普通沖床送料裝置的自動化改造含3張CAD圖
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A fuzzy PLC with gain-scheduling control resolution
for a thermal process - a case study
H.-X. Li*, S.K. Tso
Center for Intelligent Design, Automation and Manufacturing, Faculty of Science and Technology, City University of Hong Kong,
Tat Chee A venue, Kowloon, Hong Kong
Received 2 July 1998; accepted 6 November 1998
Abstract
This paper presents a case study on the practical implementation of a fuzzy-PLC system for a thermal process. The theoretical study indicates that the inferior performance of fuzzy-controlled processes around a reference point is often caused by insufficient resolution of the fuzzy inference. The limitations of ladder logic cannot support complex algorithms for resolution improvement. A simple gain adaptation method is presented here, to achieve smooth fuzzy control, that can be easily implemented in a PLC system. Real-time experiments on an unidentified thermal process show the effectiveness of the approach, as well as the robustness of the fuzzy controller with respect to the time-varying features of the process. (1999Elsevier Science ?td . All rights reserved.
Keywords: Fuzzy control; Fuzzy-plc systems; Gain scheduling; Process control; Fuzzy sets
1. Introduction
In industrial automation applications, ladder logic, a programming language running on the so-called 'programmable logic controllers' (PLCs) (Erickson, 1996), is usually used for discrete event control. For continuous control, either bang D bang-type control or PID-type controllers are more often employed. In 1974, the first fuzzy control application appeared (Mamdani, 1974). Since then, fuzzy-logic control (FLC) has been taken as the preferred method of designing controllers for dynamic systems, even where traditional methods can be used (Mamdani, 1993).
In the early 1990s, when more and more successful industrial automation applications were proving the potential of fuzzy logic, the fuzzy-PLC systems came on to the market. These systems tightly integrate fuzzy logic
with conventional industrial automation technologies. Many applications of fuzzy-PLC systems have been reported (Von Altrock and Gebhardt, 1996).
Thermal plants are very sensitive to environmental variations, and require highly robust performance for temperature control. Since the linear controller may not be robust enough with respect to the time-varying properties of the process, fuzzy-logic control (FLC) becomes a good candidate when a fuzzy-PLC system is available. On the other hand, FLC may have other problems that the linear controllers do not have. Practical experiments show inferior performance of FLC around the reference point, partially due to the complex resolution required for complex processes. A second set of fine membership functions (MFs)/look-up tables, which can provide finer control, was used in some fuzzy systems to replace the coarse MFs/tables when the error falls within preset limits (Li and Lau, 1989; Liaw and Wang, 1991). However, this method is not applicable to fuzzy-PLC systems due to the complexity of the systems and the difficulties of tuning. A simple but effective method is required to improve the performance in practice.
In this paper, a practical method is introduced, using gain scheduling. This approach can adapt to different resolution requirements by adjusting only the scaling gains. The method is effective, and can be easily implemented using ladder logic in the PLC. A properly designed fuzzy-PLC system is then very successful for controlling a thermal plant with time-varying features.
2. The architecture of fuzzy-PLC systems and a problem description
The architecture of an OMRON fuzzy-PLC system can be seen in Fig. 1. The basic function modules are I/O,
Fig. 1. Architecture of a basic fuzzy-PLC system.
processor and fuzzy-logic inference. Fuzzy inference consists of several operations, as shown in Fig. 2: fuzzification, inference, and defuzzification. Though the fuzzy-logic inference module on the PLC carries out the fuzzy-inference operation, a separate software tool on a PC programs the knowledge base required for the inference. This software tool is linked to the fuzzy-PLC system by a standard serial cable (RS232), through which the developer downloads the designed knowledge base to the fuzzy-PLC system. The fuzzy inference becomes a function to be called by the ladder logic when needed.
