M.E. Sawan

Optimal pole placement in a vertical strip

A recursive method for determining the state weighting matrix of a linear quadratic regulator problem in order to shift the open loop poles inside a vertical strip is presented. This method is capable of shifting the real and imaginary parts for continuous time systems. Aggregation is used in each step of the recursive process. Therefore each time the order of the system is reduced to first or second order. A constrained minimization problem with linear and nonlinear constraints has to be solved in order to find the state weighting matrix of the reduced order system that will shift the open loop poles inside the vertical strip.<<ETX>>

Kalman filter design for singularly perturbed systems by unified approach using delta operators

A Kalman filter design is studied in this paper. With the singular perturbation technique, the system is approximated into the composite model and the reduced model. An improved finite word-length characteristic is shown when using the delta operator approach.

Pole placement by performance criterion modification

A procedure in which a state weighting matrix was modified by introducing a degree of relative stability to relocate the optimal closed-loop eigenvalues of continuous time system was recently presented. This procedure is adapted to relocate the optimal poles to any desired location of a discrete time system. A sequential procedure to relocate the optimal eigenvalues to desired positions by proper modification in performance criterion is developed. The optimal solution of the resulting LQ problem determines the optimal gain, and the closed-loop system attains the desired spectrum. Thus, the desired properties of the Linear Quadratic (LQ) solution are retained, while placing the closed-loop system poles.<<ETX>>

Hyperbolic equations in joined domains with boundary energy dissipation

This work deals with the asymptotic behavior of solutions of two hyperbolic equations coupled in series where the energy-absorbing boundaries are presented. It is shown that under some geometrical conditions with respect to a vector field h(x) in the joined surface of the two bounded domains in the space of R/sup n/, the energy of the system will decay uniformly exponentially. Some numerical results for different design of boundary controllers of rectangular domains are presented.

Optimal eigenvalue shifting for continuous systems

A recursive method for selecting the state weighting matrix of a linear quadratic regulator problem in order to shift the open loop eigenvalues to a desired location is presented. This method is capable of shifting a complex pair to new complex or real locations. A minimization problem with linear and nonlinear constraints must be solved in order to find the desired state weighting matrix.<<ETX>>

Singularly perturbed unified systems with low sensitivity to model reduction

A method of designing a state feedback gain achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the delta operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system. The present paper extends the previous study to the discrete system and the delta operating system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

Design of Approximate Feedback Controller for Two-Time-Scale Aircraft Dynamics

A new method to obtain approximate solutions by placing the only poles of the slow subsystem for the two-time-scale aircraft dynamic systems. The two kinds of approximate solutions are obtained by a matrix block diagonalization. One is called the uncorrected solution, and the other is called the corrected solution. The former has an error of , and the latter has an error of . Of course, both solutions are robust enough even though they are reduced solutions. The excellence of the proposed method is illustrated by an numerical example of an aircraft longitudinal dynamics.

Design of Singularly Perturbed Delta Operator Systems with Low Sensitivity

A method of designing a state feedback gam achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system The present paper extends the previous study to the discrete system and the system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.⨀灕잖⨀ㄸㄳ㠱㈵㜰u3100ꤠx8f돀胊ﺖ⨀塨?⨀飾ﺖ⨀脠x8f돐码ﾖ⨀聠잖⨀샾ﺖ⨀夠x8f댐⢣잖⨀ꀀﾖ⨀yﺖ⨀ㄠx8f덐ჿﺖ⨀†烦ﺖ⨀

Rationalization of singularly perturbed systems with multiple time delay by unified approach using delta operator

By using a delta operator approach a rationalization of the singularly perturbed continuous-time system with multiple time delay is introduced. For illustration, an example is shown at the end of this paper.

H/sub /spl infin// filtering of two-time-scale systems

The singular perturbation approach to the analysis and design of two-time-scale systems is applied to the H/sub /spl infin// filtering problem. A sequential procedure is described to decompose the problem into slow and fast subproblems. In this procedure, a fast filter is designed first using the fast model; then a slow filter is designed under a condition on the value of the filter at infinity. A composite filter is formed as the parallel connection of the fast with the strictly proper part of the slow filter. The asymptotic validity of the composite filter is established.