This paper introduces an optimal fuzzy proportional-integral-derivative (PID) controller. The fuzzy PID controller is a discrete-time version of the conventional PID controller, which preserves the same linear structure of the proportional, integral, and derivative parts but has constant coefficient yet self-tuned control gains. Fuzzy logic is employed only for the design; the resulting controller does not need to execute any fuzzy rule base, and is actually a conventional PID controller with analytical formulae. The main improvement is in endowing the classical controller with a certain adaptive control capability. The constant PID control gains are optimized by using the multiobjective genetic algorithm (MOGA), thereby yielding an optimal fuzzy PID controller. Computer simulations are shown to demonstrate its improvement over the fuzzy PID controller without MOGA optimization.

An optimal fuzzy PID controller

The majority of the research work on fuzzy PID controllers focuses on the conventional two-input PI or PD type controller proposed by Mamdani (1974). However, fuzzy PID controller design is still a complex task due to the involvement of a large number of parameters in defining the fuzzy rule base. This paper investigates different fuzzy PID controller structures, including the Mamdani-type controller. By expressing the fuzzy rules in different forms, each PLD structure is distinctly identified. For purpose of analysis, a linear-like fuzzy controller is defined. A simple analytical procedure is developed to deduce the closed form solution for a three-input fuzzy inference. This solution is used to identify the fuzzy PID action of each structure type in the dissociated form. The solution for single-input-single-output nonlinear fuzzy inferences illustrates the effect of nonlinearity tuning. The design of a fuzzy PID controller is then treated as a two-level tuning problem. The first level tunes the nonlinear PID gains and the second level tunes the linear gains, including scale factors of fuzzy variables. By assigning a minimum number of rules to each type, the linear and nonlinear gains are deduced and explicitly presented. The tuning characteristics of different fuzzy PID structures are evaluated with respect to their functional behaviors. The rule decoupled and one-input rule structures proposed in this paper provide greater flexibility and better functional properties than the conventional fuzzy PHD structures.

Analysis of direct action fuzzy PID controller structures

Fuzzy PID controller: Design, performance evaluation, and stability analysis

The robotics literature of the last two decades contains many important advances in the control of flexible joint robots. This is a survey of these advances and an assessment for future developments, concentrated mostly on the control issues of flexible joint robots.

A survey on the control of flexible joint robots

This brief aims to show that a linear proportional–integral–derivative (PID) controller is theoretically valid for tracking control of robotic manipulators driven by compliant actuators. The control problem is formulated into a three-time-scale singular perturbation formula, including a slow time scale at the rigid robot dynamics, one actual fast time scale at the actuator dynamics, and another virtual fast time scale at the controller dynamics. A PID-type controller is derived to guarantee semiglobal practical exponential stability of the rigid robot dynamics, and a derivative-type controller is applied to establish global exponential stability of the actuator dynamics. Based on a state transformation to the closed-loop rigid robot dynamics and the extended Tikhonov’s theorem, it is proven that the entire system has semiglobal practical exponential stability under a proper choice of control parameters. The proposed controller is not only structurally simple and model-free resulting in low implementation cost, but also robust against external disturbances and parameter variations. The current design is only valid while the spring stiffness is relatively large compared with other parameters of the robot dynamics. Experimental results based on a single-link compliant robotic manipulator have verified effectiveness of the proposed approach.

Efficient PID Tracking Control of Robotic Manipulators Driven by Compliant Actuators

This paper presents the design and experiment of a fuzzy proportional integral derivative (PID) controller for a flexible-joint robot arm with uncertainties from time-varying loads. Experimental results have shown remarkable tracking performance of this fuzzy PID controller, and have convincingly demonstrated that fuzzy logic control can be used for flexible-joint robot arms with uncertainties and it is quite robust. In this paper, the fuzzy PID controller is first described briefly, using a simple and practical PD+I controller configuration. This configuration preserves the linear structure of the conventional PD+I controller, but has nonconstant gains: the proportional, integral, and derivative gains are nonlinear functions of their input signals, which have self-tuning (adaptive) capabilities in set-point tracking performance. Moreover, these variable gains make the fuzzy PID controller robust with faster response time and less overshoot than its conventional counterpart. The proposed design was tested using a flexible-joint robot arm driven by a DC motor in a laboratory, where the arm was experienced with time-varying loads. Control performance by the conventional and fuzzy PID controllers for such a laboratory robotic system are both included in this paper for comparison.

D. Feigenspan

Papers

Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads