Ahmad M. Kurniawana, Renantoa*, Juwaria, and Hao-Yeh Leeb

a Department of Chemical Engineering

Institut Teknologi Sepuluh Nopember, Surabaya 60111 Indonesia

b Department of Chemical Engineering

National Taiwan University of Science and Technology, E2-507. Taipei, Taiwan

*Corresponding Author’s E-mail:

Keywords: Inverse Nyquist Array; MIMO; Nonsquare; Stability Criterion; Simulation.


In many industrial process controls, multi-input multi-output (MIMO) processes are commonly found. This system can be controlled if stability of the system can be defined. There are many methods to determine the stability of a system, such as: Multivariable Nyquist Plot, Characteristic Loci Plot, and Inverse Nyquist Array (INA). All of them can only be used in a process that have equal number of inputs and outputs. This process is referred to as square system. But sometimes, more input have to be put dawn to a process to make the best quality of the output or reduction of some input have to be taken from a process due to cost deficiency. This processes are called as non-square processes. Most control method cannot be applied directly to the non-square MIMO process systems because of their complexities. Therefore, behavior of the non-square MIMO process system has to be studied to make sure that the process can be controlled properly.

In this paper, the idea of modification of Inverse Nyquist Array (INA) to analyse characteristic of a non-square MIMO system is first put forward. Inverse Nyquist Array is a method which is proposed by Rosenbrock in 1969 to indicate the degree of interaction among loops and it can evaluate the stability of MIMO system. However, this method is still need to be improved because it can only applied in the square system. In this paper, the modification of Inverse Nyquist Array is taken place by applying pseudo inverse to the INA, and than studied the result based on nyquist plot output.

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