EP3304223A1 - Procédé et appareil permettant la mise au point robuste de régisseurs de processus basés sur des modèles et utilisés avec des processus à entrée multiple sortie multiple (mimo) incertains - Google Patents

Procédé et appareil permettant la mise au point robuste de régisseurs de processus basés sur des modèles et utilisés avec des processus à entrée multiple sortie multiple (mimo) incertains

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Publication number
EP3304223A1
EP3304223A1 EP16802269.7A EP16802269A EP3304223A1 EP 3304223 A1 EP3304223 A1 EP 3304223A1 EP 16802269 A EP16802269 A EP 16802269A EP 3304223 A1 EP3304223 A1 EP 3304223A1
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EP
European Patent Office
Prior art keywords
time
tuning
controller
mimo
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
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EP16802269.7A
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German (de)
English (en)
Other versions
EP3304223A4 (fr
Inventor
Ning He
Dawei Shi
Michael Forbes
Johan U. Backstrom
Tongwen Chen
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Honeywell Ltd Canada
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Honeywell Ltd Canada
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Priority claimed from US14/729,930 external-priority patent/US9971318B2/en
Application filed by Honeywell Ltd Canada filed Critical Honeywell Ltd Canada
Publication of EP3304223A1 publication Critical patent/EP3304223A1/fr
Publication of EP3304223A4 publication Critical patent/EP3304223A4/fr
Withdrawn legal-status Critical Current

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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
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
    • 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
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/26—Pc applications
    • G05B2219/2646—Printing

Definitions

  • This disclosure relates generally to industrial process control systems. More specifically, this disclosure relates to a method and apparatus for robust tuning of model-based process controllers used with uncertain multiple-input, multiple- output (MIMO) processes.
  • MIMO multiple-input, multiple- output
  • Model predictive control (MPC) techniques use one or more models to predict the future behavior of an industrial process. Control signals for adjusting the industrial process are then generated based on the predicted behavior. MPC techniques have become widely accepted in various industries, such as the oil and gas, pulp and paper, food processing, and chemical industries.
  • This disclosure provides a method and apparatus for robust tuning of model-based process controllers used with uncertain multiple-input, multiple-output (MIMO) processes.
  • MIMO multiple-input, multiple-output
  • a method in a first embodiment, includes obtaining information identifying (i) uncertainties associated with multiple time-domain parameters of a model and (ii) time-domain performance specifications for a model-based industrial process controller.
  • the model mathematically represents a MIMO industrial process.
  • the method also includes generating multiple tuning parameters for the controller based on the uncertainties and the time-domain performance specifications.
  • the tuning parameters include vectors of tuning parameters associated with the controller, and each vector includes values associated with different outputs of the industrial process.
  • an apparatus in a second embodiment, includes at least one memory configured to store information identifying (i) uncertainties associated with multiple time-domain parameters of a model and (ii) time-domain performance specifications for a model-based industrial process controller.
  • the model mathematically represents a MIMO industrial process.
  • the apparatus also includes at least one processing device configured to generate multiple tuning parameters for the controller based on the uncertainties and the time-domain performance specifications.
  • the tuning parameters include vectors of tuning parameters associated with the controller, and each vector includes values associated with different outputs of the industrial process.
  • a non-transitory computer readable medium contains instructions that when executed cause at least one processing device to obtain information identifying (i) uncertainties associated with multiple time-domain parameters of a model and (ii) time-domain performance specifications for a model- based industrial process controller.
  • the model mathematically represents a MIMO industrial process.
  • the instructions when executed also cause at least one processing device to generate multiple tuning parameters for the controller based on the uncertainties and the time-domain performance specifications.
  • the tuning parameters include vectors of tuning parameters associated with the controller, and each vector includes values associated with different outputs of the industrial process.
  • FIGURE 1 illustrates an example web manufacturing or processing system according to this disclosure
  • FIGURE 2 illustrates an example internal model control structure employed for model predictive control (MPC) of an uncertain multiple-input, multiple-output (MIMO) process according to this disclosure
  • FIGURES 3A through 5B illustrate details of an example technique for robust tuning of a model-based process controller used with an uncertain MIMO process according to this disclosure.
  • FIGURES 1 through 5B discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. Those skilled in the art will understand that the principles of the invention may be implemented in any type of suitably arranged device or system.
  • This disclosure provides techniques that support robust tuning of MPC and other model-based controllers that are used with multiple-input, multiple-output (MIMO) multivariable processes having model uncertainty.
