New design and stability analysis of fuzzy proportional-derivative control systems

Malki, Heidar; Li, Huaidong; Chen, Guanrong

doi:10.1109/91.324804

Cited by 248 publications

(79 citation statements)

References 15 publications

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“…Availability of the structure information may lead to more effective and less conservative, thus more practical, analysis and design techniques that require less trial-and-error effort and produce better control performance. Development of these techniques can, and should, utilize the well-developed conventional (nonlinear) control theory as fuzzy control problems have already been translated into nonlinear control problems (e.g., [4], [13], [17], [22], and [27]). For example, we utilized the explicit relationship between a class of fuzzy controllers and the conventional PI (and PD) controllers that we derived in [22], [23] to more effectively and practically design the fuzzy control systems.…”

mentioning

confidence: 99%

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Ying

2006

IEEE Trans. Fuzzy Syst.

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Abstract-A fuzzy controller uses either Zadeh or product fuzzy AND operator, with the former being more frequently used than the latter. We have recently published a novel technique for deriving analytical input-output relation for the fuzzy controllers that use Zadeh AND operator and arbitrary trapezoidal input fuzzy sets, including triangular ones as special cases. In this paper, we have developed a general technique based on that technique to cover arbitrary types of input fuzzy sets. Moreover, we have established some necessary and sufficient conditions to characterize general relationship between shape of input fuzzy sets and shape of input space divisions, an important and integral issue because analytical relationship differs in different regions of input space. The new technique and the shape relations are applicable to any type of fuzzy controllers (e.g., Mamdani type or Takagi-Sugeno type). The analytical structures that we have derived provide an unprecedented opportunity to insightfully and rigorously examine the advantages and shortcomings of different design choices available for various components of the fuzzy controllers. We have focused on type selection for input fuzzy sets of Mamdani fuzzy controllers. Our preliminary analysis indicates that the fuzzy controllers using trapezoidal fuzzy sets may be understood (and possibly analyzed and designed) more sensibly and easily in the context of conventional control theory than the fuzzy controllers using any other types of fuzzy sets. Our proposition is that trapezoidal fuzzy sets should be the first choice and used most of time. Possible implication for automatic learning of input fuzzy sets via neural networks or genetic algorithms is briefly discussed.

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mentioning

confidence: 99%

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Ying

2006

IEEE Trans. Fuzzy Syst.

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“…They studied the bounded-input and boundedoutput (BIBO) stability of fuzzy controllers using small gain theorem [1,2,12,16,17] . Malki et al [18] proposed a new design and stability analysis of fuzzy proportional derivative controller. Further, Chen et al [2,19] have developed fuzzy PID controller, which is a combination of fuzzy PI and fuzzy D controller having same structure as mentioned earlier.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Parallel Fuzzy P + Fuzzy I + Fuzzy D Control Systems

Kumar

Mittal

Singh

2013

Int. J. Autom. Comput.

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The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP + FI + FD) controller. It addresses the stability analysis of parallel FP + FI + FD controller. The famous "small gain theorem" is used to study the bounded-input and bounded-output (BIBO) stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP + FI + FD controller. FP + FI + FD controller is derived from the conventional parallel proportional plus integral plus derivative (PID) controller. The parallel FP + FI + FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.Keywords: Proportional plus integral plus derivative (PID), fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP + FI + FD) controller, fuzzy control, bounded-input and bounded-output (BIBO) stability, nonlinear process.

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“…Especially, PID (proportional, integral, and derivative), PI, and PD type FLCs are most common. In this paper, we consider a fuzzy PI controller, as PD FLCs are only suitable for a limited class of systems [11]. Moreover, rule-base design and tuning for PID FLCs are complicated due to many parameters [5].…”

Section: A Overall Structurementioning

confidence: 99%

Adaptive Fuzzy Control for Utilization Management

Suzer

Kang

2008

2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC)

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Abstract-An increasing number of real-time systems are embedded in mission critical systems such as target tracking systems, in which workloads may dynamically vary, for example, depending on the number of targets in the area of interest. Feedback control has been applied to support real-time performance in dynamic environments, producing promising initial results. However, mathematical system modeling necessary for feedback control is challenging. To reduce the difficulty of system modeling, we apply fuzzy control for direct nonlinear mappings between the utilization error (= target utilization − current utilization) and the workload adjustment required to achieve the target utilization via IF-THEN rules. Moreover, via online adaptation, our fuzzy controller can amplify or dampen its own fuzzy control signal, if necessary, to expedite the convergence to the desired utilization. In our simulation study, our approach quickly converges to the target utilization when the workload significantly changes. In contrast, the tested baselines oscillate between overload and underutilization.

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New design and stability analysis of fuzzy proportional-derivative control systems

Cited by 248 publications

References 15 publications

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Stability Analysis of Parallel Fuzzy P + Fuzzy I + Fuzzy D Control Systems

Adaptive Fuzzy Control for Utilization Management

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