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Fuzzy Supervised PID Control of a Flow Rate Process

Submitted by Mariagrazia Dotoli, 30.11.2001, TE

Problem

A flow rate process exhibits several nonlinear features: the flowmeter is linear in a limited range, the electrovalve exhibits hysteresis and the actuator is affected by saturation. Thus the task of controlling the flow-rate is strongly dependent on the operating condition and, in particular, on the setpoint. It is relatively easy to tune a PID controller when the system works at a specific condition, i.e. when the reference input matches the designed value. On the contrary, if such a PID is employed in a condition different from the designed one, the system performances deteriorate. The purpose of this investigation is to make the PID controller adaptive, i.e. capable of controlling the flow-rate at every operating condition. Since PID controllers are widely used in industry, the problem addressed is of interest for several other applications.

Solution

In order to make the PID controller adaptive, we employ a hierarchical control strategy, consisting of a fuzzy supervisor and of the PID controller itself: the fuzzy supervisor modifies the PID tuning on-line, according to rules with three inputs, the reference, the error and the control action. The first input affects extensively the PID controlled system, while the two additional inputs provide information about the system steady state precision and response speed. Clearly, the supervisor outputs are the PID parameters: the proportional gain, the integral time constant and the derivative time constant.

The fuzzy supervisor is designed as follows. Using the Ziegler-Nichols technique, several optimal configurations of the PID parameters are obtained, each corresponding to a particular operating condition. A tuning table recording the PID parameters is thus produced. On the basis of such a table, a simplified fuzzy supervisor with the set point as a single input is designed. Afterwards, the fuzzy rule base is modified taking into account additional information from the two further inputs. The resulting set of rules is subsequently refined performing some experiments and comparing several system performance indices, namely rise, delay and settling time, integral time absolute error and overshoot.

Status and results

The proposed schema guarantees a good performance in any operating condition. Specifically, the unsupervised and supervised configurations resulted in similar dynamics for all values of the set point. It is to be remarked that the fuzzy supervisor was tuned automatically and compared to a traditional unsupervised PID previously optimized.

Adaptivity and portability

Advantages of the proposed method are the fuzzy-supervised PID adaptivity to different operating conditions, the ability to provide smooth transitions from an operating region to another, the preservation of the performance standards and the linguistic approach to the supervision. The main disadvantage is tuning the supervisor parameters, which is not straightforward and requires considerable process knowledge from the designer. Thus, the developed strategy can be reused, but the process knowledge required is extensive.

More information

Further details are given in:

M. Dotoli, B. Maione and B. Turchiano, " Fuzzy-Supervised PID Control: Experimental Results", EUNITE 2001, Annual Symposium on "Intelligent Technologies, Hybrid Systems and their Implementation in Smart Adaptive Systems", Tenerife, 13-14 December 2002.

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