Classifications

• • 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
  • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
  • G05B13/0275—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using fuzzy logic only
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
  • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10S706/00—Data processing: artificial intelligence
  • Y10S706/90—Fuzzy logic

Definitions

• Fuzzy logic control has been widely applied to the industrial environment in recent years. Although many of the applications are relatively small in scale, such as in washing machines, elevators, automobiles and video cameras, there is a considerable amount of interest in applying fuzzy logic systems to process control. In the field of process control, research has been conducted into the use of FLCs similar to
• PID Proportional Integral, Derivative
• the present invention provides a method and apparatus for fuzzy logic control which incorporates automatic self-tuning, thus satisfying the abovenoted discrepancies in prior approaches.
• the present invention contemplates an automatically tunable fuzzy logic controller.
• the dynamic characteristics of the process under control are determined and are used to calculate process control parameters for application to the fuzzy logic controller to control the process.
• a fuzzy logic controller is employed for controlling a process by selectively connecting the output of the fuzzy logic controller to the process under control.
• the fuzzy logic controller is tuned by disconnecting the fuzzy logic controller from the process, and by applying to the process a controllable signal generator which causes the process to undergo controlled induced
• tuning module determines how to calculate control parameters within the fuzzy logic controller in order to optimally tune the fuzzy logic controller to control the process under consideration.
• the signal generator is then disconnected, and the tuned fuzzy logic controller is then reconnected in order to control the process.
• a fuzzy logic controller which is employed for process control is tuned by injecting a perturbation signal into the closed loop including the fuzzy logic controller and process to cause the process to undergo controlled induced oscillation. Then, during induced oscillation, the process is monitored by a tuning module and dynamic
• controller then controls the process in a closed-loop fashion.
• a fuzzy logic controller is tuned by a tuning module by determining the dynamic process characteristics using a pattern recognition tuning method which analyzes the response of the process to process upset conditions, and from the response calculates dynamic process characteristics. Then, from these dynamic process characteristics, control parameters for the fuzzy logic controller are determined in order to optimally tune the fuzzy logic controller to control the process.
• the tuning module may employ a model matching tuning method to determine dynamic process characteristics.
• the dynamic process characteristics determined during the tuning procedure may include, for example, the ultimate gain, ultimate period and time delay of the process.
• the control parameters which are determined from the dynamic process are determined from the dynamic process
• characteristics may include, for example, a control error scaling factor, a change in control error scaling factor and a control action scaling factor.
• Figure 1 is a block diagram of a fuzzy logic controller.
• Figure 2 is a block diagram of an automatically tunable fuzzy logic controller connected to a process in a closed loop process controlled system, in accordance with the present invention.
• Figure 3 is a block diagram of an exemplary embodiment of an automatically tunable fuzzy logic controller for controlling a process, in accordance with the present invention.
• FIG. 4 is a block diagram of another
• Figure 5 is a block diagram of yet another embodiment of an automatically tunable fuzzy logic controller system for controlling a process, in accordance with the present invention.
• Figures 6A and B are graphs of a process input and process output signal during controlled induced oscillation tuning of the fuzzy logic controller, in accordance with the present invention.
• Figures 7A, B, C and D illustrate exemplary membership functions, used in the fuzzy logic controller of the present invention.
• Figures 8A and B are tabular representations of exemplary fuzzy logic controller rules used in the present invention.
• Figures 9A and B are an exemplary block diagram and a corresponding mathematical model of a process which is controlled to illustrate the advantages of the present invention.
• Figures 10A, B, C and D are graphs illustrating the comparative performance of the fuzzy logic controller of the present invention.
• Figure 11 is a table illustrating the
• a fuzzy logic controller (FLC) 10 used in the present invention is composed of three basic parts, illustrated in Figure 1.
• input signal fuzzification block 11 transforms the continuous input signal or signals into linguistic fuzzy variables such as, for example, Small, Medium and Large by use of so-called membership functions (described in more detail below).
• membership functions described in more detail below.
• FLC 10 may be any type of fuzzy logic controller
• the fuzzy engine block 12 carries out rule inference, and allows human experience to be
• Defuzzification block 13 converts the inferred control action produced by fuzzy engine block 12 back into a continuous signal that interpolates between simultaneously satisfied rules, as determined by fuzzy engine block 12.
• fuzzy logic is sometimes referred to as continuous logic or interpolative reasoning. Fuzzy engine block 12 and defuzzification block 13 are described in more detail below.
• FLC 10 Two distinct features of FLC 10 are that human experience can be integrated and that fuzzy logic provides a non-linear relationship induced by the membership functions of the fuzzification block 11, the rules of the fuzzy engine block 12, and the interpolation of the defuzzification block 13.
• FLC 10 also includes an accumulator 14 which functions to accumulate the changes in control action, ⁇ u, which occur over time, in order to produce the control action, u.
• the control action, u since the FLC operates in a sampled data mode, the control action, u, is calculated for any point in time as the control action for the previous sampling time, added to the change in control action.
• u(t + ⁇ t) u(t) + ⁇ u, where ⁇ t is the sampling interval.
• Process 16 may be any type of process which is desired to be controlled.
• an output signal or a process variable, y is sensed from process 16 and applied to summing block 17 for comparison against a set point, sp.
• the difference between process variable, y, and set point sp, is an error signal, e, which is supplied to FLC 14, along with the change in control error, ⁇ e.
• the control action, u, produced by FLC 10 is applied to process 16.
• FLC 10 operates to drive process variable, y, to be substantially equal to set point, sp.
• tuning system 18 which senses various measurable quantities existing within the fuzzy logic controller system, in order to determine the dynamic process characteristics of process 16.
• the quantities that may be measured by tuning system 18 include, for example, process variable, y, set point, sp, error signal, e, and the control action, u.
• measurable quantities within the fuzzy logic controller system other than those illustrated in Figure 2 may be measured by tuning system 18 in order to determine the dynamic process characteristics of process 16.
• tuning system 18 calculates appropriate control parameters for FLC 10, which are forwarded to FLC 10 through line 19. Then, process 16 is thereafter controlled in a closed-loop fashion by the newly tuned FLC 10, until such time as retuning is desired or required.
• tuning system 18 for automatically tuning fuzzy logic controller 10, in accordance with the present invention.
• tuning system 18 is shown composed of tuning module 21 and switch 22.
• tuning module 21 functions to determine the dynamic characteristics of process 16.
• Tuning Module 21 in Figure 3 may also operate to determine the dynamic process characteristics of process 16 using a pattern recognition method of process characterization, such as that presented in U.S. Patent No. 4,602,326, the disclosure of which is expressly incorporated herein by reference.
• a pattern recognition method of tuning the characteristics of process 16 are determined by observing process variable, y, as it responds to a process upset condition.
• the pattern of process variable, y, produced as a result of the process upset is then analyzed to determine the dynamic characteristics of process 16.
• the control parameters for FLC 10 are calculated from the determined process characteristics, and these control
• tuning module 21 parameters are transferred from tuning module 21 to FLC 10 through controllable switch 22.
• tuning system 18 includes a controllable signal generator 41, tuning module 42, controllable switch 43 and summing block 44. This embodiment operates to determine the dynamic
• tuning system 18 includes tuning module 51, controllable signal generator 52 and controllable switch 53.
• tuning module 51 either automatically or under operator control, places switch 53 in position 2, which substitutes the output of controllable signal generator 18 for the control action, u, produced by FLC 10.
• Tuning module 51 then controls the operation of controllable signal generator 52 by monitoring process variable, y, error signal, e, and the output of controllable signal generator 18, to perform controlled induced oscillation tuning of FLC 10.
• tuning module 51 After completion of the induced oscillation tuning procedure, tuning module 51 returns switch 53 to position 1, and calculates dynamic process characteristics for process 16. Then, from these dynamic process characteristics, tuning module 51 calculates control parameters and applies them to FLC 10 through line 19. Then, process 16 is
• FIG. 6A and 6B graphically illustrated is a portion of an exemplary induced oscillation tuning procedure, which may be used to automatically tune a FLC, in accordance with one embodiment of the present invention. It should be understood that other types of automatic tuning procedures may also be used, such as, for example, model matching pattern recognition or signal
• FIG. 6A depicted is the output, y, of process 16, and depicted in Figure 6B is the input, u, of process 16, when switch 53 ( Figure 5) is placed in position 2 and is connected to the output of signal generator 52.
• signal generator 52 applies a square wave signal having a selectable peak to peak value of 2d, centered about the value of the control signal, u, before induced oscillation was initiated.
• process output, y will exhibit an oscillation having a peak to peak value of 2a, and a period of T u . This period is also known as the ultimate period of process 16.
• the selected tuning procedure is used to calculate, from the quantities d, a, and T u , derived from the induced oscillation illustrated in Figures 6A and 6B, dynamic process characteristics including proportional gain K c and integral time constant T i , which are tunable
• ⁇ u FLC( ⁇ e,e) (1)
• FLC( ⁇ ) represents the non-linear relationship of the FLC
• ⁇ u represents the change in control action
• e is the control error
• ⁇ e is the change in control error. Since the FLC operates in a sampled data mode, the control action, u, is
• u(t+ ⁇ t) u(t) + ⁇ u, where ⁇ t is the sampling interval.
• the control error, e for any sampling period is equal to the difference between the set-point, sp, and the measured variable, y.
• fuzzification block 11 may be defined based on prior knowledge about the process. To illustrate how to define the membership functions for the control error, e, change of control error, ⁇ e, and change in control action, ⁇ u, it is convenient to use the scaled variables:
• S e , S ⁇ e and S ⁇ u are scaling factors for e, ⁇ e and ⁇ u, respectively.
• e * , ⁇ e * and ⁇ u * are scaled so that they each have values that are greater than or equal to -1, and less than or equal to 1.
