scholarly journals Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design

2010 ◽  
Author(s):  
Alisha R. Schor ◽  
H. Harry Asada
Keyword(s):  
State Space ◽  
Controller Design ◽  
Chemical Diffusion ◽  
Pole Placement ◽  
Integral Control ◽  
Output State ◽  
Chemical Inputs ◽  
Chemical Distribution ◽  
Low Order

Chemical distribution is an important factor in many biological systems, driving the phenomenon known as chemotaxis. In order to properly study the effects of various chemical inputs to an in vitro biological assay, it is necessary to have strict control over the spatial distribution of these chemicals. This distribution is typically governed by diffusion, which by nature is a distributed parameter system (DPS), dependent on both space and time. Much study and literature within the controls community has been devoted to DPS, whose dynamics are marked by partial differential equations or delays. They span an infinite-dimensional state-space, and the mathematical complexity associated with this leads to the development of controllers that are often highly abstract in nature. In this paper, we present a method of approximating these systems and expressing them in a manner that makes a DPS amenable to control using a very low order model. In particular, we express the PDE for one-dimensional chemical diffusion as a two-input, two-output state-space system and show that standard controllers can manipulate the outputs of interest, using pole placement and integral control via an augmented state model.

Design of State Space Controllers for Industrial Twin Shaft Gas Turbines

2005 ◽  
Author(s):  
Markus Beukenberg ◽  
Michael Brodmann ◽  
Hans Weibel ◽  
Detlef Mu¨ller
Keyword(s):  
State Space ◽  
Gas Turbines ◽  
Controller Design ◽  
Mathematic Model ◽  
Pole Placement ◽  
Operating Point ◽  
Design Procedures ◽  
Industrial Gas Turbines ◽  
Linear State ◽  
Complex Mathematical Model

This paper depicts the development of a new control strategy for industrial gas turbines to improve the control accuracy in the entire operating range. In the first step, a complex mathematical model has been developed, which is implemented into the controller dynamic simulation. An automatic operating point dependent linearization process permits the model to be displayed in a linear state space description. Three established controller design procedures have been applied to the process. In the past, only a small number of state space control designs have been presented for industrial gas turbines. These approaches use low order mathematical descriptions, which often do not describe the system behavior in detail. This paper presents a controller design for a more detailed mathematic model of the 15th order. It is indicated, that certain controller designs are difficult to realize or even fail. These effects result from unfavourable numerical conditions (depending on the operating point) in combination with the high order of the approximated linear system description. The tested pole placement designs show favorable closed loop system dynamic behavior and were improved by adding an integrating part to the controller.

scholarly journals State Space Based Linear Controller Design for the Inverted Pendulum

2019 ◽  
Vol 12 (2) ◽  
pp. 130-147 ◽  
Author(s):  
Miklós Kuczmann
Keyword(s):  
State Space ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Pole Placement ◽  
Space Representation ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Linear Controller ◽  
Inverted Pendulum System

In a previous survey paper the detailed PID controller design to stabilize the inclination angle as well as the horizontal movement of an inverted pendulum system has been presented. In this paper the linear controller design based on the state space representation is shown step by step. Pendulum model is based on EulerLagrange modeling, and the nonlinear state space model is linearized in the unstable upward position, finally pole placement by Ackermann formula and Bass–Gura equation, moreover linear quadratic optimal control are presented. The pendulum has been inserted into a virtual reality laboratory, which is suitable to use in model based control teaching.

scholarly journals Implementation of a Communication Satellite Orbit Controller Design Using State Space Techniques

2012 ◽  
Vol 29 (1) ◽  
pp. 29
Author(s):  
M.T HLA ◽  
Y.M Lae ◽  
S.L Kyaw ◽  
M.N Zaw
Keyword(s):  
State Space ◽  
Controller Design ◽  
Damping Ratio ◽  
Dynamic Control ◽  
State Space Model ◽  
Satellite Orbit ◽  
Design Tool ◽  
Pole Placement ◽  
Peak Time ◽  
Communication Satellite

