design have been described. However, a part of each design may be applied to other designs. For example, a part of the constraints in the target value response design may be applied to the disturbance response design.
- target value response design and control are performed instead of disturbance response design and control has been described, but both may be combined.
- the control target 10 is controlled by applying the correction amount vector (correction pattern) obtained by the target value response design
- the correction amount vector (correction pattern) obtained by the disturbance response design is further added. You may comprise as follows. In this case, the disturbance response design may be executed when the control to which the correction amount vector (correction pattern) obtained by the target value response design is applied is in a stable state.
- the temperature is described as an example, but a physical quantity other than the temperature may be controlled.
- the above target temperature corresponds to the target value
- the hot plate corresponds to an appropriate actuator.
- the present invention can be applied to configurations other than a configuration having a hot plate and a workpiece.
- the above processing can also be realized as a control system design method executed by the processing unit. Further, the present invention can be realized by a program or a program medium including instructions for causing the processing unit to execute the above-described processing, a computer-readable recording medium storing the program, a non-temporary recording medium, and the like.
- a correction amount of the target value for a multipoint control system that controls multi-point temperatures in the control target and controls the control target according to a correction target value corrected according to a correction amount given a preset target value.
- a control system design device for designing A correction amount calculation unit for calculating the correction amount of the target value;
- the correction amount calculation unit When the target value of multiple input channels is changed sequentially, the time series data of the manipulated variable for each input channel change and the time series data of multi-point temperatures in the control target are obtained.
- the manipulated variable influence matrix C mv in which the manipulated variable unit pulse response time-series data obtained based on the manipulated variable time-series data and the temperature obtained based on the multi-point temperature time-series data are described.
- a temperature influence matrix C temp in which time series data of unit pulse responses of Obtain the time series data of the manipulated variable when applying the test disturbance and the time series data of the above multi-point temperatures, Obtain a known manipulated variable vector M ref in which time series data of manipulated variables when a test disturbance is applied and a known temperature vector T ref in which time series data of multipoint temperatures when a test disturbance is applied are arranged,
- the evaluation function to be minimized is a function based on the variance of the above-mentioned multiple predicted temperatures of the control target with respect to the average temperature, and parameters of the evaluation function are calculated from the temperature influence matrix C temp and the known temperature vector T ref .
- the constraint condition is that the manipulated variable falls within a predetermined range, and parameters of the constraint condition are calculated from the manipulated variable influence matrix C mv and the known manipulated variable vector M ref . A correction amount of the target value that minimizes the evaluation function under the constraint condition is calculated.
- the correction amount calculation unit includes: Parameters Q, p and r when the evaluation function F ( ⁇ ) is expressed by the following equation (F1) are calculated from the temperature influence matrix C temp and the known temperature vector T ref by the following equation (F2): The parameters A in and A ub when the constraint condition is expressed by the following equation (F3) are calculated from the manipulated variable influence matrix C mv and the known manipulated variable vector M ref by the following equation (F4):
- the correction amount vector ⁇ of the target value is calculated by solving the convex quadratic programming problem represented by the evaluation function and the constraint conditions by a predetermined method.
- I lmax unit matrix of (lmax ⁇ lmax) e 0 : vector of lmax ⁇ number of input channels, each element is 1 vector lmax: number of time-series data of temperatures predicted for one input channel ⁇ : correction Vector representing quantity N: Number of output channels
- a correction amount of the target value for a multipoint control system that controls multi-point temperatures in the control target and controls the control target according to a correction target value corrected according to a correction amount given a preset target value.
- a control system design device for designing A correction amount calculation unit for calculating the correction amount of the target value;
- the correction amount calculation unit When the target value of multiple input channels is changed sequentially, the time series data of the manipulated variable for each input channel change and the time series data of multi-point temperatures in the control target are obtained.
- the manipulated variable influence matrix C mv in which the manipulated variable unit pulse response time-series data obtained based on the manipulated variable time-series data and the temperature obtained based on the multi-point temperature time-series data are described.
