2DOF multi-objective optimal tuning of disturbance reject fractional order PIDA controllers according to improved consensus oriented random search method

The consensus curve M(E) states a dynamic boundary that governs optimization process depending on the value of E. As E decreases, it implies that set point control performance is getting better, the value of consensus curve M(E) increases to meet higher disturbance rejection expectation. The logarithmic consensus coefficient α is used for scaling of dynamic boundary of RDR objective. As the parameter α increases and dynamic boundary M(E) increases for higher disturbance rejection performance. This leads a mechanism that increase of set point performance imposes the increase of disturbance rejection performance. The logarithmic consensus coefficient can be expressed as α=-RDRdB∗log10Emin∗ where Emin∗ is a desired optimal value of min{E} and RDRdB∗ is a desired optimal value for minω∈[ωmin,ωmax]{RDRdB(ω)}. Determination of the logarithmic consensus coefficient α defines a consensus curve for optimal search of multi objective optimization method. The following figure illustrates a consensus curvature for the logarithmic consensus coefficient α=2. [Display omitted] This study presents a Fractional Order Proportional Integral Derivative Acceleration (FOPIDA) controller design methodology to improve set point and disturbance reject control performance. The proposed controller tuning method performs a multi-objective optimal fine-tuning strategy that implements a Consensus Oriented Random Search (CORS) algorithm to evaluate transient simulation results of a set point filter type Two Degree of Freedom (2DOF) FOPIDA control system. Contributions of this study have three folds: Firstly, it addresses tuning problem of FOPIDA controllers for first order time delay systems. Secondly, the study aims fine-tuning of 2DOF FOPIDA control structure for improved set point and disturbance rejection control according to transient simulations of implementation models. This enhances practical performance of theoretical tuning method according to implementation requirements. Thirdly, the paper presents a hybrid controller tuning methodology that increases effectiveness of the CORS algorithm by using stabilizing controller coefficients as an initial configuration. Accordingly, the CORS algorithm performs the fine-tuning of 2DOF FOPIDA controllers to achieve an improved set point and disturbance rejection control performances. This fine-tuning is carried out by considering transient simulation results of 2DOF FOPIDA controller implementation model. Moreover, Reference to Disturbance