A fuzzy variable is defined by a set of membership functions (MFs). The support for a given MF is the set of points in the region for which the grade k is positive. The resolution of each MF depends on the grade (μ) distribution over its support. Since there is a crisp-fuzzy or fuzzy-crisp conversion, the resolution of the fuzzy inference depends heavily on the resolution of both the fuzzy input and output variables, while the resolution of a fuzzy variable depends on the MF design. Inappropriate MFs of a fuzzy variable may lose some input information, resulting in a poor resolution. Theoretically, the spread of a MF should match its information domain to achieve the best resolution. The terms 'coarse' and 'fine' can be used to describe the fuzzy variable or its MFs. A large information domain requires a wide spread for the MF, which can be considered as a coarse MF, while a small information domain requires a narrow spread for the MF, which can be regarded as a fine MF. There is no similar resolution problem for a crisp variable, or for its operation.
The thermal process presented here is a nonlinear time-varying process, with the temperature as the controlled variable. The nonlinear nature of the thermal process requires different resolutions of the controller in different states. In the transient period, large errors necessitate a coarse control that requires coarse input/output variables, while in the steady-state period, small errors need Tner control, which requires fine input/output variables. This resolution requirement has no influence on a linear controller, but may affect an FLC system due to the mismatch between the spread of the MFs and the information domain. It has been suggested that one should use a second set of finer MFs (with a narrow spread) to improve the performance in the steady-state period (Li and Lau, 1989). However, this type of variable MF system is di|cult to design and to tune, and is also inappropriate to the application of fuzzy-PLC systems.
3. Resolution adaptation using gain scheduling
The fuzzy variable being called in this paper is assumed to be single-resolution, defined by the uniform-support MFs shown in Fig. 3, rather than multi-resolution, described by non-uniform-support MFs.
Fig. 2. Architecture of a fuzzy inference system.
Fig. 3. Single-resolution membership functions for input and output variables.
Fig. 4. The effect of the input scaling gain N on resolution.
Definition.：A coarse variable has fewer MFs, while a fine one has more MFs defined over the variable domain.
Theorem 1 (Input resolution adjustment ).：1he resolution of a fuzzy input variable, defined by specific MFs , can be controlled by its scaling gain N as shown in Fig .4. 1he resolution is unchanged when N =1; it becomes finer when N<1, and coarser when N>1.
Proof.：The proof is very simple. If two MFs have the same μ values for their supports, then these two MFs have the same resolution. A coarse MF will have a large spread and a wide distribution, and vice versa. Changing the scaling gain of the input variable is equivalent to inversely changing the spread of the MF or the input domain. As shown in Fig. 4, the scaled variable e can achieve equivalent results by using F (E ) instead of F (e). In other words, tuning the scaling gain N can make a fuzzy variable with coarse MFs achieve a result equivalent to that of one with fine MFs, as long as their MFs have the same shape, and vice versa.
The resolution of the fuzzy inference depends heavily on the defuzzification method. One of the most popular methods is the centre-of-gravity method (COG), by which the inference output U is calculated according to the following:
(1)
If is small, a variation of the input (grade ) will cause a small variation in the output U, making the output resolution finer. Since an output variable with more MFs has a smaller
in the output domain, it can generate a finer inference output than one with fewer MFs. In
other words, fine-output MFs produce a small crisp output, and coarse-output MFs produce a large one, for the same grade of inputs. The resolution of the output variable can be adjusted by a scaling gain, as described in Theorem 2.
Theorem 2 (Output resolution adjustment).：1he resolution of a fuzzy output variable, defined by specific MFs , can be controlled by its scaling gain K , as shown in Fig.5.1he resolution is unchanged when K "1; it becomes finer when K<1, and coarser when K>1.
Proof.：The centre of gravity (COG) for a scaled output variable in Eq. (2) indicates that reducing the output scaling gain K can reduce the crisp output generated by the coarse-output MFs. On the other hand, increasing the gain can increase the crisp output produced by the fine output MFs. Therefore, a coarse variable can achieve a result equivalent to that of a fine variable by using
gain scheduling properly, and vice versa, as shown in Fig. 5.