  • MIMO multiple-input, multiple-output
  • a specific example described below involves robust tuning of machine-direction (MD) MPC controllers for paper or other web manufacturing or processing systems.
  • MD machine-direction
  • these techniques can be used to achieve satisfactory closed-loop responses that are quantified by characteristics such as overshoots, total variations, and settling times under parametric uncertainty within a limited tuning time.
  • An efficient visualization technique for an uncertain MIMO process is described to characterize the set of possible step responses for outputs of the MIMO process due to the parametric uncertainty.
  • the tuning problem can be formulated as an optimization problem with an implicit objective function and constraints. Based on the visualization technique and properties of performance indices, an automatic tuning algorithm is described to solve the optimization problem. In addition, a technique to predict the computation time of the tuning algorithm is described, which could be used to improve user- friendlines
  • Example features of the techniques can include:
  • an algorithm (such as a MATLAB algorithm) that provides robust performance envelope visualization for a multivariable process.
  • a user interface can be provided that allows users to enter model uncertainly specifications and performance specifications.
  • the user interface can also allow users to view resulting tuning parameters and visualize the resulting controller performance.
  • FIGURE 1 illustrates an example web manufacturing or processing system 100 according to this disclosure.
  • the system 100 includes a paper machine 102, a controller 104, and a network 106.
  • the paper machine 102 includes various components used to produce a paper product namely a paper web 108 that is collected at a reel 1 10.
  • the controller 104 monitors and controls the operation of the paper machine 102, which may help to maintain or increase the quality of the paper web 108 produced by the paper machine 102.
  • the machine direction (MD) of the web 108 denotes the direction along the (longer) length of the web 108.
  • the paper machine 102 includes at least one headbox 1 12, which distributes a pulp suspension uniformly across the machine onto a continuous moving wire screen or mesh 1 13.
  • the pulp suspension entering the headbox 1 12 may contain, for example, 0.2-3% wood fibers, fillers, and/or other materials, with the remainder of the suspension being water.
  • An array of steam actuators 1 16 produces hot steam that penetrates the paper web 108 and releases the latent heat of the steam into the paper web 108.
  • An array of rewet shower actuators 1 18 adds small droplets of water (which may be air atomized) onto the surface of the paper web 108.
  • the paper web 108 is then often passed through a calender having several nips of counter-rotating rolls.
  • Arrays of induction heating actuators 120 heat the shell surfaces of various ones of these rolls.
  • a thick stock flow actuator 122 controls the consistency of incoming stock received at the headbox 1 12.
  • a steam flow actuator 124 controls the amount of heat transferred to the paper web 108 from drying cylinders.
  • the actuators 122-124 could, for example, represent valves controlling the flow of stock and steam, respectively. These actuators may be used for controlling the dry weight and moisture of the paper web 108. Additional flow actuators may be used to control the proportions of different types of pulp and filler material in the thick stock and to control the amounts of various additives (such as retention aid or dyes) that are mixed into the stock.
  • one or more properties of the paper web 108 may be continuously or repeatedly measured.
  • the web properties can be measured at one or various stages in the manufacturing process. This information may then be used to adjust the paper machine 102, such as by adjusting various actuators within the paper machine 102. This may help to compensate for any variations of the web properties from desired targets, which may help to ensure the quality of the web 108.
  • the paper machine 102 includes one or more scanners 126-128, each of which may include one or more sensors.
  • Each scanner 126- 128 is capable of measuring one or more characteristics of the paper web 108.
  • each scanner 126-128 could include sensors for measuring the tension, caliper, moisture, anisotropy, basis weight, color, gloss, sheen, haze, surface features (such as roughness, topography, or orientation distributions of surface features), or any other or additional characteristics of the paper web 108.
  • Each scanner 126-128 includes any suitable structure or structures for measuring or detecting one or more characteristics of the paper web 108, such as one or more sets of sensors.
  • the use of scanners represents one particular embodiment for measuring web properties.
  • Other embodiments could be used, such as those including one or more stationary sets or arrays of sensors, deployed in one or a few locations across the web or deployed in a plurality of locations across the whole width of the web such that substantially the entire web width is measured.
  • the controller 104 receives measurement data from the scanners 126- 128 and uses the data to control the paper machine 102. For example, the controller 104 may use the measurement data to adjust any of the actuators or other components of the paper machine 102.
