Abstract

This paper presents the design of a controller for MIMO systems. Performance analysis and controller design for SISO systems are easier than that for MIMO systems. These difficulties are due to the coupling or interactions between the various inputs and output variables. An input 𝐮𝟏, 𝐟𝐫𝐨𝐦 𝐭𝐡𝐞 𝐬𝐞𝐭 𝐮𝐢 ,𝐢 = 𝟏, 𝐦; not only affects the output 𝐲𝟏, 𝐟𝐫𝐨𝐦 𝐭𝐡𝐞 𝐬𝐞𝐭 𝐲𝐢 ,𝐢 = 𝟏, 𝐩; but may affect all the other outputs 𝐲𝐢 ,𝐢 = 𝟐, 𝐩.Similarly, each input 𝐮𝐣 , may also affect output 𝐲𝐤, 𝐤 ≠ 𝐣. In many cases cross-coupling between the inputs and outputs is low and hence conventional SISO controllers may perform well. If a multivariable system exhibits strong cross-coupling between the various inputs and outputs, a multivariable controller has to be designed for achieving satisfactory performance. A popular approach to deal with control loop interactions is to design non-interacting or decoupling control schemes. The role of decoupler is to decompose a multivariable process into a series of independent single-loop sub-system. If such a controller is designed, complete or ideal decoupling occurs and the multivariable process can be controlled using independent loop controllers.

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