FUZZY PID CONTROLLERS: AN OVERVIEW
Abstract
The aim of this study is to examine various studies on fuzzy PID controllers in literature and to classify these fuzzy controllers into categories . There exist three major categories: Direct action (DA) type fuzzy PID controllers, fuzzy gain scheduling (FGS) type fuzzy PID controllers, and hybrid type fuzzy PID controllers. The DA type fuzzy PID controllers are further classified according to the number of the input variables; namely single input, two input, and three input fuzzy PID controllers.
Keywords: Fuzzy controllers, fuzzy PID controllers, tuning mechanisms.
1．INTRODUCTION
The best-known controllers used in industrial control processes are proportional-integral-derivative (PID) controllers because of their simple structure and robust performance in a wide range of operating conditions. However, the PID controller being linear is not suited for strongly nonlinear systems. Fuzzy Control is often mentioned as an alternative to PID control [1]. Most fuzzy controllers used in the industry have the same structure as incremental PI or PID controllers. The parameterization using rules and fuzzy membership functions makes it easy to add nonlinearities, logic, and additional input signals to control law [2]. Therefore, in recent years, fuzzy logic controllers (FLC), especially Fuzzy PID controllers have been widely used for industrial processes owing to their heuristic nature associated with simplicity and effectiveness for both linear and nonlinear systems.
The first fuzzy logic control algorithm implemented by Mamdani (1974) [3] was constructed to synthesize the linguistic control protocol of a skilled human operator. Although, this type of FLC application was successful compared to classical controllers, the design procedure is dependent on the experience and knowledge of the operator and it is limited by the elucidation of the heuristic rules of control. In order to avoid this major difficulty or drawback of depending on the control experience of the operator, Mac Vicar- Whelan (1976) [4] firstly proposed some general rules for the structure of fuzzy controllers. These fuzzy rules devised by Mac Vicar-Whelan approach to a deterministic (PI) or (PD) controller in the limit as quantization levels of control and measurement variables become infinitely fine [5].
In literature, various structures for fuzzy PID (including PI and PD) controllers and fuzzy non-PID controllers have been proposed. A classification of fuzzy controllers is sketched in Figure 1. In general, the application of fuzzy PID controllers can be classified into three major categories according to the way of their construction [6, 7]:
- When a typical FLC is constructed as a set of heuristic control rules, control signal is directly deduced from the knowledge base and the fuzzy inference as it is done in Mc Vicar-Whelan [4] or diagonal rule-base [8] generation approaches [9-11]. Since the fuzzy controller directly drives the process, controllers in this category are referred as “Direct Action” (DA) type [12].
- When the gains of the conventional PID controller are tuned on-line in terms of the knowledge base and fuzzy inference, while still the conventional PID controller generates the control signal [13, 14], the overall controllers of this category are referred as “Fuzzy Gain Scheduling”(FGS) type [15].
- When a conventional PID controller and a DA- type FLC are combined, the overall controllers are referred as “Hybrid” type [15, 16].
- In the rest of the paper, various studies on fuzzy PID controllers in literature will be examined and they will be classified according to the above mentioned three major categories.
Figure 1. A classification of fuzzy controllers
2.DIRECT ACTION TYPE FUZZY PID
CONTROLLERS
2.1 Types of Fuzzy PID Controllers
Fuzzy PID controllers can be constructed either using two inputs or three inputs. Therefore, DA fuzzy PID controllers can be classified into three categories:
- Single input fuzzy PID controllers,
- Two input fuzzy PID controllers,
- Three input fuzzy PID controllers.
- Single input fuzzy PID controllers:
The error signal is the essential and fundamental control component in PID control. Using error as the only input, a single input fuzzy PID controller can be formed. As it is seen in Figure 2 [17], this is simply a nonlinear mapping of error into fuzzy proportional action cascaded to a conventional PID controller.
Figure 2. Single input fuzzy PID controller with one rule base.
The other way of forming a single input fuzzy PID is shown in Figure 3. In this structure, there exist three distinct rule bases using again only error as the input variable to generate three separate fuzzy proportional action [12, 15].
Figure 3. Single input fuzzy PID controller with three separate rule bases.
- Two input fuzzy PID controllers:
If two inputs are used in forming a fuzzy PID controller then one can obtain either fuzzy PD or fuzzy PI controller. For instance, if the inputs are chosen as error (e) and derivative (or chance) of error (e) then one ends up with a fuzzy PD controller as shown in Figure 4. When the inputs are chosen as error (e) and the integral (or the sum) of error then the controller becomes absolute form fuzzy PI controller. If the inputs are chosen as error (e) and derivative (or chance) of error (e) then an incremental form fuzzy PI controller can be obtain, but the output is achieved as the deriv
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