  • the controller 104 includes any suitable structure for controlling the operation of at least part of the paper machine 102, such as a computing device. Note that while a single controller 104 is shown here, multiple controllers 104 could be used, such as different controllers that control different variables of the web.
  • the network 106 is coupled to the controller 104 and various components of the paper machine 102 (such as the actuators and scanners).
  • the network 106 facilitates communication between components of the system 100.
  • the network 106 represents any suitable network or combination of networks facilitating communication between components in the system 100.
  • the network 106 could, for example, represent a wired or wireless Ethernet network, an electrical signal network (such as a HART or FOUNDATION FIELDBUS network), a pneumatic control signal network, or any other or additional network(s).
  • the controller(s) 104 can operate to control one or more aspects of the paper machine 102 using one or more models.
  • each model could associate one or more manipulated variables with one or more controlled variables.
  • a controlled variable generally represents a variable that can be measured or inferred and that is ideally controlled to be at or near a desired setpoint or within a desired range of values.
  • a manipulated variable generally represents a variable that can be adjusted in order to alter one or more controlled variables.
  • At least one operator console 130 can communicate with the controller 104 over a network 132.
  • the operator console 130 generally represents a computing device that supports one or more techniques for robust tuning of MPC and other model-based controllers that are used to control MIMO processes having model uncertainty.
  • the techniques for robust tuning of model-based controllers are described in more detail below.
  • the techniques for robust tuning generally involve identifying tuning parameters for a controller and outputting the tuning parameters to the controller for use during subsequent control operations.
  • the network 132 represents any suitable network or combination of networks that can transport information, such as an Ethernet network.
  • the operator console 130 includes one or more processing devices 134, one or more memories 136, and one or more interfaces 138.
  • Each processing device 134 includes any suitable processing or computing device, such as a microprocessor, microcontroller, digital signal processor, field programmable gate array, application specific integrated circuit, or discrete logic devices.
  • Each memory 136 includes any suitable storage and retrieval device, such as a random access memory (RAM) or Flash or other read-only memory (ROM).
  • Each interface 138 includes any suitable structure facilitating communication over a connection or network, such as a wired interface (like an Ethernet interface) or a wireless interface (like a radio frequency transceiver).
  • the operator console 130 is described as implementing the technique(s) for robust tuning of model-based controllers, other types of devices could also be used.
  • the operator console 130 could interact with a server 140, and the server 140 could actually execute the algorithms used to implement one or more techniques for robust tuning of model-based controllers.
  • the operator console 130 could present a graphical user interface and interact with a user.
  • the server 140 could include one or more processing devices, one or more memories, and one or more interfaces (similar to the operator console 130).
  • FIGURE 1 illustrates one example of a web manufacturing or processing system 100
  • various changes may be made to FIGURE 1 .
  • other systems could be used to produce other paper or non-paper products.
  • the system 100 could include any number of paper machines or other machinery having any suitable structure, and the system 100 could include any number of controllers.
  • FIGURE 1 illustrates one example operational environment in which MPC or other model-based controller(s) can be tuned. This functionality could be used in any other suitable system, regardless of whether the system is used to manufacture or process webs of material.
  • the parameter tuning problem for an MPC or other model-based controller is often challenging, and it becomes even more challenging when MIMO processes are considered.
  • One conventional approach for parameter tuning of an MPC controller is to fix all MPC tuning parameters except one in order to identify a tuning problem with one degree of freedom (1DOF). By adjusting this parameter, an analysis of the relationship between the closed-loop performance of the controller and the corresponding degree of freedom can occur, and some tuning guidelines can be developed based on this type of analysis.
  • MPC parameters for a MIMO system can be tuned by solving two semi-definite programming problems sequentially in order to achieve a desired closed-loop performance.
  • controller parameters are tuned by matching an unconstrained MIMO MPC with a preassigned multivariable controller so that the properties of the preassigned controller could be inherited.
  • Still other conventional approaches have involved a tuning-friendly MPC framework in which a tuning parameter is used to adjust a controller's performance.
  • a user-friendly tuning approach for uncertain MIMO processes is still missing.
  • U.S. Patent Application Serial No. 13/907,495 discloses a two degree of freedom (2DOF) MPC tuning framework.
  • U.S. Patent Application Serial No. 14/314,221 uses this framework to, among other things, provide for robust tuning of a single-input, single-output (SISO) system.
