autotuning of decentralized and centralized pid control systems for non-square systems

This paper presents a systematic procedure to obtain the decentralized and centralized pid controller settings for a non-square stable multi-input and multi-output (mimo) system using a simultaneous relay autotuning method with the incorporation of higher-order harmonics. in general, the assumption of filtering the higher-order harmonics will be acceptable when the system has the characteristics of a low-pass filter. however, higher-order harmonics have an impact on the controller parameter evaluation and it needs attention. therefore, this research addresses the control of non-square stable mimo systems in their original non-square form instead of squaring them by adding or deleting variables, and also the significance of higher-order harmonics in non-square stable mimo systems is considered. to enhance the controller performance, higher-order harmonics are taken into consideration by observing the initial dynamics of the relay response. the decentralized and centralized control systems’ performances are explored by simulation on two different 3 inputs and 2 outputs models with different levels of interactions. for these models, simulation studies were carried out for both servo and regulatory operations. the performance of the centralized control system is improved for systems with interaction (relative gain is more than 1) by 18-41% for servo operation and 14-31% for regulatory operation. also, the performance is improved for decentralized controllers for systems with a relative gain of less than one. the time integral analysis comparison between centralized and decentralized control schemes with the incorporation of higher-order harmonics using the simultaneous relay autotuning method is implemented. the effectiveness and performance of the proposed scheme are also analyzed even in the presence of robustness and the effect of measurement noise.