A new sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty is presented, This sufficient condition is a sum of terms each of which involves the i-th right eigenvector, the i-th left eigenvector, and the real part of the i-th eigenvalue. This new robustness result is less conservative than an earlier result which involves the modal matrix and the real part of the eigenvalue which is closest to the imaginary axis in the complex plane. A robust design is computed for the Extended Medium Range Air to Air Missile and the new design is compared with an earlier orthogonal projection eigenstructure assignment design. The new design method uses the MATLABm Optimization Toolbox to minimize the integral of the roll rate with constraints on the real part of the dutch roll and roll mode eigenvalues, the damping ratios of the dutch roll and roll mode, the aileron and rudder deflection rates, and the sufficient condition for robust stability. The new design satisfies the robustness condition while also yielding an improved transient response. INTFKIWCTIONRecently, Sobel and Cloutier (1991) applied eigenstructure assignment to the design of an autopilot for the Extended Medium Range Air to Air Technology (EMRAAT) missile. An important difference between this application and other eigenstructure assignment applications which have appeared in the literature is that the lateral dynamics of the EMRAAT missile does not have a well defined dutch roll mode. Therefore, eigenstructure assignment is utilized not only for mode decoupling, but also to create distinctly separate dutch roll and roll modes. Sobel and Cloutier (1991) use the approach suggested by Andry et. a1 (1983) in which the i-th desired eigenvector vd is chosen for mode decoupling. Then, the i-th achievable eigenvector vi is chosen as the projection of v : onto the so-called achievability subspace. Sobel and Cloutier (19911 show that their design achieves improved decoupling between an initial sideslip angle and the integrated roll rate (which is approximately equal to the bank angle) when compared to a linear quadratic regulator design proposed by Bossi and Langehough (1988). However, the design of Sobel and Cloutier (1991) does not consider that the missile's aerodynamic parameters are uncertain. A sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty has been proposed by Sobel et. al. (1989). This result, which is based upon the Gronwall lemma, ensures robust stability if the nominal eigenvalues lie to the left of a vertical line in the complex plane. This line is determined by the maximum eigenvalue of a matrix which involves the product of the uncertainty structure, the nominal closed loop modal matrix, and the inverse of the nominal closed loop modal matrix. Yu and Sobel (1991) proposed a robust eigenstructure assignment design method which optimizes the sufficient condition for stabi...
Omer Farook is a member of the faculty of Electrical and Computer Engineering Technology at Purdue University, Nothwest. Farook received the diploma of licentiate in mechanical engineering and B.S. M.E. in 1970 and 1972, respectively. He further received B.S.E.E. and M.S.E.E. in 1978 and 1983, respectively, from Illinois Institute of Technology. Farook's current interests are in the areas of embedded system design, hardware-software interfacing, digital communication, networking, image processing, and biometrics, C++, Python, PHP and Java languages. He has a keen interest in pedagogy and instruction delivery methods related to distance learning. He has a deep commitment to social justice and in achieving economic and educational equity.Dr. Jai P. Agrawal, Purdue University Northwest Jai P. Agrawal is a professor in electrical and computer engineering technology at Purdue University Northwest. He received his Ph.D. in electrical engineering from University of Illinois, Chicago, in 1991, dissertation in power electronics. He also received M.S. and B.S. degrees in electrical engineering from Indian Institute of Technology, Kanpur, India, in 1970 and 1968, respectively The pedagogy of the course delivery is based on "Interactive Learning Model", utilizing the methodology of Outcome Based Education. Outcome Based Education's end result is the students' design projects performed at the end of the course. The course is conducted in a lab or studio like settings, that integrates both lecture and laboratory work in the same settings. The paper elaborates the benefits derived through the pedagogical approaches of keeping the learner actively engaged in all aspects of discovery and design. The course interactively involves the learner in directing and defining the material under discourse.Paper provides a road map and serves as pointer to host of design tools that are available that can be incorporated in a similar freshman course offering for Engineering Technology and Engineering programs. Paper provides the content details in terms of topics covered as well as all the labs performed during the course. The paper presents the details of pedagogical approach that was implemented in successful implementation of this course.
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