(2)
With
Based on Theorems 1 and 2, the resolution-adaptation strategy can be summarised as in Table 1. By adjusting the input/output scaling gains instead of the MFs themselves, conversion between variables with different resolutions can be achieved so that control resolution can be enhanced.
Fig. 5. The effect of the output scaling gain K on resolution.
Fig. 6. Definition of two regions for gain scheduling.
The gain scheduling should be designed on the phase plane, and based on the dynamics of the controlled process. Two regions are suggested, as shown in Fig. 6, with one small region defined around the equilibrium point for the fine control, and the rest of the phase plane for the coarse control. The control switching is managed by two switching states () as follows.
(i) Coarse control is used when and .
(ii) Fine control is used when and .
Fig. 7. A simplified diagram of the thermal process with three different sensing locations.
One set of scaling gains is used for coarse control, to speed up the transient response. When the error falls within the preset limits, the second set of scaling gains is used for fine control, which can smoothen the response around the set point. The switching states are chosen by observing the behaviour of the industrial plant concerned.
4. Experiment
The thermal plant used for the experiment is based on a real industrial process, with the process temperature as the controlled variable. As shown in Fig. 7, heated air is blown from the left-hand side to the right-hand side, in order to heat up the whole chamber. It is very difficult to
maintain robust performance, due to the sensitiveness of the process to the environmental disturbance. Since the process is highly nonlinear, the mathematical model of the process is unknown and unidentified. Therefore, no simulation study is carried out. However, the dominant
part of the thermal process can be crudely estimated as a low-order system in the form given by the transfer function in Eq. (3), through some simple measurements. The process parameters are time-varying and thus un- known. There are three different delay situations, which can be approximately estimated to be , 0.5 and 0.8 s, respectively, due to the three different sensing loca- tions, shown in Fig. 7.
(3)
The experiment aims to compare a fuzzy control system with its linear counterparts in discrete time. Since the dominant part of the process is a low-order system, a PI-type controller may be sufficient. Therefore, the comparison will be carried out between a fuzzy-PI controller and a linear PI controller. Both of them are implemented on an OMRON PLC system (C200) with 12-bit resolution. The fuzzy-inference module is an OMRON FLC unit (FL01) (OMRON, 1992) that can be integrated with an OMRON PLC. The fuzzy-PI with gain scheduling is implemented as shown in Fig. 8. The gain scheduling is performed using ladder logic. The rule base is chosen as consisting of the linear rules shown in Table 2. The input MFs are chosen to be of the triangular
type, and the output MFs are simplified as singletons, as shown in Fig. 3.
Fig. 8. Implementation of the gain-adaptive fuzzy-PI structure in a fuzzy-PLC system.
Table 2
A linear two-dimensional rule base with limiter
Practical systems always have some power limitations, which may cause the 'windup' phenomenon for the integral action existing in both the PI and the fuzzy-PI control systems. The output of a PLC system is usually adjusted to match the power limitations of the process. Anti-windup techniques (Astrom and Hagglund, 1988) can help a PI controller to overcome the problem. However, there is still no 'anti-windup' method for fuzzy-PI control. Therefore, for a fair comparison and easy implementation, both control systems are tested without using any 'anti-windup' method. The experimental procedure is planned as follows.
(1) Tune both the linear and the fuzzy control systems to their optimum performance under the small-delay condition.
(2) Let both control systems work in different delay situations without changing their parameters, to test their performance robustness.
The coarse scaling gains can be determined by the linea counterpart in the following procedure (Ying, 1994):
? Tune the PI controller to its optimum,,,through a Ziegler-Nichols-type method.
Table 3
Choice of scaling gains for FLC
? Determine the gains of the FLC using,
? The input gain is chosen as unity for the best resolution.
The fine gains should be designed to satisfy the following requirements. requirements.
(1) A finer control resolution around the equilibrium state, which requires a larger input gain and a smaller output gain, according to Theorems 1 and 2.
(2) Unchanged stability conditions, which are affected by the ultimate gain (multiplying input and output gains): and for the system shown in Fig. 8.