This research is of great importance for controlling the altitude of a satellite, especially one used for global communications in a geo-stationary orbit. The objective of this research was to advance a design based on the modelling of an orbit controller for a satellite orbiting into a circular orbit. This encompasses a good understanding of the system’s dynamics. Once a satellite is launchedinto a desired orbit, it never remains in this ideal orbit. The external forces present in space cause perturbations to the ideal orbit. To bring the satellite back into the desired orbit, on-board thrusters provide the in-orbit propulsion. In this research, the altitude of the satellite was controlled by a thruster fashioned by the on-board thrusters installed in the radial and tangential directions. However,dictated by the controllable prerequisite, we achieved dynamic system stabilization with the aid of two thrusters as well as one thruster. Thus, the feedback dynamic control system responded to both the two-input and the single-input cases. The model developed was effectively a linearized, normalizedand state-space model. The simulation of this model was based on the MATLAB environment. The design evolved accordingly was used to revise the effect of pole placement on the controlling parameters, such as settling time, peak time, overshoot, and damping ratio of the closed-loop system. This enabled us to make predictions on the stability requirements for several dynamic systems ofthe type considered. The design tool thus developed was applied to an actual current communication satellite design. The design results were evaluated and recommendations completed. 

scholarly journals Anℋ∞Optimal Robust Pole Placement with Fixed Transparent Controller Structure on the Basis of Nonnegativity of Even Spectral Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Andrej Sarjaš ◽  
Rajko Svečko ◽  
Amor Chowdhury
Keyword(s):  
Controller Design ◽  
Polynomial Equation ◽  
Pole Placement ◽  
Robust Controller ◽  
Reference Tracking ◽  
Common Criteria ◽  
Sensitivity Problem ◽  
The Common ◽  
Partial Fraction Decomposition ◽  
Iterative Evolution

This paper presents the synthesis of an optimal robust controller with the use of pole placement technique. The presented method includes solving a polynomial equation on the basis of the chosen fixed characteristic polynomial and introduced parametric solutions with a known parametric structure of the controller. Robustness criteria in an unstructured uncertainty description with metrics of normℋ∞are for a more reliable and effective formulation of objective functions for optimization presented in the form of a spectral polynomial with positivity conditions. The method enables robust low-order controller design by using plant simplification with partial-fraction decomposition, where the simplification remainder is added to the performance weight. The controller structure is assembled of well-known parts such as disturbance rejection, and reference tracking. The approach also allows the possibility of multiobjective optimization of robust criteria, application of mixed sensitivity problem, and other closed-loop limitation criteria, where the common criteria function can be composed from different unrelated criteria. Optimization and controller design are performed with iterative evolution algorithm.

An in vitro setup to test the relevance and the accuracy of low-order vocal folds models

2007 ◽  
Vol 121 (1) ◽  
pp. 479-490 ◽  
Author(s):  
Nicolas Ruty ◽  
Xavier Pelorson ◽  
Annemie Van Hirtum ◽  
Ines Lopez-Arteaga ◽  
Avraham Hirschberg
Keyword(s):  
Vocal Folds ◽  
Low Order

Stewart Platform Model with Uncertain Parameters

2010 ◽  
Vol 164 ◽  
pp. 177-182 ◽  
Author(s):  
Lukas Březina ◽  
Tomáš Březina
Keyword(s):  
State Space ◽  
Controller Design ◽  
State Space Model ◽  
Stewart Platform ◽  
Dynamics Model ◽  
H Infinity ◽  
Uncertain Dynamics ◽  
Six Dof ◽  
Linear State ◽  
Nominal Position

The paper deals with development of uncertain dynamics model of a six DOF parallel mechanism (Stewart platform) suitable for H-infinity controller design. The model is based on linear state space models of the machine obtained by linearization of the SimMechanics model. The linearization is performed for two positions of the machine in its workspace. It is the nominal position and the position where each link of the machine reaches its maximal length. The uncertainties are then represented as differences between parameters of corresponding state-space matrices. The uncertain state space model is then obtained using upper linear fractional transformation. There are also mentioned several notes regarding H-infinity controller designed according to the obtained model.

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