  • SISO single-input, single-output
  • This disclosure uses the 2DOF MPC tuning framework to help simplify the tuning of MPC or other model-based controllers for MIMO systems with some model uncertainty associated with the MIMO systems.
  • FIGURE 2 illustrates an example internal model control structure 200 employed for MPC of an uncertain MIMO process according to this disclosure.
  • This closed-loop system includes three main parts: a process model (Go) 202, an MPC controller 204, and user-specified filters (F r and Fd) 206-208.
  • the process model 202 is used to mathematically represent a multivariable MIMO process (G p ) 210.
  • G p multivariable MIMO process
  • time delay 212 associated with feedback in the closed-loop system, which is shown here as a first-order delay but could include delay(s) of other or additional order(s).
  • G p ⁇ m X n and Go e m X n are transfer function matrices of the real industrial process and the nominal process model, respectively.
  • all subsystems in G p and Go have a first-order-plus-dead-time (FOPDT) structure. Therefore, the real process G 210 can be represented as:
  • G p (s) is typically not known with exact certainty.
  • a nominal model Go(s) can be identified as an approximation of G p (s).
  • the nominal model Go(s) could be expressed as:
  • k ⁇ , and T? can be obtained from a process identification software tool based on input/output data of the real process or in any other suitable manner.
  • Parametric uncertainty can be modeled in the following form:
  • H u denote the control horizon
  • H p denote the prediction horizon (where 1 ⁇ H u ⁇ H p ).
  • the MPC controller 204 in FIGURE 2 operates to solve the following finite-horizon optimal control problem:
  • U re f and Y re f are reference signal vectors of U Hu and ⁇ , respectively, and Qi,
  • Q 2 , and Q 3 are weighting matrices.
  • the two user-specified filters F r and Fa 206-208 in FIGURE 2 are used respectively for filtering an output target y tg t(k) and an estimated disturbance — !j(k) - ij(k)), which constitute the MIMO 2DOF MPC structure.
  • the reference trajectory Y re f(k) can be calculated as follows:
  • F r (-) and F d ( ) are projection filters generated according to f r (z) and fd(z), and where d (z).
  • f r (z) and fd(z) denote a reference tracking filter and a disturbance rejecting filter, which in some embodiments can be defined as follows:
  • ⁇ [ ⁇ , ⁇ 2 , X m ] as the reference tracking performance ratio vector, and define fd(z) as having the following form:
  • a reference tracking performance ratio defines a ratio between a desired closed-loop reference tracking response time of a controller and an open-loop response time of an industrial process.
  • a disturbance rejection performance ratio defines a ratio between a desired closed-loop disturbance rejecting response time of a controller and the open-loop response time of the industrial process.
  • Qi 1
  • Q 2 0.01 x I
  • Q j 0, although other values could be used.
  • one part of the 2DOF MPC tuning problem is the design of f r ,i(z) and fd,i(z) in Equations (9) and (10).
  • the design of fr,j(z) is based on, given the i th output, the open-loop transfer function from the input that dominates the output that is selected to construct this filter.
  • One reason for this is to make the speed of the closed-loop response dependent on the speed of the dominant or primary open-loop response of the system according to the requirements for a specific product being produced.
  • fd,i(z) the same design procedure can be applied, except that ⁇ ⁇ ⁇ , ⁇ can be used instead of ⁇ such that the output target and the estimated disturbance can be filtered separately.
  • ⁇ and ⁇ ⁇ ⁇ are vectors with appropriate dimensions and are utilized to tune the closed-loop performance of the control structure 200, instead of (or in addition to) tuning the weighting matrices in an MPC cost function.
  • Performance indices are specified via values such as overshoot, total variation, and settling time for each output of the MIMO process. This maintains the user-friendliness of the proposed tuning approach.
  • the expressions of the closed-loop responses typically cannot be obtained explicitly, and the tuning problem is therefore difficult to formulate.
  • the complexity of the tuning problem can increase based on the system's size, and the relationship between the ⁇ -parameters and each output of the MIMO system can be unclear.
  • the computation time of the tuning procedure should not only be limited by a specified amount of time but also be predictable without running the algorithm.
  • the operator console 130, server 140, or other component(s) support an efficient heuristic approach to find a solution to the tuning problem for an MPC or other model-based controller used with an uncertain MIMO process. This approach supports the following capabilities.
  • the tuning problem is cast into a constrained optimization problem and then transformed into a number of individual multiple-input, single-output (MISO) tuning problems, based on which the tuning problem is simplified.