- a temperature influence matrix C temp in which time series data of unit pulse responses of Obtain time-series data of the manipulated variable in a stable state controlled by a predetermined target value and time-series data of the above-mentioned multi-point temperatures, Obtain a known manipulated variable vector M ref in which time series data of manipulated variables in the stable state are arranged, and a known temperature vector T ref in which time series data of the multipoint temperatures in the stable state are arranged,
- the evaluation function to be minimized is a function based on the variance of the above-mentioned multiple predicted temperatures of the control target with respect to the average temperature, and parameters of the evaluation function are calculated from the temperature influence matrix C temp and the known temperature vector T ref .
- the operation amount is within a predetermined range for the first constraint condition, and the parameter of the first constraint condition is calculated from the operation amount influence matrix C mv and the known operation amount vector M ref .
- the second constraint condition is that the average temperature of the multiple points at a predetermined time becomes a target value or a corrected target value, and parameters of the second constraint condition are a temperature influence matrix C temp and a known temperature vector. Calculated from T ref , A correction amount of the target value that minimizes the evaluation function is calculated under the first and second constraint conditions.
- the correction amount calculation unit includes:
- the third constraint condition is that the average temperature of the multiple points becomes a target value or a corrected target value at a desired settling time, and parameters of the third constraint condition are a temperature influence matrix C temp and a known temperature vector T ref. Calculated from The correction amount vector ⁇ of the target value that minimizes the evaluation function under the first to third constraints is calculated.
- the correction amount calculation unit includes: Parameters Q, p and r when the evaluation function F ( ⁇ ) is expressed by the following equation (F1) are calculated from the temperature influence matrix C temp and the known temperature vector T ref by the following equation (F2): The parameters A in , A ub , A eq, and b eq when the constraint condition is expressed by the following equation (F5), the manipulated variable influence matrix C mv , the temperature influence matrix C temp, and the known manipulated variable Calculate from the vector M ref and the known temperature vector T ref by the following equation (F6), The correction amount vector ⁇ of the target value is calculated by solving the convex quadratic programming problem represented by the evaluation function and the constraint conditions by a predetermined method.
- K t1_to_t2 coefficient matrix for extracting elements from time t1 to t2
- SVp upper limit value of target value for judging stability
- SVn lower limit value of target value for judging stability
- e 1 vector of lmax ⁇ number of input channels
- ⁇ vector representing the correction amount
- N number of output channels 0 (x, y) : x-row y-column matrix or vector satisfying the corresponding row and column with 0 SV last :
- K t3 Coefficient vector for extracting elements at time t3
- a correction amount of the target value for a multipoint control system that controls multi-point temperatures in the control target and controls the control target according to a correction target value corrected according to a correction amount given a preset target value.
- a control system design device for designing A correction amount calculation unit for calculating the correction amount of the target value;
- the correction amount calculation unit When the target value of multiple input channels is changed sequentially, the time series data of the manipulated variable for each input channel change and the time series data of multi-point temperatures in the control target are obtained.
- the manipulated variable influence matrix C mv in which the manipulated variable unit pulse response time-series data obtained based on the manipulated variable time-series data and the temperature obtained based on the multi-point temperature time-series data are described.
- a temperature influence matrix C temp in which time series data of unit pulse responses of Obtain time-series data of the manipulated variable in a stable state controlled by a predetermined target value and time-series data of the above-mentioned multi-point temperatures, Obtain a known manipulated variable vector M ref in which time series data of manipulated variables in the stable state are arranged, and a known temperature vector T ref in which time series data of the multipoint temperatures in the stable state are arranged,
- the evaluation function to be minimized is the maximum value d of the difference width between each predicted temperature of the multipoint to be controlled and the average temperature of the multipoint,
- the operation amount is within a predetermined range for the first constraint condition, and the parameter of the first constraint condition is calculated from the operation amount influence matrix C mv and the known operation amount vector M ref .
- the second constraint condition is that the average temperature of the multiple points at a predetermined time becomes a target value or a corrected target value, and parameters of the second constraint condition are a temperature influence matrix C temp and a known temperature vector.
- T ref a temperature influence matrix
- a fourth constraint the difference E n of the average temperature of each predicted temperature and the multi-point of the multipoint control target, and it becomes -d or + d or less with respect to the maximum value d of the difference width
- a parameter of the fourth constraint condition is calculated from a temperature influence matrix C temp and a known temperature vector T ref ;
- a correction amount of the target value that minimizes the evaluation function is calculated under the first, second, and fourth constraint conditions.
