Patent Application
20130282147
1. Field of the Invention
The present invention relates to automated control techniques, and particularly to a system and method for process monitoring and control utilizing fuzzy logic control to integrate automatic process control with statistical process control.
2. Description of the Related Art
Statistical process control (SPC) is the application of statistical methods to the monitoring and control of a process to ensure that it operates at its full potential to produce conforming product. Under SPC, a process behaves predictably to produce as much conforming product as possible with the least possible waste. While SPC has been applied most frequently to controlling manufacturing lines, it applies equally well to any process with a measurable output. Key tools in SPC are control charts, a focus on continuous improvement, and designed experiments.
Much of the power of SPC lies in the ability to examine a process and the sources of variation in that process using tools that give weight to objective analysis over subjective opinions and that allow the strength of each source to be determined numerically. Variations in the process that may affect the quality of the end product or service can be detected and corrected, thus reducing waste, as well as the likelihood that problems will be passed on to the customer. With its emphasis on early detection and prevention of problems, SPC has a distinct advantage over other quality methods, such as inspection, that apply resources to detecting and correcting problems after they have occurred.
In addition to reducing waste, SPC can lead to a reduction in the time required to produce the product or service from end to end. This is partially due to a diminished likelihood that the final product will have to be reworked, but it may also result from using SPC data to identify bottlenecks, wait times, and other sources of delays within the process. Process cycle time reductions coupled with improvements in yield have made SPC a valuable tool from both a cost reduction and a customer satisfaction standpoint.
Statistical Process Control may be broadly broken down into three sets of activities: understanding the process, understanding the causes of variation, and elimination of the sources of special cause variation. In understanding a process, the process is typically mapped out and the process is monitored using control charts. Control charts are used to identify variation that may be due to special causes, and to free the user from concern over variation due to common causes. This is a continuous, ongoing activity. When a process is stable and does not trigger any of the detection rules for a control chart, a process capability analysis may also be performed to predict the ability of the current process to produce conforming (i.e. within specification) product in the future action.
When excessive variation is identified by the control chart detection rules, or the process capability is found lacking, additional effort is exerted to determine causes of that variance. The tools used include Ishikawa diagrams, designed experiments and Pareto charts. Designed experiments are critical to this phase of SPC, as they are the only means of objectively quantifying the relative importance of the many potential causes of variation.
Once the causes of variation have been quantified, effort is spent in eliminating those causes that are both statistically and practically significant (i.e., a cause that has only a small but statistically significant effect may not be considered cost-effective to fix; however, a cause that is not statistically significant can never be considered practically significant). Generally, this includes development of standard work, error-proofing and training. Additional process changes may be required to reduce variation or align the process with the desired target, especially if there is a problem with process capability.
For digital SPC charts, so-called “SPC rules” usually come with some rule specific logic that determines a “derived value” that is to be used as the basis for some setting correction. Most SPC charts work best for numeric data with Gaussian assumptions.
SPC is traditionally applied to processes that vary about a fixed mean, and where successive observations are viewed as independent. The SPC approach seeks to reduce variability by detecting and eliminating assignable causes of variation. SPC can be viewed as a top-down tool that is usually driven by upper management as part of a company wide quality improvement policy. The role of SPC is to change the process when assignable causes occur. SPC does not control the process, but performs a monitoring function that signals when control is needed (identification and removal of root causes).
On the other hand, automatic process control (APC) is usually applied to processes in which successive observations are related over time, and where the mean drifts dynamically. APC seeks to reduce variability by transferring it from the output variable to a related process input (i.e., controllable) variable. It actively reverses the effect of process disturbances by making regular adjustments to manipulatable process variables. APC is usually discussed in the framework of a process with a drifting mean, and the objective of the process adjustment is to keep the output quality characteristic on target. APC is viewed as a bottom-up procedure driven by process control or manufacturing engineers. The role of APC is to continuously adjust the process to counteract ongoing forces that will cause the process to drift off-target if compensations are not made. APC does not remove the root or assignable causes. Rather, it uses continuous adjustments to keep process variables on targets.
SPC and APC systems were initially thought to be incompatible. However, there have recently been advances in the integration of the two. Most integration schemes involve the use of SPC techniques for monitoring functions and APC techniques for process regulation. Other attempts have involved the derivation of SPC controllers that are used alone, which does not result in true integration. It would be desirable to provide a truly integrated SPC and APC process monitoring and control system.