  • MISO multiple-input, single-output
  • the overshoot, total variation, and settling time of each output can be considered as tuning measurements. Since the parametric uncertainty defined in Equation (3) results in a set of perturbed systems, the worst- case time-domain performance indices can be employed. Definitions for the worst- case overshoot, settling time, and total variation are as follows.
  • the worst-case overshoot OS of a set of step responses with the same final value is the maximum value in all responses minus the final value divided by the final value.
  • the worst-case settling time T s of a set of step responses with the same final value is the minimum time required for all responses to reach and stay within a range of a pre-specified percentage of the final value.
  • the worst-case total variation TV assuming the system converges to a target value within n steps, is:
  • the tuning time (denoted t ) can be an important factor in a successful industrial process controller tuner design.
  • the total time consumption of a tuning algorithm should not be more than half a minute, and in some embodiments this requirement can be considered as a hard constraint for the tuning algorithm disclosed in this patent document.
  • tuning time is normally not considered in existing MIMO tuning algorithms because (i) the limited computation time might affect the feasibility of these algorithms and (ii) the computation time is normally not predictable.
  • a hard constraint on the tuning time can further increase the difficulty of solving the MIMO tuning problem.
  • some objectives of the tuning algorithm disclosed here include (i) determining ⁇ and so that a closed-loop system (such as that shown in FIGURE 2) is robustly stable and all outputs track their targets with fast responses, small overshoots, and small total variations, (ii) doing so within an acceptable tuning time, and (iii) doing so under the parametric uncertainties defined in Equation (3).
  • the tuning problem can be formulated as:
  • ⁇ [ ⁇ , ⁇ 2 , X m ] and [Xd,i, Xd, 2 , ⁇ , , m ].
  • ⁇ and Xd are tuned by minimizing the worst-case settling times of all outputs with the corresponding worst-case OS and TV lying within certain tolerable regions.
  • the tuning time may be no more than half a minute ( ⁇ ⁇ 30s).
  • ENVELOPE ALGORITHM MIMO SYSTEMS
  • This section describes a performance visualization technique to obtain the worst-case overshoots, settling times, and total variations for the outputs of a MIMO system.
  • One goal here is to graphically characterize the envelopes of the responses of a set of MIMO systems satisfying G p (s)ell given the values of ⁇ and Xd.
  • the approach mentioned above may not be used directly with a MIMO process due to the following factors.
  • the number of extreme-case systems depends on the number of model parameters and becomes a large number even for a low-dimensional MIMO system (for instance, a 2-by-2 system includes four FOPDT subsystems and thus requires 84 extreme-case systems).
  • the computation time of the visualization method in the approach mentioned above increases rapidly as the number of extreme-case systems increases.
  • the tuning procedure should be short (such as less than 30 seconds) and the performance visualization is only a small step in the overall tuning procedure, the computation time allowed for obtaining the envelopes may be very limited.
  • the parameters of a MIMO system can be defined as follows:
  • Equation (3) the MIMO system with the parametric uncertainty as defined in Equation (3) can be approximated as:
  • VE : ⁇ G p (s) :k € ⁇ k. k ⁇ . r e ⁇ r. r ⁇ .
  • the envelopes of the step responses of a MIMO system with an MPC or other model-based controller can be obtained using the algorithm shown in Table I below. Although this approach may not be guaranteed to be optimal, it is intuitive in that the extreme behavior of the step responses mostly happens when all extreme process parameters are reached simultaneously. The effectiveness of this algorithm has been verified via extensive simulations.
  • the tuning algorithm represents an iterative tuning procedure that determines the values of ⁇ and X ⁇ j based on the visualization technique described in the prior section.
  • the relationship between the ⁇ -parameters and the performance indices of each output, such as 08 ⁇ ( ⁇ , d) and T s ,i(X, ⁇ ) in Equation (12) is explored.
  • an empirical analysis can be carried out to aid the tuning procedure.
  • the closed-loop system's behavior is governed by the F r and F d filters 206-208.
  • both filters 206-208 have diagonal structures and ⁇ and ⁇ ⁇ ⁇ only exist on the diagonal entries, it is intuitive to assume that the closed-loop response of the i th output is dominated by the i th elements in ⁇ and ⁇ (which are denoted ⁇ and ⁇ , ⁇ ).
  • the corresponding F r and Fd filters 206-208 can be designed based on the dominant or primary open-loop system producing that output.