- the correction amount calculation unit includes:
- the third constraint condition is that the average temperature of the multiple points becomes a target value at a desired settling time, and the parameters of the third constraint condition are calculated from the temperature influence matrix C temp and the known temperature vector T ref ,
- the correction amount vector ⁇ of the target value that minimizes the evaluation function under the first to fourth constraint conditions is calculated.
- the correction amount calculation unit includes: The parameters A in , A ub , A eq, and b eq when the constraint condition is expressed by the following equation (F7), the manipulated variable influence matrix C mv , the temperature influence matrix C temp, and the known manipulated variable Calculate from the vector M ref and the known temperature vector T ref by the following equation (F8),
- the control system design apparatus according to the configuration example 8 that calculates the correction amount vector ⁇ of the target value by solving the linear programming problem expressed by the evaluation function and the constraint condition by a predetermined method.
- SVp upper limit value of target value for judging stability
- SVn lower limit value of target value for judging stability
- e 1 vector of lmax ⁇ number of input channels, each element being 1 vector lmax: for one input channel
- Time series data number of predicted temperature e 3 (lmax ⁇ z) ⁇ number of output channels, each element is a vector z: number corresponding to the number of data up to settling time e 4 : lmax ⁇ output
- N number of output channels
- 0 (x, y) a matrix or vector of x rows and y columns satisfying the corresponding rows and columns with 0
- I lmax unit matrix (lmax ⁇ lmax)
- SV last: target temperature change after the final target value or modify the target value
- K t3 coefficients for extracting the elements of the time t3 Vector
- a control system design device according to any one of Configuration Examples 1 to 3,
- a correction pattern application unit that outputs a correction pattern based on the correction amount calculated by the control system design device when a disturbance is detected;
- a control system comprising: the target value set in advance; and an adder that adds the correction pattern from the correction pattern application unit to obtain the correction target value and supplies the correction target value to the controller.
