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 JAMP  Vol.7 No.2 , February 2019
Model-Following Designs Using Direct State Derivative Measurement Feedback in Novel Reciprocal State Space Form
Abstract: The paper introduces effective and straightforward algorithms of both explicit and implicit model-following designs with state derivative measurement feedback in novel reciprocal state space form (RSS) to handle state derivative related performance output and state related performance output design cases. Applying proposed algorithms, no integrators are required. Consequently, implementation is simple and low-cost. Simulation has also been carried out to verify the proposed algorithms. Since acceleration can only be modeled as state derivative in state space form and micro-accelerometer which is the state derivative sensor is getting more and more attentions in many microelectromechanical and nanoelectromechanical systems (MEMS/NEMS) applications, the proposed algorithms are suitable for MEMS/NEMS systems installed with micro-accelerometers.
Cite this paper: Tseng, Y. and Wu, R. (2019) Model-Following Designs Using Direct State Derivative Measurement Feedback in Novel Reciprocal State Space Form. Journal of Applied Mathematics and Physics, 7, 394-409. doi: 10.4236/jamp.2019.72030.
References

[1]   Campbell, S.L. (1982) Singular Systems of Differential Equations II. Pitman, Marshfield, Mass., USA.

[2]   Newcomb, R.W. (1981) The Semistate Description of Nonlinear Time Variable Circuits. IEEE Transactions on Circuits and Systems, 28, 62-71.
https://doi.org/10.1109/TCS.1981.1084908

[3]   Brenan, K.E. (1986) Numerical Simulation of Trajectory Prescribed Path Control Problems by the Backward Differentiation Formulas. IEEE Transactions on Automatic Control, 31, 266-269.
https://doi.org/10.1109/TAC.1986.1104236

[4]   Tseng, Y.W. (2009) Vibration Control of Piezoelectric Smart Plate Using Estimated State Derivatives Feedback in Reciprocal State Space Form. International Journal of Control Theory and Applications, 2, 61-71.

[5]   Pantelides, C.C. (1988) The Consistent Initialization of Differential Algebraic Systems. SIAM Journal on Scientific and Statistical Computing, 9, 213-231.
https://doi.org/10.1137/0909014

[6]   Kulah, H., Chae, J., Yazdi, N. and Najafi, K. (2006) Noise Analysis and Characterization of a Sigma-Delta Capacitive Microaccelerometer. IEEE Journal of Solid-State Circuits, 41, 352-361.
https://doi.org/10.1109/JSSC.2005.863148

[7]   Verghese, G.C., Levy, B.C. and Kailath, T. (1981) A Generalized State Space for Singular Systems. IEEE Transactions on Automatic Control, 26, 811-831.
https://doi.org/10.1109/TAC.1981.1102763

[8]   Cobb, D. (2006) State Feedback Impulse Elimination for Singular Systems over a Hermite Domain. SIAM Journal on Control and Optimization, 44, 2189-2209.
https://doi.org/10.1137/040618515

[9]   Liu, D., Zhang, G. and Xie, Y. (2009) Guaranteed Cost Control for a Class of Descriptor Systems with Uncertainties. International Journal of Information & Systems Sciences, 5, 430-435.

[10]   Saadni, M.S., Chaabane, M. and Mehdi, D. (2006) Robust Stability and Stabilization of a Class of Singular Systems with Multiple Time Varying Delays. Asian Journal of Control, 8, 1-11.
https://doi.org/10.1111/j.1934-6093.2006.tb00245.x

[11]   Varga, A. (2000) Robust Pole Assignment for Descriptor Systems. Proceeding of the Mathematical Theory of Networks and Systems, Perpignan, 12-16 August 2000.
https://core.ac.uk/download/pdf/11096417.pdf

[12]   Cobb, D. (2010) Eigenvalue Conditions for Convergence of Singularly Perturbed Matrix Exponential Functions. SIAM Journal on Control and Optimization, 48, 4327-4351.
https://doi.org/10.1137/09075113X

[13]   Yeh, F.B. and Huang, H.N. (2000) H Infinity State Feedback Control of Smart Beam-Plates via the Descriptor System Approach. Tunghai Science, 2, 21-42.

[14]   Tseng, Y.W. (2008) Control Designs of Singular Systems Expressed in Reciprocal State Space Framework with State Derivative Feedback. International Journal of Control Theory and Applications, 1, 55-67.

[15]   Tseng, Y.W. and Wang, Y.N. (2013) Sliding Mode Control with State Derivative Output Feedback in Reciprocal State Space Form. Abstract and Applied Analysis, 2013, Article ID: 590524.
https://www.hindawi.com/journals/aaa/2013/590524/
https://doi.org/10.1155/2013/590524


[16]   Tseng, Y.W., Kwak, S.K. and Yedavalli, R.K. (2003) Stability, Controllability and Observability Criteria for the Reciprocal State Space Framework. Proceedings of the 2003 American Control Conference, Denver, 4-6 June 2003, 5093-5097.
https://ieeexplore.ieee.org/document/1242535

[17]   Tseng, Y.W. and Hsieh, J.G. (2013) Optimal Control for a Family of Systems in Novel State Derivative Space Form with Experiment in a Double Inverted Pendulum System. Abstract and Applied Analysis, 2013, Article ID: 715026.
https://www.hindawi.com/journals/aaa/2013/715026/
https://doi.org/10.1155/2013/715026


[18]   Stevens, B.L. and Lewis, F.L. (1992) Aircraft Control and Simulation. John Wiley and Sons, Inc., New York, 421-437.

[19]   Kreindler, E. and Rothschild, D. (1976) Model-Following in Linear Quadratic Optimization. Journal of AIAA, 14, 835-842.
https://doi.org/10.2514/3.7160

 
 
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