  • OSi( , ⁇ ) and T s, i(X, ⁇ ) are functions of only ⁇ and ⁇
  • T s ,i( , ⁇ ) ⁇ ⁇ , ⁇ ( ⁇ , ⁇ ⁇ , ⁇ ).
  • FIGURES 3A and 3B Examples of these properties are illustrated in FIGURES 3A and 3B via a typical 2-by-3 MD process.
  • FIGURE 3 A illustrates a numerical verification of OS,( , ⁇ )
  • FIGURE 3B illustrates a numerical verification of ⁇ ⁇ ⁇ , Xd).
  • OS OS
  • FIGURE 3A illustrates a numerical verification of OS
  • FIGURE 3B illustrates a numerical verification of ⁇ ⁇ ⁇ , Xd.
  • FIGURES 3A and 3B two observations can be made. First, from the right graphs in FIGURES 3A and 3B, it can be seen that the adjustment of ⁇ and ⁇ , ⁇ does not affect the overshoot and settling time of the second output significantly if at all, which verifies the idea above. Second, the overshoot could be empirically treated as a monotonic function of ⁇ , and the settling time could be considered as a unimodal function of ⁇ , which can basically be determined by the 2DOF MPC structure.
  • Equation (12) the tuning problem in Equation (12) can be simplified from a MIMO tuning problem to m individual MISO tuning problems in which ⁇ and ⁇ , ⁇ are tuned for the i th output separately.
  • the new MISO tuning problem can be expressed as:
  • a MIMO tuning algorithm can solve all MISO tuning problems simultaneously by searching for the optimal ⁇ -parameters for all of the MISO systems along m identical counter-lines at the same time. Because of this, the proposed tuning algorithm is almost as fast as solving only one MISO tuning problem. The fast algorithm is feasible because the counter-line searching is based on the worst-case performance indices calculated by Algorithm 1 and, when Algorithm 1 is executed, the performance indices are computed for all of the MISO systems.
  • the MIMO tuning algorithm described below includes two sub-algorithms.
  • Algorithm 2 Find A c (TV * ,A d ) and T ⁇ (TV * ; A d ).
  • the worst-case settling time can be approximately a unimodal function of ⁇ , ⁇ .
  • the underlying assumption is that X ⁇ i,i controls the robust stability, so a smaller Xd,i leads to an aggressive and oscillatory response while a larger leads to a sluggish response.
  • the fast tuning algorithm described above not only solves the MIMO tuning problem efficiently, it also provides the ability to accurately predict the tuning time.
  • the ability to accurately predict the tuning time is highly demanded or desired with algorithms designed for commercial tuner software because the user-friendliness can be improved.
  • the proposed tuning algorithm is a line search- based method, the computation time can be estimated based on the number of iterations needed for convergence and the time required for each iteration. The number of iterations may only depend on the predefined search region and stop criteria, and the iteration time can be decided by the time required for numerically evaluating the performance indices (the duration of which can be computed based on the time required to call Algorithm 1 , which can also be pre-calculated).
  • the tuning time can be predicted with Algorithm 4 in Table IV. ] ⁇ ⁇
  • Algorithm 4 Predict t ⁇ ( ⁇ , A d ). l : Input A d , ⁇ and the uncertainty intervals [k, fe], [ ⁇ , ⁇ ] and [T, T] ;
  • ⁇ ⁇ (( ⁇ ⁇ ⁇ ⁇ + ⁇ .3 ⁇ 4 ) ⁇ 2 + ⁇ ⁇ , ⁇ X (IA X TV + TJ) ⁇ ; 1 1 : end
  • NTV and N T are the numbers of extreme-case systems considered to calculate the total variation and the settling time. According to Algorithm 1, both values can be eight by default, but the number of extreme-case systems considered in Algorithm 1 can be optimized to further save computation time.
  • tp is the time cost for a single run of the simulation (based on which the running time of Algorithm 1 can be obtained). As a computer may need more time to run a program for the first time, the average of multiple runs (such as three) can be used as the simulation time.
  • ⁇ (line 7) and ⁇ ⁇ (line 9) are the iteration numbers for Algorithm 2 and 3, respectively. The formula in line 10 is constructed based on the structure of the tuning algorithm.
  • the proposed tuning algorithm is illustrated with reference to an example extracted from a real application involving MD paper machine control.
  • the example illustrates the efficiency of the proposed algorithms.