- a control system design device according to any one of configuration examples 4 to 9,
- a correction pattern application unit that outputs a correction pattern based on the correction amount calculated by the control system design device when a change in the target temperature is detected or when the target temperature is changed;
- a control system comprising: the target value set in advance; and an adder that adds the correction pattern from the correction pattern application unit to obtain the correction target value and supplies the correction target value to the controller.
- the present invention can be used in a system that performs multipoint control.
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Abstract
Description
図1は、本実施形態における制御系のブロック図である。
制御系1は、制御対象10と、多点温度コントローラ20と、目標温度修正量算出部(制御系設計装置)30を備える。なお、多点温度コントローラ20と目標温度修正量算出部30により、制御対象10に対する制御装置又は制御システムを構成してもよい。
図2は、外乱応答設計処理のフローチャートである。
まず、ステップS11では、修正量算出部30(例えば処理部、以下同様)は、チャンネル毎に目標温度を予め定められた形状に変化させ、各チャンネルの温度と各チャンネルの操作量の応答波形データを取得する(S11)。例えば、修正量算出部30は、複数の入力チャンネルのうちの任意の入力チャンネルの目標温度を変化させたときの、当該入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得する。修正量算出部30は、目標温度を変化させる入力チャンネルを順次変更して、全ての入力チャンネルに対して操作量と温度の時系列データを得る。得られた時系列データは、修正量算出部30の記憶部に記憶される。なお、ステップS11は、PID制御器21が制御対象10を制御して安定した状態で開始される。
M:入力チャンネル数
N:出力チャンネル数
Ts:パルス周期(パルス幅)
kmax:目標温度修正パターンで印加するパルスの個数
τ:予測する温度の時間間隔
lmax:予測する温度データの個数。例えば0秒~τ×(lmax-1)秒まで予測する。
次に、目標値応答の設計と制御について説明する。本実施形態では、上述の外乱応答設計に代えて目標値応答設計を行うことができる。
多点の平均温度が所望の整定時間で目標値又は修正目標値になることを規定する。
次に、目標値応答の設計の他の例について説明する。上述の目標値応答設計1の評価関数及び制約条件を以下のようにしてもよい。他の処理は上述の目標値応答設計1と同様である。
制約条件としては、操作量の飽和に関する第1制約条件と、最終温度に関する第2制約条件と、整定時間に関する第3制約条件に加えて、平均温度からの差温に関する第4制約条件を規定することができる。なお、整定時間に関する第3制約条件を除外してもよい。例えば、第1~第3制約条件は、目標値応答設計1と同様である。第4制約条件として、
制御する各点の平均温度からの差温Enが±d℃以内であることを規定する。
図13は、本実施形態における制御系(外乱応答設計時)の効果を示す図である。図13(a)は、修正パターン適用前の応答波形(w11~w15)を示し、図13(b)は、修正パターンを適用した場合の応答波形(w21~w25)を示す。図13(c)は、修正パターンを適用した場合の操作量の変化(ch1~ch3)を示す。図13(a)及び図13(b)において、縦軸は、ワークの各点の温度平均値と各点との差温(℃)を示し、横軸は、ワークを熱板に置載してからの経過時間(秒)を示す。図13(c)において、縦軸は、各チャンネルの操作量の最大出力を100とした割合(%)で示し、横軸は、ワークを熱板に置載してからの経過時間を示す。
なお、上述の実施形態では外乱応答設計と目標値応答設計をそれぞれ説明したが、各設計の一部を他の設計に適用してもよい。例えば、目標値応答設計における制約条件の一部を外乱応答設計に適用してもよい。また、上述の実施形態では、外乱応答設計及び制御に代えて目標値応答設計及び制御を行う例を説明したが、両者を組み合わせてもよい。例えば、目標値応答設計により求められた修正量ベクトル(修正パターン)を適用して制御対象10を制御している際に、外乱応答設計により求められた修正量ベクトル(修正パターン)をさらに加算するように構成してもよい。この場合、該外乱応答設計は、目標値応答設計により求められた修正量ベクトル(修正パターン)を適用した制御が安定状態にあるときに実行されてもよい。
