![]() ![]() The relay feedback test was first proposed by Astrom and Hagglund (1984) for process control practitioners as a closed-loop tool for system identification and control. The sequential identification and the expert controller design methods form the basic structure for the multivariable autotuner that allows loop tuning without breaking the loop and without interrupting production, in process industries. Whenever closed loop performance degrades, loops must be retuned with correct input-output pairs. With increase in complexity of the process, it becomes difficult to control the loops properly. ![]() Introduction Chemical processes are complex and non-linear in nature due to interactions (Seborg et. This closed-loop equation not only enables us to assess the effect of interactions between inputs and outputs but is also useful to back calculate/estimate the exact process model parameters, appearing in the analytical expressions for linear 3-by-3 MIMO systems, from experimental response.ฤก. These analytical expressions, in a closed form solution are useful to identify unknown system parameters, to understand interactions, to diagnosis the fault at the earlier stage, and subsequently for auto tuning. MIMO systems with lower-order transfer functions with different time delays are used to illustrate the derivation. Generalized expressions are formulated based on the observation that a relay feedback test consists of a series of step inputs and a stable limit cycle implies a convergent infinite series. Analytical expressions for relay responses in time domain for the interactive transfer functions (off-diagonal elements) of the systems are derived and are validated. Relay feedback tests are carried out onmulti input multi output systems.
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