  • this example involves a 2-by-3 process of a paper machine, where a controller uses a model to control the Conditioned Weight (CW) and Moisture (M) of paper products.
  • Inputs to the process are Base Stock Flow (SF) to the headbox, Main Steam (MS) in the drying cylinders, and Machine Speed (S).
  • SF Base Stock Flow
  • MS Main Steam
  • S Machine Speed
  • This model was identified using an advanced industrial control software package.
  • the prediction horizon H p is 68, and the control horizon H u is 27.
  • the tuning procedure took 9.56 seconds on a desktop computer with an i5 processing core and 6GB of memory, and the predicted tuning time from Algorithm 4 was 10.00 seconds.
  • the obtained closed-loop step response envelopes as well as the tuning results are shown in FIGURES 4A and 4B for all outputs.
  • the MPC optimization parameters H p , H u , Qi, Q 2 , and Q 3 are chosen to be the same as those used for the above tuning results, and the following constraints on control signals are incorporated in the MPC implementation:
  • model-based controller may or may not be used in a web manufacturing or processing system since MPC and other model-based controllers can be used in a wide variety of industries.
  • the same or similar techniques could be used to tune any suitable model-based controller in any suitable industry.
  • various functions described above are implemented or supported by a computer program that is formed from computer readable program code and that is embodied in a computer readable medium.
  • computer readable program code includes any type of computer code, including source code, object code, and executable code.
  • computer readable medium includes any type of medium capable of being accessed by a computer, such as read only memory (ROM), random access memory (RAM), a hard disk drive, a compact disc (CD), a digital video disc (DVD), or any other type of memory.
  • ROM read only memory
  • RAM random access memory
  • CD compact disc
  • DVD digital video disc
  • a “non-transitory” computer readable medium excludes wired, wireless, optical, or other communication links that transport transitory electrical or other signals.
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Abstract

Selon la présente invention, un procédé consiste à obtenir des informations qui identifient (i) des incertitudes associées à plusieurs paramètres de domaine temporel d'un modèle (202), et (ii) des spécifications de performances de domaine temporel pour un régisseur de processus industriel (104, 204) basé sur des modèles. Le modèle représente mathématiquement un processus industriel MIMO (210). Le procédé consiste également à générer plusieurs paramètres de mise au point pour le régisseur sur la base des incertitudes et des spécifications de performances de domaine temporel. Les paramètres de mise au point incluent des vecteurs de paramètres de mise au point associés au régisseur, et chaque vecteur comprend des valeurs associées à des sorties différentes du processus industriel. Les paramètres de domaine temporel peuvent inclure un gain de processus, une constante de temps, et un délai pour chaque paire entrée-sortie du modèle. Les spécifications de performances de domaine temporel peuvent comprendre des exigences relatives aux dépassements dans le pire cas, aux temps de stabilisation et aux variations totales. Les incertitudes peuvent être spécifiées sous la forme d'intervalles où se trouvent les paramètres de domaine temporel.
EP16802269.7A 2015-06-03 2016-05-18 Procédé et appareil permettant la mise au point robuste de régisseurs de processus basés sur des modèles et utilisés avec des processus à entrée multiple sortie multiple (mimo) incertains Withdrawn EP3304223A4 (fr)

Applications Claiming Priority (2)

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US14/729,930 US9971318B2 (en) 2014-03-18 2015-06-03 Method and apparatus for robust tuning of model-based process controllers used with uncertain multiple-input, multiple-output (MIMO) processes
PCT/CA2016/000153 WO2016191849A1 (fr) 2015-06-03 2016-05-18 Procédé et appareil permettant la mise au point robuste de régisseurs de processus basés sur des modèles et utilisés avec des processus à entrée multiple sortie multiple (mimo) incertains

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EP3304223A1 true EP3304223A1 (fr) 2018-04-11
EP3304223A4 EP3304223A4 (fr) 2019-01-23

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US6697767B2 (en) * 2000-10-18 2004-02-24 The National University Of Singapore Robust process identification and auto-tuning control
US7650195B2 (en) * 2005-10-27 2010-01-19 Honeywell Asca Inc. Automated tuning of large-scale multivariable model predictive controllers for spatially-distributed processes
CN101925866B (zh) * 2008-01-31 2016-06-01 费希尔-罗斯蒙特系统公司 具有用来补偿模型失配的调节的鲁棒的自适应模型预测控制器
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