**Author details**

Solving the system of equations given in (56), first, solve Equation i) to find the numerical value of *KD*. Then, replace the numerical value of *KD* in Equation ii) and find the numerical value of *KP*. To find the numerical value of *KI*, solve Equation v) or replace the values of *KD* and *KP* in Equation iii) or you can substitute the value of *KP* in Equation iv). With the numerical values of the gains *KD*, *KP* and *KI*, it replaces in the simulator developed in the MATLAB/SIMULINK software to monitor the

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

**Figure 4** shows the performance of the PID-Specified controller, which has the

determined by the internal product of the vector of gains with the propagation matrix in purchase with the controller with the gains determined by the second method of ZN.

The study presented a methodology for adjusting the gains of a PID controller in terms of the internal product of the gains and the propagation matrix. In addition, the relevance of the matrix was shown, which enabled impact assessment of the PID actions associated with the plant parameters. The proposed methodology complied with the project specifications and ensured high controller efficiency without suppressing the PID terms caused by the adjustments. The three PID controller terms were adjusted. Therefore, this methodology can be considered as an alternative to conventional methods for the computation of *KD*, *KP*, and *KI* gains

*Specified* gain vector

transfer function parameters specified by the designer and the *Kpid*

parameters in practical applications and highly complex control plants.

The authors would like to thank PPGEE of the UFMA for the resources to develop this work. We are especially grateful to FAPEMA for research incentive

performance of the proposed method.

*Plant III - PID-ZN x PID-specified.*

**5. Conclusions**

**Figure 4.**

**Acknowledgements**

**82**

José Pinheiro de Moura1,2\*† and João Viana da Fonseca Neto2†

1 State University of Maranhão, Brazil

2 Federal University of Maranhão, Brazil

\*Address all correspondence to: josepinheiro@professor.uema.br

† These authors contributed equally.

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
