Markov Data-Based LQG Control1

1998 ◽  
Vol 122 (3) ◽  
pp. 551-559 ◽  
Author(s):  
Guojun Shi ◽  
Robert E. Skelton
Keyword(s):  
Control Problem ◽  
State Space ◽  
Controller Design ◽  
Design Method ◽  
State Space Model ◽  
Closed Form Expression ◽  
Space Model ◽  
Weighting Matrix ◽  
Full State ◽  
Lqg Control

In this paper the Markov data-based LQG control problem is considered. The Markov data-based LQG control problem is to find the optimal control sequence which minimizes a quadratic cost function over some finite interval [0, N]. To solve this problem, we show that a complete input-output description of the system is not necessary. Obviously, a complete state space model is not necessary for this problem either. The main contributions of this paper include: (i) develop a new data-based LQG controller in a recursive form and a batch-form, (ii) derive a closed-form expression for the system’s optimal performance in terms of the Markov parameters, (iii) develop an algorithm for choosing the output weighting matrix, and (iv) demonstrate that the amount of information about the system required by the data-based controller design is less than the amount required to construct the full state space model. A numerical example is given to show the effectiveness of the data-based design method. [S0022-0434(00)02503-X]

scholarly journals A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Michael J. Panza
Keyword(s):  
Transfer Function ◽  
Closed Form ◽  
State Space ◽  
Infinite Series ◽  
State Space Model ◽  
Closed Form Expression ◽  
Space Model ◽  
Finite State ◽  
Acoustic Reverberation ◽  
Finite State Space

The acoustic reverberation between two parallel reflecting planes can be represented by an infinite series of the images caused by the planes. To provide a more useful model for analysis and control, the infinite series version of the Green’s function is converted into a finite state space model that retains the high frequency character that enables broadband noise inputs to be examined. The infinite series is first summed into a very accurate, approximate closed form expression in the time domain in terms of a radical function. The radical is then transformed into an expression containing exponentials which have exact Laplace transforms that lead to an overall closed form transfer function for the system. The system transfer function is transformed into a third-order state space model that theoretically contains all of the frequency characteristics of the infinite series representation. The accuracy of the state space model is examined by comparing it to the infinite series solution for three typical types of acoustical inputs: exponential for impulse noise, single frequency sine for harmonic noise, and a multifrequency Schroeder phased harmonic sequence for random noise.

scholarly journals Structural Analysis and Control of a Model of Two-Site Electricity and Heat Supply

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Hikaru Hoshino ◽  
Yoshihiko Susuki ◽  
T. John Koo ◽  
Takashi Hikihara
Keyword(s):  
Control Problem ◽  
Equilibrium Point ◽  
State Space ◽  
Heat Supply ◽  
State Space Model ◽  
The State ◽  
Model Parameters ◽  
Space Model ◽  
Energy Flows

This paper introduces a control problem of regulation of energy flows in a two-site electricity and heat supply system, where two combined heat and power (CHP) plants are interconnected via electricity and heat flows. The control problem is motivated by recent development of fast operation of CHP plants to provide ancillary services of power system on the order of tens of seconds to minutes. Due to the physical constraint that the responses of the heat subsystem are not necessary as fast as those of the electric subsystem, the target controlled state is not represented by any isolated equilibrium point, implying that stability of the system is lost in the long-term sense on the order of hours. In this paper, we first prove in the context of nonlinear control theory that the state-space model of the two-site system is nonminimum phase due to nonexistence of isolated equilibrium points of the associated zero dynamics. Instead, we locate a one-dimensional (1D) invariant manifold that represents the target controlled flows completely. Then, by utilizing a virtual output under which the state-space model becomes minimum phase, we synthesize a controller that achieves not only the regulation of energy flows in the short-term regime but also stabilization of an equilibrium point in the long-term regime. Effectiveness of the synthesized controller is established with numerical simulations with a practical set of model parameters.

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