上述の実施形態では具体的な数を例に挙げて説明したが、本実施の形態の装置及びシステムは以下のように構成することもできる。
制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する多点制御系に対して、上記目標値の修正量を設計する制御系設計装置であって、
上記目標値の修正量を算出する修正量算出部
を備え、
上記修正量算出部は、
複数の入力チャンネルの目標値を順次変化させたときの、各入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得し、
該操作量の時系列データに基づいて求めた操作量の単位パルス応答の時系列データを配列した操作量の影響度行列Cmvと、上記多点の温度の時系列データに基づいて求めた温度の単位パルス応答の時系列データを配列した温度の影響度行列Ctempを求め、
試験外乱を印加したときの操作量の時系列データと上記多点の温度の時系列データを取得し、
試験外乱を印加したときの操作量の時系列データを配列した既知操作量ベクトルMrefと、試験外乱を印加したときの多点の温度の時系列データを配列した既知温度ベクトルTrefを求め、
最小化する評価関数を制御対象の上記多点の予測温度の平均温度に対する分散に基づく関数とし、該評価関数のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
制約条件を、操作量が予め定められた範囲に収まることとし、該制約条件のパラメータを操作量の影響度行列Cmvと既知操作量ベクトルMrefから算出し、
上記制約条件の下で上記評価関数を最小化する目標値の修正量を算出する。
構成例1の制御系設計装置において、上記修正量算出部は、
上記評価関数F(θ)を次式(F1)で表したときのパラメータQ、p及びrを、温度の影響度行列Ctempと既知温度ベクトルTrefから次式(F2)で算出し、
上記制約条件を次式(F3)で表したときのパラメータAin及びAubを、操作量の影響度行列Cmvと既知操作量ベクトルMrefから次式(F4)で算出し、
上記評価関数と上記制約条件で表される凸二次計画問題を予め定められた手法で解くことで目標値の修正量ベクトルθを算出する。
e0:lmax×入力チャンネル数のベクトルであって、各要素が1のベクトル
lmax:1入力チャンネルに対して予測する温度の時系列データ数
θ:修正量を表すベクトル
N:出力チャンネル数
構成例1又は2の制御系設計装置において、試験外乱を印加する際に、目標温度を一旦小さくして、その後試験外乱を印加する。
制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する多点制御系に対して、上記目標値の修正量を設計する制御系設計装置であって、
上記目標値の修正量を算出する修正量算出部
を備え、
上記修正量算出部は、
複数の入力チャンネルの目標値を順次変化させたときの、各入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得し、
該操作量の時系列データに基づいて求めた操作量の単位パルス応答の時系列データを配列した操作量の影響度行列Cmvと、上記多点の温度の時系列データに基づいて求めた温度の単位パルス応答の時系列データを配列した温度の影響度行列Ctempを求め、
所定の目標値が与えられて制御された安定状態での操作量の時系列データと上記多点の温度の時系列データを取得し、
該安定状態での操作量の時系列データを配列した既知操作量ベクトルMrefと、該安定状態での上記多点の温度の時系列データを配列した既知温度ベクトルTrefを求め、
最小化する評価関数を制御対象の上記多点の予測温度の平均温度に対する分散に基づく関数とし、該評価関数のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
第1制約条件を、操作量が予め定められた範囲に収まることとし、該第1制約条件のパラメータを操作量の影響度行列Cmvと既知操作量ベクトルMrefから算出し、
第2制約条件を、予め定められた時間における上記多点の平均温度が目標値又は修正目標値になることとし、該第2制約条件のパラメータを、温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
上記第1及び第2制約条件の下で上記評価関数を最小化する目標値の修正量を算出する。
構成例4の制御系設計装置において、上記修正量算出部は、
第3制約条件を、上記多点の平均温度が所望の整定時間で目標値又は修正目標値になることとし、該第3制約条件のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
上記第1乃至第3制約条件の下で上記評価関数を最小化する目標値の上記修正量ベクトルθを算出する。
構成例4又は5の制御系設計装置において、上記修正量算出部は、
上記評価関数F(θ)を次式(F1)で表したときのパラメータQ、p及びrを、温度の影響度行列Ctempと既知温度ベクトルTrefから次式(F2)で算出し、
上記制約条件を次式(F5)で表したときのパラメータAin、Aub、Aeq及びbeqを、操作量の影響度行列Cmvと、温度の影響度行列Ctempと、既知操作量ベクトルMrefと、既知温度ベクトルTrefから次式(F6)で算出し、
