Analytical Methods in Vibrations

A method, computer system, and program product for optimizing a useful objective function with respect to a dynamic parameter vector and a static parameter vector. The method, called the static/dynamic control (MDC) method, either minimizes or maximizes the useful objective function subject to a state equation, initial conditions, terminal conditions, constraints, and dynamic limitations. The SDC method includes an algorithm having two formulations: a period formulation and a fully continuous formulation. With the period formulation, the dynamic optimization variables associated with the dynamic limitations are permitted to be discontinuous, parametric functions of time. With the fully continuous formulation, the dynamic optimization variables are permitted to be continuous, non-parametric functions of time. The SDC method is computer implementable and employs an iterative process including an inner loop and an outer loop. The inner loop terminates when the objective function has changed by a satisfactory amount during a fixed outer-loop iteration. The outer loop terminates when the SDC procedure converges. The SDC method may be used to optimize a spacecraft trajectory objective and a spacecraft design objective simultaneously. Optimizing spacecraft objectives via SDC does not require approximating the physics or dynamics of space flight. Thus, any number of gravitating bodies, gravitational harmonics, radiation pressure, atmospheric drag, and general relativistic corrections can be accounted for when using the SDC method. The SDC method does not require prespecification of a planetary flyby sequence for space flight and is capable of identifying optimal flyby sequences.

Static/dynamic control for optimizing a useful objective

Application of MSPCA to Sensor Fault Diagnosis

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Online constrained receding horizon control for astronomical adaptive optics

Genetic-algorithm-based global design optimization of tree-type robotic systems involving exponential coordinates

When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. In this paper we develop algorithms to “update” the DCT and DST to reflect the modified window contents using less computation than by directly evaluating the modified transform via standard Fast Transform algorithms. Our algorithms constitute an improvement over previous DCT/ DST update algorithms because our approach establishes independence between the DCT and the DST: the algorithm for DCT makes use only of DCT terms, and similarly for DST. Algorithms are derived for use without windowing and with split-triangular, Hanning, Hamming and Blackman windows.

Independently updating the DCT and DST for shifting windowed data

In this paper, an algorithm is developed to apply Hann, Hamming, Blackman and related windows directly in the transform domain for the discrete cosine transform and discrete sine transform. These algorithms are useful in applications where windowing is required in order to minimize edge effects caused by implicit symmetries in the transform domain that are not replicated in the real-world data. Examples of such applications include data communication, adaptive system identification and filtering, real-time analysis of financial market data, etc. Software implementations in C language are also given.

Transform domain technique for windowing the DCT and DST

When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. DCTs and DSTs are defined where the denominator in the transform kernel is either an odd or an even integer, resulting in transforms known as the even DCT (EDCT), even DST (EDST), odd DCT (ODCT) and odd DST (ODST). Each is available in types I to IV, for a total of 16 different transforms. The widely used transform commonly called the "DCT" is actually the EDCT-II. In this paper we extend our previous work using the EDCT-II and EDST-II, and show that a similar approach yields algorithms for the ODCT-II and ODST-II. We develop algorithms to "update" the ODCT-II and ODST-II simultaneously to reflect the modified window contents using less computation than directly evaluating the modified transform via standard Fast Transform algorithms. These algorithms are able to handle arbitrary step sizes up to the length of the transform, i.e. the algorithm simultaneously updates the ODCT-II and ODST-II to reflect inclusion of r, where 1 ≤ r ≤ N-1, additional data points and removal of r old points from the signal. Examples of applications where this algorithm would be useful include target recognition where time constraints may not permit the immediate processing of every incoming data point, adaptive system identification, etc.

Rapid update of odd DCT and DST for real-time signal processing

Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) are widely used in image and data compression applications. To process the DCT or DST of a signal a portion of length N is extracted by windowing. By shifting the window point by point the entire signal can be processed. The algorithms are developed that are capable of updating the DCT and DST independently to reflect the modified window contents i.e. for calculating the DCT of the shifted sequence no DST coefficients are used and similarly for calculating the DST of the shifted sequence no DCT coefficients are used. These algorithms constitute an improvement over previous DCT/DST update algorithms as it establishes independence between the DCT and the DST. The update algorithms used to calculate the transform of the shifted sequence uses less computation as compared to directly evaluating the modified transform via standard fast transform algorithms. Firstly, the r-point, 1≤ r ≤ N-1, update algorithms are derived in the presence of the rectangular window. Thereafter, one point independent windowed update in the presence of split-triangular, Hanning, Hamming and Blackman windows are developed. The algorithms were implemented in C language to test their correctness. Thereafter the hardware circuits capable of computing the independent update of DCT-II for the rectangular window of size N =8 and step size of 1 and 4 are developed. The windowed update algorithms are derived for DCT and DST type-I through IV, however the hardware implementation of type-II is given as it is the most frequently used transform.

Discrete cosine transform-only and discrete sine transform-only windowed update algorithms for shifting data with hardware implementation

This paper presents the dynamics and control of a control moment gyroscope actuated inverted pendulum. The control technique utilizes partial feedback linearization, an appropriate global change of coordinates which transform the dynamics of the system into a lower nonlinear subsystem and a chain of double integrators. A control Lyapunov function is designed in order to stabilize the overall system using a backstepping procedure.

Y.P. Kakad

Papers

Independently updating the DCT and DST for shifting windowed data

Transform domain technique for windowing the DCT and DST

Rapid update of odd DCT and DST for real-time signal processing

Discrete cosine transform-only and discrete sine transform-only windowed update algorithms for shifting data with hardware implementation

The Control Moment Gyroscope Inverted Pendulum