Underlying algorithms for designing multivariable decoupling and multiloop PI/PID controllers in a sequential fashion are addressed. A single-loop technique, composed of biased relay identification schemes and tuning formulae leading to the minimum weighted integral of square error, is developed to tune each loop in the predetermined sequence of loop closing. The proposed tuning technique is appropriate for a wide range of process dynamics in a multivariable environment. A method is then proposed to design decouplers to compensate for the effect of interactions and tune the resultant weakly interacting, single-loop PI/PID controllers sequentially. The decouplers, together with the single-loop controllers, constitute the multivariable decoupling controller. If the interactions are not significant, multiloop PI/PID controllers, which do not incorporate decouplers, could be employed. Simulation and comparative results are shown for one 2 × 2 and one 3 × 3 multivariable system from the literature. Despite its simplicity, the proposed design method yields superior multivariable designs on the basis of performance, robust stability, and integrity.

This paper addresses the identification of models using multiple sinusoidal forcing subject to practical difficulties such as unknown initial states, offsets, slow and periodic disturbances, noise, and unknown model structures. A linear regression equation is derived by integrating the system equation excited by a single sinusoid and extended to the case of concurrent multiple sinusoids. The regression equation can be used to estimate the model parameters including time delay in a least-squares fashion. A simple scheme based on the condition number of the matrix formed by the regression vector is presented to infer the best model order. Two-stage sinusoidal testing, represented as two sets of sinusoids applied sequentially, is then developed to generate response data that are informative enough to deal with the aforementioned identification difficulties. This requires only the application of the regression equation for concurrent multiple sinusoids modified in a clever and sequential manner.

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