上記評価関数と上記制約条件で表される凸二次計画問題を予め定められた手法で解くことで目標値の修正量ベクトルθを算出する。
SVp:安定を判断する目標値の上限値
SVn:安定を判断する目標値の下限値
e1:lmax×入力チャンネル数のベクトルであって、各要素が1のベクトル
lmax:1入力チャンネルに対して予測する温度の時系列データ数
e3:(lmax-z)×出力チャンネル数のベクトルであって、各要素が1のベクトル
z:整定時間までのデータ数に相当する数
θ:修正量を表すベクトル
N:出力チャンネル数
0(x、y):対応する行及び列を0で満たすx行y列の行列又はベクトル
SVlast:目標温度変更後の最終的な目標値又は修正目標値
Kt3:時刻t3の要素を抽出するための係数ベクトル
制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する多点制御系に対して、上記目標値の修正量を設計する制御系設計装置であって、
上記目標値の修正量を算出する修正量算出部
を備え、
上記修正量算出部は、
複数の入力チャンネルの目標値を順次変化させたときの、各入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得し、
該操作量の時系列データに基づいて求めた操作量の単位パルス応答の時系列データを配列した操作量の影響度行列Cmvと、上記多点の温度の時系列データに基づいて求めた温度の単位パルス応答の時系列データを配列した温度の影響度行列Ctempを求め、
所定の目標値が与えられて制御された安定状態での操作量の時系列データと上記多点の温度の時系列データを取得し、
該安定状態での操作量の時系列データを配列した既知操作量ベクトルMrefと、該安定状態での上記多点の温度の時系列データを配列した既知温度ベクトルTrefを求め、
最小化する評価関数を制御対象の上記多点の各予測温度と上記多点の平均温度との差幅の最大値dとし、
第1制約条件を、操作量が予め定められた範囲に収まることとし、該第1制約条件のパラメータを操作量の影響度行列Cmvと既知操作量ベクトルMrefから算出し、
第2制約条件を、予め定められた時間における上記多点の平均温度が目標値又は修正目標値になることとし、該第2制約条件のパラメータを、温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
第4制約条件を、制御対象の上記多点の各予測温度と上記多点の平均温度との差Enが、上記差幅の最大値dに対して-d以上+d以下になることとし、該第4制約条件のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
上記第1、第2及び第4制約条件の下で上記評価関数を最小化する目標値の修正量を算出する。
構成例7の制御系設計装置において、上記修正量算出部は、
第3制約条件を、上記多点の平均温度が所望の整定時間で目標値になることとし、該第3制約条件のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
上記第1乃至第4制約条件の下で上記評価関数を最小化する目標値の上記修正量ベクトルθを算出する。
構成例7又は8の制御系設計装置において、上記修正量算出部は、
上記制約条件を次式(F7)で表したときのパラメータAin、Aub、Aeq及びbeqを、操作量の影響度行列Cmvと、温度の影響度行列Ctempと、既知操作量ベクトルMrefと、既知温度ベクトルTrefとから次式(F8)で算出し、
上記評価関数と上記制約条件で表される線形計画問題を予め定められた手法で解くことで目標値の修正量ベクトルθを算出する構成例8に記載の制御系設計装置。
SVn:安定を判断する目標値の下限値
e1:lmax×入力チャンネル数のベクトルであって、各要素が1のベクトル
lmax:1入力チャンネルに対して予測する温度の時系列データ数
e3:(lmax-z)×出力チャンネル数のベクトルであって、各要素が1のベクトル
z:整定時間までのデータ数に相当する数
e4:lmax×出力チャンネル数のベクトルであって、各要素が1のベクトル
θ:修正量を表すベクトル
N:出力チャンネル数
0(x、y):対応する行及び列を0で満たすx行y列の行列又はベクトル
Ilmax:(lmax×lmax)の単位行列
SVlast:目標温度変更後の最終的な目標値又は修正目標値
Kt3:時刻t3の要素を抽出するための係数ベクトル
制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する制御器と、
構成例1乃至3のいずれかに記載の制御系設計装置と、
外乱を検出した際に上記制御系設計装置で算出された修正量に基づく修正パターンを出力する修正パターン適用部と、
予め設定される上記目標値と、上記修正パターン適用部からの修正パターンを加えて上記修正目標値を求めて上記制御器に与える加算器と
を備えた制御システム。
制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する制御器と、
構成例4乃至9のいずれかに記載の制御系設計装置と、
目標温度の変更を検出した際又は目標温度を変更する際に上記制御系設計装置で算出された修正量に基づく修正パターンを出力する修正パターン適用部と、
予め設定される上記目標値と、上記修正パターン適用部からの修正パターンを加えて上記修正目標値を求めて上記制御器に与える加算器と
