A note on Kalman filtering

The purpose of this paper is to point out a confusing phenomenon in the teaching of Kalman filtering. Students are often confused by noting that the a posteriori error covariance of the discrete Kalman filter (DKF) is smaller than the error covariance of the continuous Kalman filter (CKF), which would mean that the DKF is better than CKF since it gives a smaller error covariance. However, simulation results show that CKF gives estimates much closer to the true states. We provide a simple qualitative argument to explain this phenomenon     

A note on definitions of trees

A number of definitions of trees appear in various courses of a computer engineering curriculum such as circuits or data structures. It is shown that a commonly used recursive definition of a tree is equivalent to a graph-theoretic definition. This puts the recursive definition in a better perspective relative to the various equivalent forms of graph-based trees. Pedagogically, as both types of definitions are often introduced to students even in the same course, this approach should provide a strong basis for students to understand their relationship.<>     

A note on passivity and losslessness

This note gives new necessary and sufficient conditions for a linear system to be passive or lossless. It will be shown that, by using the theory of operators on an indefinite J(t)-Hilbert space, both the passivity and isometric conditions for an operator to be lossless can be combined into a single condition—namely an operator is lossless if and only if it is J(t)-contractive.     

A note on high-Q active networks

Levi's and Zeheb's approach for approximating a high-Q second-order section by n sections with lower Q's is compared with the optimal solution of this problem proposed by Khazanov. Tables relating the maximum error in the approximation to the values of n and the achievable Q-reduction (QR) are also given. They should prove useful to the designer. Finally, some comments on sensitivities are added.     

Technical note self-tuning ziegler-nichols pid controller

A new digital self-tuning PID controller (STC PID) algorithm has been derived in this paper. the parameters of this controller are designed on the basis of a modified Ziegler-Nichols criterion for digital control loops. the process is modelled as a controlled regression and its parameters are estimated using the recursive least squares method (RLSM) with LD decomposition and with directional forgetting applied. the algorithm is suitable for automatic setting of digital PID controllers for the control of deterministic processes or the adaptive control of stochastic processes.     

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