Therefore, it is better to have the same ratio for the increase in the input gains and the decrease in the output gain, while maintaining the ultimate gain unchanged. This ratio has to be determined by observation of the behaviour of the process in the experiment. The fine gains found in Table 3 can provide a finer control resolution around the target, due to the larger input gains and the smaller output gain, and can still maintain the original stability due to the same ultimate gains.
Since is difficult to determine and the system is s basically a stable process, the switching rules can be approximated as follows.
(i) Coarse control is chosen when
(ii) Fine control is chosen when
By trial and error in the experiment, the switching state can be selected as 10% of the reference point.
The sampling (scan) time is about 15 ms, determined by the computational load of the PLC system. The experimental results with a small time delay are demonstrated in Figs. 9 and 10. The designed fuzzy-PLC system works quite well with a small overshoot. It seems to experience a longer delay than its linear counterpart because of the slow output accumulation of the PI function (Fig. 8). The linear PI controller can achieve a reasonably fast response. Since the time delay of the thermal plant may vary, the performance of both control systems (without updating parameters) will be affected when the time delay varies.
The experimental results for the different time delays, based on using different sensor locations, are shown in Figs. 11 and 14. The PI controller works well when the system has a short time delay, but the performance deteriorates greatly as the delay increases, becoming unstable with the long time delay (Figs. 11 and 12). FLC shows more robustness with respect to system variations, and has a larger stability range (Figs. 13 and 14). It is stable under all situations, maintaining a satisfactory performance.
Fig. 9. PI performance with delay Fig. 12. FLC performance with delay
Fig. 10. FLC performance with delay Fig. 13. PI performance with delay
Fig. 11. PI performance with delay Fig. 14. FLC performance with delay
A Conceptual Approach to Integrate Design and Control for the Epoxy Dispensing Process
H.-X. Li, S. K. Tso and H. Deng
Department of Manufacturing Engineering and Engineering Management, School of Science and Engineering, City University of Hong Kong, Hong Kong
Performance improvement of manufacturing systems in the semiconductor industry involves interdisciplinary expertise, such as physical modeling, mechanical design, electrical control, and even material science. Integration of these different disciplines is a challenging problem in the semiconductor industry. The paper presents a conceptual approach to integrate design and control methodology for complex processes with specific application to an epoxy-dispensing control system–a critical equipment in the semiconductor packaging process. This methodology includes three hierarchical levels: process design (system-level and component-level), multivariable control and the statistics-based supervision. This paper deals with conceptual design at system-level by integrating an approximate model with an axiomatic approach, and briefly introduces approaches at other levels. In the conceptual design at system level, the primitive model of the system is sufficient to show some basic properties of the process, by which the axiomatic design can be easily integrated to evaluate the system design and suggest an optimal system configuration with invariant properties to internal variations. Under minimal internal variation, the multivariable control that is intended to suppress external variations can be approximately constructed by a set of independent controllers. Statistics-based supervision will provide suitable setpoints for the multivariable control so as to maintain good performance in the dynamic environment.
Keywords: Conceptual and axiomatic design; Epoxy dispensing process; Hybrid process control
1. Introduction
Manufacturing systems in the semiconductor industry are processes with a high degree of complexity, consisting of heterogeneous subsystems and materials. Design and control for this kind of system involve different domains, such as, mechanical engineering, electrical control, software and hardware, and even material science and physics. A typical example is an epoxy dispenser which is widely used in the semiconductor industry where accurate fluid control is needed. In the die bonding process in the semiconductor industry, the epoxy dispenser is critical for the die attachment. Inconsistent dispensing quality is caused by internal and external variations, particularly when wide speed variations are required. Though much attention has been focused on the problems, little improvement has been made.
For a heterogeneous process, the factors or variables that affect the process performance could be classified into three different types:
Controllable variables that can be unconditionally handled by the external controller.
Partially controllable variables that can be handled conditionally by the external controller.
“Uncontrollable” variables that cannot be handled by the external controller.
These “uncontrollable” and even partially controllable variable often cause internal variations of the process, which will eventually affect the process performance. The relationship b
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