を備えた制御システム。
10 制御対象
20 多点温度コントローラ
21 PID制御器
22 加算器
23 修正パターン適用部
30 修正量算出部
Claims (11)
- 制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する多点制御系に対して、前記目標値の修正量を設計する制御系設計装置であって、
前記目標値の修正量を算出する修正量算出部
を備え、
前記修正量算出部は、
複数の入力チャンネルの目標値を順次変化させたときの、各入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得し、
該操作量の時系列データに基づいて求めた操作量の単位パルス応答の時系列データを配列した操作量の影響度行列Cmvと、前記多点の温度の時系列データに基づいて求めた温度の単位パルス応答の時系列データを配列した温度の影響度行列Ctempを求め、
試験外乱を印加したときの操作量の時系列データと前記多点の温度の時系列データを取得し、
試験外乱を印加したときの操作量の時系列データを配列した既知操作量ベクトルMrefと、試験外乱を印加したときの多点の温度の時系列データを配列した既知温度ベクトルTrefを求め、
最小化する評価関数を制御対象の前記多点の予測温度の平均温度に対する分散に基づく関数とし、該評価関数のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
制約条件を、操作量が予め定められた範囲に収まることとし、該制約条件のパラメータを操作量の影響度行列Cmvと既知操作量ベクトルMrefから算出し、
前記制約条件の下で前記評価関数を最小化する目標値の修正量を算出する制御系設計装置。 - 前記修正量算出部は、
前記評価関数F(θ)を次式(1)で表したときのパラメータQ、p及びrを、温度の影響度行列Ctempと既知温度ベクトルTrefから次式(2)で算出し、
前記制約条件を次式(3)で表したときのパラメータAin及びAubを、操作量の影響度行列Cmvと既知操作量ベクトルMrefから次式(4)で算出し、
前記評価関数と前記制約条件で表される凸二次計画問題を予め定められた手法で解くことで目標値の修正量ベクトルθを算出する請求項1に記載の制御系設計装置。
e0:lmax×入力チャンネル数のベクトルであって、各要素が1のベクトル
lmax:1入力チャンネルに対して予測する温度の時系列データ数
θ:修正量を表すベクトル
N:出力チャンネル数 - 試験外乱を印加する際に、目標温度を一旦小さくして、その後試験外乱を印加する請求項1に記載の制御系設計装置。
- 制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する多点制御系に対して、前記目標値の修正量を設計する制御系設計装置であって、
前記目標値の修正量を算出する修正量算出部
を備え、
前記修正量算出部は、
複数の入力チャンネルの目標値を順次変化させたときの、各入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得し、
該操作量の時系列データに基づいて求めた操作量の単位パルス応答の時系列データを配列した操作量の影響度行列Cmvと、前記多点の温度の時系列データに基づいて求めた温度の単位パルス応答の時系列データを配列した温度の影響度行列Ctempを求め、
所定の目標値が与えられて制御された安定状態での操作量の時系列データと前記多点の温度の時系列データを取得し、
該安定状態での操作量の時系列データを配列した既知操作量ベクトルMrefと、該安定状態での前記多点の温度の時系列データを配列した既知温度ベクトルTrefを求め、
最小化する評価関数を制御対象の前記多点の予測温度の平均温度に対する分散に基づく関数とし、該評価関数のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
第1制約条件を、操作量が予め定められた範囲に収まることとし、該第1制約条件のパラメータを操作量の影響度行列Cmvと既知操作量ベクトルMrefから算出し、
第2制約条件を、予め定められた時間における前記多点の平均温度が目標値又は修正目標値になることとし、該第2制約条件のパラメータを、温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
前記第1及び第2制約条件の下で前記評価関数を最小化する目標値の修正量を算出する制御系設計装置。 - 前記修正量算出部は、
第3制約条件を、前記多点の平均温度が所望の整定時間で目標値又は修正目標値になることとし、該第3制約条件のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
前記第1乃至第3制約条件の下で前記評価関数を最小化する目標値の前記修正量ベクトルθを算出する
請求項4に記載の制御系設計装置。 - 前記修正量算出部は、
前記評価関数F(θ)を次式(1)で表したときのパラメータQ、p及びrを、温度の影響度行列Ctempと既知温度ベクトルTrefから次式(2)で算出し、
前記制約条件を次式(5)で表したときのパラメータAin、Aub、Aeq及びbeqを、操作量の影響度行列Cmvと、温度の影響度行列Ctempと、既知操作量ベクトルMrefと、既知温度ベクトルTrefから次式(6)で算出し、
前記評価関数と前記制約条件で表される凸二次計画問題を予め定められた手法で解くことで目標値の修正量ベクトルθを算出する請求項5に記載の制御系設計装置。
