There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Matrix Differential Calculus with Applications in Statistics and Econometrics

In this paper, a novel design method for determining the optimal proportional-integral-derivative (PID) controller parameters of an AVR system using the particle swarm optimization (PSO) algorithm is presented. This paper demonstrated in detail how to employ the PSO method to search efficiently the optimal PID controller parameters of an AVR system. The proposed approach had superior features, including easy implementation, stable convergence characteristic, and good computational efficiency. Fast tuning of optimum PID controller parameters yields high-quality solution. In order to assist estimating the performance of the proposed PSO-PID controller, a new time-domain performance criterion function was also defined. Compared with the genetic algorithm (GA), the proposed method was indeed more efficient and robust in improving the step response of an AVR system.

A particle swarm optimization approach for optimum design of PID controller in AVR system

The future of PID control

This paper describes the development of a fuzzy gain scheduling scheme of PID controllers for process control. Fuzzy rules and reasoning are utilized online to determine the controller parameters based on the error signal and its first difference. Simulation results demonstrate that better control performance can be achieved in comparison with Ziegler-Nichols controllers and Kitamori's PID controllers. >

Fuzzy gain scheduling of PID controllers

Since most processes have nonlinearities, controller design schemes to deal with such systems are required. On the other hand, proportional-integral-derivative (PID) controllers have been widely used for process systems. Therefore, in this paper, a new design scheme of PID controllers based on a data-driven (DD) technique is proposed for nonlinear systems. According to the DD technique, a suitable set of PID parameters is automatically generated based on input/output data pairs of the controlled object stored in the database. This scheme can adjust the PID parameters in an online manner even if the system has nonlinear properties and/or time-variant system parameters. Finally, the effectiveness of the newly proposed control scheme is evaluated on some simulation examples, and a pilot-scale temperature control system.

Design of a Data-Driven PID Controller

A self-tuning PID controller design scheme is proposed, which is able to deal with systems with unknown or time-varying parameters. The proposed scheme is derived based on the relationship between PID control and generalized minimum variance control (GMVC) laws. Furthermore, a suitable set of some user-specified parameters included in the GMVC criterion is sought by using a genetic algorithm recursively. A numerical simulation example shows the effectiveness of the newly proposed control scheme.

A design of self-tuning PID controllers using a genetic algorithm

In the paper, a new multivariable self-tuning PID controller design scheme is proposed which has a static matrix precompensator to reduce the interaction terms of the process transfer function matrix adjusted by an online estimator. The p×p precompensated multivariate system is then controlled via ‘p’ univariate self-tuning PID controllers whose parameters are adjusted by a second identifier placed around the precompensated plant. The PID parameters are calculated online based on the relationship between the PID and generalised minimum variance control laws. The scheme is experimentally evaluated on a 2 × 2 level plus temperature control system. Experimental results illustrate the effectiveness of this scheme.

Design and experimental evaluation of a multivariable self-tuning PID controller

In this paper, a new multivariable self-tuning PID controller design scheme is proposed. The proposed control scheme has a static matrix pre-compensator in order to reduce the interaction terms of the process transfer function matrix. The static matrix pre-compensator is adjusted by an online estimator. The p/spl times/p pre-compensated multivariate system is then controlled via 'p' univariate self-tuning PID controllers, whose parameters are adjusted by a second identifier placed around the pre-compensated plant. The PID parameters are calculated online based on the relationship between the PID and generalized minimum variance control laws. The proposed scheme is experimentally evaluated on a 2/spl times/2 level plus temperature control system. Experimental results illustrate the effectiveness of this new scheme.

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Toru Yamamoto

Papers

Design of a Data-Driven PID Controller

A design of self-tuning PID controllers using a genetic algorithm

Design and experimental evaluation of a multivariable self-tuning PID controller

Design and experimental evaluation of a multivariable self-tuning PID controller

A Design of Self-Tuning PID Controllers Based on the Generalized Minimum Variance Control Law