Thus, a system and method for process monitoring and control solving the aforementioned problems is desired.
The system for process monitoring and control integrates statistical process control (SPC) with automatic process control (APC) through the use of a fuzzy logic (FZL) controller. In order to relate the inputs to the output, fuzzy inference rules are applied, the fuzzy rule base being based on applying the use of the APC controller during normal situations, and then deviating to SPC as soon as abnormalities are first detected. For example, when the output error is negligible and the change in the output quality characteristic is almost zero, the fuzzy logic controller (FZLC) will provide a utilization factor parallel for applying the APC controller. The FZLC has two inputs: the output error ert, and the rate of change of the output quality characteristic dyt. The FZLC has a single output; the controller utilization factor wt. When ert is large and dyt is high, the controller utilization factor wt will utilize the application of the SPC controller.
These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.
Similar reference characters denote corresponding features consistently throughout the attached drawings.
Fuzzy logic is a formal methodology for representing, manipulating, and implementing a human's heuristic knowledge regarding how best to control a process. Fuzzy logic is defined as a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 0 or 1 (i.e., true or false). The basic idea behind fuzzy logic is to mimic the fuzzy feature of human thinking for the effective control of uncertain systems through fuzzy logic reasoning. Fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans. Furthermore, fuzzy logic is well suited to low-cost implementations based on relatively inexpensive sensors, low-resolution converters, and microcontroller chips. Such systems may be easily upgraded by adding new rules to improve performance, or by adding new features.
A fuzzy logic control (FZLC) system is a control system based on fuzzy logic. Fuzzy logic controllers, such as controller 12 of
The input variables in a fuzzy control system are generally mapped by sets of membership functions, known as “fuzzy sets”. Given mappings of input variables into membership functions along with their truth values, the controller 12 can make decisions about which action is to be taken based on a set of rules, which are typically expressed in conventional logical form, such as “IF variable IS property THEN action”. The AND, OR, and NOT operators of Boolean logic can also exist in FZL, and are usually defined as the minimum, maximum, and complement, respectively. This combination of fuzzy operations and rule-based inference describes a fuzzy expert system, such as the system 10.
Referring to
As shown in
In order to relate the inputs to the output, fuzzy inference rules are developed. For system 10, a rule base 16 is based on applying the use of the APC controller during normal situations, and then deviating to SPC as soon as abnormalities begin to occur. For example, when the output error is negligible and the change in the output quality characteristic is almost zero, the FZLC 12 will provide a utilization factor parallel for applying APC controller 24. However, when ert is large and dyt is high, the wt will utilize the application of SPC controller 26. For system 10, the following set of 25 rules is utilized:
1. If (ert is NMAX) and (dyt is NHI) then (wt is BIC);
2. If (ert is NMAX) and (dyt is NLO) then (wt is SAC);
3. If (ert is NMAX) and (dyt is ZERO) then (wt is SPC);
4. If (ert is NMAX) and (dyt is PLO) then (wt is SPC);
5. If (ert is NMAX) and (dyt is PHI) then (wt is SPC);
6. If (ert is NMIN) and (dyt is NHI) then (wt is BIC);
7. If (ert is NMIN) and (dyt is NLO) then (wt is SAC);
8. If (ert is NMIN) and (dyt is ZERO) then (wt is SAC);
9. If (ert is NMIN) and (dyt is PLO) then (wt w is SAC);
10. If (ert is NMIN) and (dyt is PHI) then (wt is SPC);
11. If (ert is ZERO) and (dyt is NHI) then (wt is SPC);
12. If (ert is ZERO) and (dyt is NLO) then (wt is SAC);
13. If (ert is ZERO) and (dyt is ZERO) then (wt is APC);
14. If (ert is ZERO) and (dyt is PLO) then (wt is SAC);
15. If (ert is ZERO) and (dyt is PHI) then (wt is SPC);
16. If (ert is PMIN) and (dyt is NHI) then (wt is SPC);
17. If (ert is PMIN) and (dyt is NLO) then (wt is SAC);
18. If (ert is PMIN) and (dyt is ZERO) then (wt is SAC);
19. If (ert is PMIN) and (dyt is PLO) then (wt is SAC);
20. If (ert is PMIN) and (dyt is PHI) then (wt is BIC);
21. If (ert is PMAX) and (dyt is NHI) then (wt is SPC);
22. If (ert is PMAX) and (dyt is NLO) then (wt is SPC);
23. If (ert is PMAX) and (dyt is ZERO) then (wt is SPC);
24. If (ert is PMAX) and (dyt is PLO) then (wt is SAC); and
25. If (ert is PMAX) and (dyt is PHI) then (wt is BIC).
Table 1 below summarizes the rule base 16:
In the above, it should be noted that rule 13 is conditionally based upon dyt being ZERO, rather than NORM. The NORM value is equivalent to dyt=0 (see also rules 3, 8, 18, and 23, where ZERO is used as the equivalent of NORM as a membership function of the second input dyt). As will be described in greater detail below, essentially, the system 10 applies the above set of fuzzy inference rules so that normally process monitoring and control of the monitored process is controlled by the automatic process controller 24, and the controller utilization factor wt mandates control by the automatic process controller 24 when the output error ert is negligible and the output quality characteristic dyt is almost zero. However, when the output error ert is large and the output quality characteristic dyt is high, the controller utilization factor wt mandates control by the statistical process controller 26. Intermediate values of the output error err and the output quality characteristic dyt may dictate a shift to larger control by the automatic process controller 24, larger control by the statistical process controller 26, or control by both the automatic process controller 24 and the statistical process controller 26. These, however, are general tendencies, and reference should be made to rules 1-25 and Table 1 for specific fuzzy rules. It should be noted that although a membership function for ASC (larger automatic control) is established, an ASC output is not shown. The only case for which pure automatic control is applied is when both ert and dyt are zero.
In the FZLC 12, the center of area (COA) method is used by the defuzzification module 20. This method calculates the center of gravity of the distribution for the control action, which is mathematically expressed as:
where Z* represents the number of quantization levels of the output, zj is the amount of control output at the quantization level j, and μc(zj) represents its membership value in C.
Automatic process controllers, statistical process controllers and fuzzy logic controllers are all known. It should be understood that APC 24, SPC 26 and FZLC 12 may be any suitable type of controllers. Such controllers are shown in U.S. Pat. Nos. 4,344,128; 5,862,054; 6,078,911; 6,330,484; 6,424,876; 6,446,357; 7,469,195; and 7,957,821, each of which is herein incorporated by reference in its entirety.
In the following, the Absolute Efficiency (AE) is used as a performance index. This index measures the absolute efficiency of variation reduction, which is expressed as:
where σD is the standard deviation of the disturbance, and σe is the standard deviation of the controlled output,
As shown in
u(t)=w(t)·uAPC(t)+[1−w(t)]·uSPC(t), (3)
where u(t) represents the final control action, uSPC (t) represents the control action from the SPC controller 26, uAPC(t) represents the control action from the APC controller 24, and w(t) is the controller factor, where 0≦w(t)≦1. As shown in
The process can further be affected by noises, disturbances and environmental changes, such as external temperature changes. In order to overcome such factors, it is required to have a workable pH control methodology that combines maintaining the product quality on target, maintaining the controller performance, and keeping the system robust against external factors. As shown in
As an example of the process illustrated in
HCl+NaOH→NaCl+H2O. (4)
The differential equations describing the pH neutralization process are as follows:
where κ0a is the overall concentration containing the anion of the acid, κ0b is the overall concentration containing the cation of the base, and V is the volume of the reactor. The steady-state operating conditions are given in Table 2 below:
The pH value in the CSTR 40 is measured by pH sensor 56 and transmitted to the pH controller 52, which is preferably a proportional-integral-derivative (PID) controller, in which the control output is calculated and then sent to the flow control valve 48, which adjusts the base flow rate 42. The control objective is to maintain the pH value at the set point (pHset=1). The agitator 60 is also included to ensure proper mixing, and baffles may be added to prevent the formation of vortices. The overall process is described by the following first-order plus time delay (FOPTD) model:
where Kc is the gain of the process model, d is the time delay, and T is the time constant.
The reactor tank level is kept constant by an overflow control system. This is achieved by level transmitter 64, which sends the feedback signal to the flow controller 54, which calculates the output according to the PID control law, and then sends the control signal to the flow control valve 50, which adjusts the acid flow rate.