SVp:安定を判断する目標値の上限値
SVn:安定を判断する目標値の下限値
e1:lmax×入力チャンネル数のベクトルであって、各要素が1のベクトル
lmax:1入力チャンネルに対して予測する温度の時系列データ数
e3:(lmax-z)×出力チャンネル数のベクトルであって、各要素が1のベクトル
z:整定時間までのデータ数に相当する数
θ:修正量を表すベクトル
N:出力チャンネル数
0(x、y):対応する行及び列を0で満たすx行y列の行列又はベクトル
SVlast:目標温度変更後の最終的な目標値又は修正目標値
Kt3:時刻t3の要素を抽出するための係数ベクトル - 制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する多点制御系に対して、前記目標値の修正量を設計する制御系設計装置であって、
前記目標値の修正量を算出する修正量算出部
を備え、
前記修正量算出部は、
複数の入力チャンネルの目標値を順次変化させたときの、各入力チャンネルの変化に対する操作量の時系列データと制御対象における多点の温度の時系列データを取得し、
該操作量の時系列データに基づいて求めた操作量の単位パルス応答の時系列データを配列した操作量の影響度行列Cmvと、前記多点の温度の時系列データに基づいて求めた温度の単位パルス応答の時系列データを配列した温度の影響度行列Ctempを求め、
所定の目標値が与えられて制御された安定状態での操作量の時系列データと前記多点の温度の時系列データを取得し、
該安定状態での操作量の時系列データを配列した既知操作量ベクトルMrefと、該安定状態での前記多点の温度の時系列データを配列した既知温度ベクトルTrefを求め、
最小化する評価関数を制御対象の前記多点の各予測温度と前記多点の平均温度との差幅の最大値dとし、
第1制約条件を、操作量が予め定められた範囲に収まることとし、該第1制約条件のパラメータを操作量の影響度行列Cmvと既知操作量ベクトルMrefから算出し、
第2制約条件を、予め定められた時間における前記多点の平均温度が目標値又は修正目標値になることとし、該第2制約条件のパラメータを、温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
第4制約条件を、制御対象の前記多点の各予測温度と前記多点の平均温度との差Enが、前記差幅の最大値dに対して-d以上+d以下になることとし、該第4制約条件のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
前記第1、第2及び第4制約条件の下で前記評価関数を最小化する目標値の修正量を算出する制御系設計装置。 - 前記修正量算出部は、
第3制約条件を、前記多点の平均温度が所望の整定時間で目標値になることとし、該第3制約条件のパラメータを温度の影響度行列Ctempと既知温度ベクトルTrefから算出し、
前記第1乃至第4制約条件の下で前記評価関数を最小化する目標値の前記修正量ベクトルθを算出する請求項7に記載の制御系設計装置。 - 前記修正量算出部は、
前記制約条件を次式(7)で表したときのパラメータAin、Aub、Aeq及びbeqを、操作量の影響度行列Cmvと、温度の影響度行列Ctempと、既知操作量ベクトルMrefと、既知温度ベクトルTrefとから次式(8)で算出し、
前記評価関数と前記制約条件で表される線形計画問題を予め定められた手法で解くことで目標値の修正量ベクトルθを算出する請求項8に記載の制御系設計装置。
SVn:安定を判断する目標値の下限値
e1:lmax×入力チャンネル数のベクトルであって、各要素が1のベクトル
lmax:1入力チャンネルに対して予測する温度の時系列データ数
e3:(lmax-z)×出力チャンネル数のベクトルであって、各要素が1のベクトル
z:整定時間までのデータ数に相当する数
e4:lmax×出力チャンネル数のベクトルであって、各要素が1のベクトル
θ:修正量を表すベクトル
N:出力チャンネル数
0(x、y):対応する行及び列を0で満たすx行y列の行列又はベクトル
Ilmax:(lmax×lmax)の単位行列
SVlast:目標温度変更後の最終的な目標値又は修正目標値
Kt3:時刻t3の要素を抽出するための係数ベクトル - 制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する制御器と、
請求項1乃至3のいずれかに記載の制御系設計装置と、
外乱を検出した際に前記制御系設計装置で算出された修正量に基づく修正パターンを出力する修正パターン適用部と、
予め設定される前記目標値と、前記修正パターン適用部からの修正パターンを加えて前記修正目標値を求めて前記制御器に与える加算器と
を備えた制御システム。 - 制御対象における多点の温度を制御し、予め設定される目標値を与えられる修正量に応じて修正した修正目標値に従い制御対象を制御する制御器と、
請求項4乃至9のいずれかに記載の制御系設計装置と、
目標温度の変更を検出した際又は目標温度を変更する際に前記制御系設計装置で算出された修正量に基づく修正パターンを出力する修正パターン適用部と、
予め設定される前記目標値と、前記修正パターン適用部からの修正パターンを加えて前記修正目標値を求めて前記制御器に与える加算器と
を備えた制御システム。
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