• Possible sets of fuzzy membership functions for e * , ⁇ e * and ⁇ u * are given in Figures 7A, B, C, and D.
• the number of membership functions for each variable can vary, depending on the resolution required for that variable. Generally speaking, more membership functions offer more digress of freedom to the functional relationship of the controller.
• a conventional PID controller can be reproduced using a FLC with two membership functions for each input variable e * and ⁇ e * and with linear defuzzification.
• Figure 7A illustrates two membership functions, which may be used for input variables, e * and ⁇ e *
• Figure 7B illustrates three membership
• Figure 7D shows five membership functions used for change in control action, ⁇ u * , when control error, e * , and change in control error,
• fuzzy engine block 12 operates to apply inference rules to the operation of the membership functions of fuzzification block 11.
• inference rule for a FLC can be described as follows:
• Figures 7A-D (negative large, negative small, zero, and so forth). A fundamental requirement of these rules is that they perform negative feedback control for the sake of stability.
• An exemplary set of four rules is illustrated in tabular form in Figure 8A, and an exemplary set of sixteen rules is shown in Figure 8B. Four rules are used when each of e * and ⁇ e * are conditioned by two membership functions
• defuzzification block 13 establish the required change in control action, ⁇ u * , from the membership functions of control error, e * , and change in control error, ⁇ e * , defuzzification of the scaled change in control action, ⁇ u * , is performed by defuzzification block 13.
• the known center of gravity method of defuzzification is used, however, other types of defuzzification methods would also be acceptable, such as, for example, center of mass defuzzification, and generalized center of gravity defuzzification.
• Defuzzification using the center of gravity method uses either Lukasiewicz logic, or Zadeh logic, or a combination of Lukasiewicz and Zadeh logic.
• the Zadeh AND function is used, and either the Lukasiewicz OR function or Zadeh OR function is used.
• the scaled change in control action, ⁇ u * is descaled by multiplication by scaling factor S ⁇ u to arrive at descaled change in control action, ⁇ u.
• the change in control action, ⁇ u (which may be either positive or negative), is added to the control action applied during the last sampling interval, u(t), to arrive at the control action to be applied for the present sampling interval, u(t+ ⁇ t).
• tuning is accomplished within tuning system 18 (see also Figures 2-5) by calculating values for the scaling factors S e , S ⁇ e and S ⁇ u , as functions of dynamic process characteristics that are derived from the process under control during an automatic tuning procedure.
• characteristics such as the critical gain, K c , and integral time constant, T i , are determined for the process under consideration.
• a controlled induced oscillation procedure calculates proportional gain, K c , and integral time constant,
• equations (6) and (8) may be expressed as equations (10) and (11), respectively:
• control error scaling factor, S e is calculated according to the equation:
• control error scaling factor, S e change in control error scaling factor, S ⁇ e , and the scaling factor for the control action, S ⁇ u .
• S ⁇ u is determined as a function of the maximum responding speed of the actuator that is being controlled by control action, u.
• Typical actuators include, for example, valves, pumps, and heating elements, each of which
• e m which is a function of the operation region of the FLC
• tuning is concluded. If, however, the calculated S e is greater than e m , then the control error scaling factor, S e , is set equal to e m and S ⁇ e and S ⁇ u are calculated from rearranged equations (10) and (12) (or from rearranged equations (11) and (12)), and tuning is completed.
• FIGS. 9A and 9B shown are an exemplary block diagram of a process which is controlled in order to illustrate the advantages of the present invention, and a mathematical model of the process.
• the process includes a tank 60 which contains liquid 61.
• Tank 60 includes discharge port 62, from which liquid 61 is
• Liquid flows into tank 60 under control of valves 63 and 64.
• Liquid level detecting device 66 produces a measured variable, y, which is indicative of the level of liquid 61 within tank 60, and controller 67 controls valve 63, as a function of measured variable, y, and set-point, sp, in order to control the level of liquid 61 within tank 60.
• Valve 64 is controlled by a load control signal, q, in order to permit assessment of the performance of controller 66 in response to
• Figure 9B represents a mathematical model of the process of Figure 9A.
• the slew rate of valve 63 is modeled by slew rate limiting block 68, and the contributions to measured variable, y, as a result of control signal, u, and load control signal, q, are modeled respectively by blocks 69 and 70.
• Figure 10D compares the performance of the same controllers used to produce the traces of Figure 7C, with the imposition of random noise to simulate hydraulic agitation.
• Trace 78 is a tuned PI
• trace 79 is a tuned FLC controller. As can be seen by comparing the traces of
• Figures 10A-10D in virtually every instance, the FLC controller which has been tuned in accordance with the present invention, has a substantially better performance than a comparable PI controller.
• Figure 11 presents a table showing the calculated Integral Absolute Error (IAE) (a measure of control performance) for the FLC of the present invention and the PI which are plotted together in Figures IOC and 10D.
• IAE Integral Absolute Error

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• 1993
  • 1993-08-11 US US08/105,899 patent/US6330484B1/en not_active Expired - Lifetime
• 1994
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