In this example, the pH controller is a PID controller with the following control parameters: Kp=1.7667; τi=3.9750; τd=3.9750; Ki=1.6000; Kd=0.1667. By combining the information from the FOPTD model and the PID controller settings, a block diagram for this process was built and simulated. The resulting response is shown in
where Kp is the proportional gain constant, u(t) is the control action, τi is the integral time constant, τd is the derivative time constant, and e(t) is the error given as the output deviation from target of controlled variable. The discrete time equivalent for a PID controller is as follows:
where T is the time constant.
The above uses the Taguchi method for robust parameter design, which is based on the design of experiments theory, along with the use of orthogonal arrays (OAs) to study large numbers of decision variables with a small number of experiments in order to reach a near optimum parameter combination. The method classifies the inputs to the system into two types: control factors, which are factors that can be controlled and manipulated; and noise factors, which are factors that are difficult or expensive to be controlled. The basic idea underlying the Taguchi method is to exploit the interactions between the control and noise variables, and then identify the appropriate settings of the control parameters for which the system's performance is robust against variation in noise factors. The ultimate goal is to make the system response close to the target with low variation in performance.
In the Taguchi method, objective functions arise from quality measures using quadratic loss functions. The method uses the SNR as a measure of the MSD. The larger the SNR, the more robust the performance becomes. SNR is different for different types of quality characteristics. In the present method, the “smaller the better” type characteristic is utilized, where the quality characteristic never takes negative values, and its ideal value is zero. As SNR increases, the performance becomes progressively worse. Thus, SNR considers the deviation from zero, and as the name suggests, it penalizes large responses. The SNR is calculated as
In the above, the control factors selected for the PD control rule were Kp, τi, and τd, which may all be changed under the objective of minimizing the MSD. For each control factor, three levels are selected. The noise factors are identified from the process model itself, since these may be impossible to control. The FOPTD function is given as:
Thus, the noise factors are selected as Kc, d and T. For each noise factor, two levels are selected.
For APC controller tuning, the control factors Kp, τi, and τd were set as shown below in Table 3:
The noise factors were identified by the process model described above in equation (7) to be KC, d and T. For each factor, two levels were selected, as shown below in Table 4:
After selecting the orthogonal arrays to be used (as described above with regard to the Taguchi methodology), and conducting experiments, the following results were obtained (shown below in Table 5 and in the table of
As shown in
For the SPC process model utilized, the process is described by a linear transfer function having an error term incorporated therein. It is derived by extracting the information from the closed loop process input and output data, and then deriving the process model by using linear regression, as y(t)=b0+b1u(t)+e(t), where u(t) is the input (control action), y(t) is the output (measured quality characteristic), e(t) is the error (deviation of the process output from the target), and b0, b1 are model parameters, which are estimated as
From the experimental results above, the extracted data from the closed loop step response allowed for the calculation of model parameters b0, b1, yielding a process model of the following form:
y(t)=1 2775−0.2467x(t)+e(t). (8)
The control action u(t) is given by
where φ is an adjustment factor. Thus, for the experimental data given above, the control action is given by:
The FZLC is constructed as described above with regard to Table 1 and equation (1). For fuzzification, the membership functions for ert, dyt and wt are set according to the values below in Table 6. The 25 fuzzy inference rules of Table 1 were applied, and the COA method was used for defuzzification (equation (1)):
The process was simulated to operate by all three control schemes separately, including: the existing PID control, the SPC control, and the fuzzy integrated SPC/APC control of system 10. The output responses for the three control schemes are compared in
By comparing the output under the fuzzy integrated SPC/APC system 10 to the output under the existing PID control scheme, the results indicate a decrease of 30.83% in MSD, an increase of 14.58% in the SNR, and an increase of 12.69% in the AE. These results improve even further when the process is derived under SPC control action.
The process was next controlled by all three control schemes and was set to operate under assignable causes by introducing white noise and including a shift of 0.04 units in the process mean at t=26 sec. Exponentially-weighted moving average (EWMA) control charts for λ=0.1 and L=6 were generated, and their plots are respectively shown in
The output statistics are summarized below in Table 8:
These results indicate a decrease of 66.67% in MSD, an increase of 13.86% in the SNR, and an increase of 32.18% in the AE (and twice the increase in ARL). This indicates the effectiveness of the fuzzy-integrated SPC/APC system 10 over the existing PID control scheme and the SPC control scheme in terms of optimizing the level of quality, performance and robustness.
It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.
