International Journal of Advanced Engineering Research and Science (IJAERS) [Vol-5, Issue-5, May- 2018] https://dx.doi.org/10.22161/ijaers.5.5.28 ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 218 A Novel Constraint Narrowing Technique for MIMO Unstable System Laxmikant M. Deshpande 1 , Dr. A.M.Bhavikatti 2 1 Research scholar, VTU Belgaum, Kranataka, India 2 Prof. & Head, Dept.of ECE, BKIT, Bhalki, Karnataka State, India Abstract— Frequency response data collection can be a boon for modeling of MIMO uncertain plant. System stability can be assessed either by transfer function or by state-space method. Both will arrive at matrix transformation and further decision approach. Both can be considered for diagonalization of matrix. It is a proven fact that when the matrix is diagonalized the elements of the principle diagonal are the Eigen values and these Eigen values are closed loop poles from which stability can be assessed. The feature of such a diagonal matrix is that its principle diagonal elements contain gains of all the feedback paths. Singular value decomposition is used here for diagonalization. Singular value decomposition technique has been demonstrated by many authors but, application of PCA with Euclidian norm has not been paid attention so far. The systems numerical array is fed to a digital processing tool such as Mat lab and SVD-PCA (Singular Value Decomposition- Principal Component Analysis) is applied to determine the reduction of disturbance or noise and to provide minimum sensitivity and error correction. There are Hull, Box and KB consistency narrowing techniques used previously and the idea is extended further and an SVD-PCA-Norm technique which is now referred as LA criteria has been demonstrated here. Keywords— Constraint Narrowing, Degree of Freedom, Hull consistency, ICST, MIMO, Pre-filter, QFT. I. INTRODUCTION Good performance of control system is the result of combination of feed-forward and feedback control systems. Stability is the constraint applicable to feedback control due to the uncertainty in tracking and measured noise filtering, whereas sensor availability and modeling errors limit the performance of feed-forward system. Generally, a 2-DOF is selected for demonstration in which the output of the plant and reference are available to the control system. The number of degree of freedom is defined as the number of closed loop transfer function that can be designed independently. In 2-DOF closed loop systems, there are transfer functions from disturbance to output and reference to output can be designed independently. Many control requirements are assessed in frequency domain. The ability of the control system to reject the disturbances whose frequency components are concentrated on a certain band determines its performance. It is a proven fact that the effective control band is the one whose worst-case sensitivity is below 6 dB which indicates a minimum attenuation of 50% of output disturbance. In PCA actually very few components are selected which is as good as rejecting frequency components in a particular band and thus amounts to 50% of disturbance rejection. For disturbance rejection a comparison of the worst case open loop response and the closed loop response will determine how effective control design has been. In other words, there are finite set of constraints which specify which value combination from given variable domains are admitted and the value combination satisfying all constraints, that means rounding off errors and this has been done by PCA-Euclidian Norm. II. DESIGN CONSTRINATS AND SATISFACTION Quantitative Feedback Theory (QFT) is for robust stability, tracking and disturbance rejection. The constraints applied over certain intervals are sensitivity S (jw), Complementary Sensitivity T(jw), Gain Margin, Phase Margin, Resonant Peak, and Bandwidth. These constraints over the interval are satisfied in order to get good stability and disturbance rejection by having:  High Gain at Low Frequency  Low Gain at High Frequency  Sensitivity must lie between 1 - 1.5  Complementary Sensitivity must lie between 1.2 - 2.0  Gain Margin should be in the range of 1.7-4.0  Phase Margin should be in the range of 30 0 - 45 0  Damping Ratio  =0.64 for maximum response speed