Wave digital simulation of passive systems in linear state-space form

Abstract Gimbals are mechatronic systems well known for their use in the stabilization of cameras which are under the effect of sudden movements. Gimbals help keeping cameras at previously defined fixed orientations, so that the captured images have the highest quality. This paper focuses on the design of a Linear Quadratic Gaussian, LQG, controller, based on the physical modeling of a commercial Gimbal with two degrees of freedom (2DOF), which is used for first-person applications in unmanned aerial vehicle (UAV). This approach is proposed to make a more realistic representation of the system under study, since it guarantees high accuracy in the simulation of the dynamic response, as compared to the prediction of the mathematical model of the same system. The development of the model starts by sectioning the Gimbal into a series of interconnected links. Subsequently, a fixed reference system is assigned to each link body and the corresponding homogeneous transformation matrices are established, which will allow the calculation of the orientation of each link and the displacement of their centers of mass. Once the total kinetic and potential energy of the mechanical components are obtained, Lagrange’s method is utilized to establish the mathematical model of the mechanical structure of the Gimbal. The equations of motion of the system are then expressed in state space form, with two inputs, two outputs and four states, where the inputs are the torques produced by each one of the motors, the outputs are the orientation of the first two links, and the states are the aforementioned orientations along with their time derivatives. The state space model was implemented in MATLAB’s Simulink environment to compare its prediction of the transient response with the prediction obtained with the representation of the same system using MATLAB’s SimMechanics physical modelling interface. The mathematical model of each one of the three-phase Brushless DC motors is also expressed in state space form, where the three inputs of each motor model are the voltages of the corresponding motor phases, its two outputs are the angular position and angular velocity, and its four states are the currents in two of the phases, the orientation of the motor shaft and its rate of change. This model is experimentally validated by performing a switching sequence in both the simulation model and the physical system and observing that the transient response of the angular position of the motor shaft is in accordance with the theoretical model. The control system design process starts with the interconnection of the models of the mechanical components and the models of the Brushless DC Motor, using their corresponding state space representations. The resulting model features six inputs, two outputs and eight states. The inputs are the voltages in each phase of the two motors in the Gimbal, the outputs are the angular positions of the first two links, and the states are the currents in two of the phases for each motor and the orientations of the first two links, along with their corresponding time derivatives. An optimal LQG control system is designed using MATLAB’s dlqr and Kalman functions, which calculate the gains for the control system and the gains for the states estimated by the observer. The external excitation in each of the phases is carried out by pulse width modulation. Finally, the transient response of the overall system is evaluated for different reference points. The simulation results show very good agreement with the experimental measurements.

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Stewart Platform Model with Uncertain Parameters

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.164.177 ◽

2010 ◽

Vol 164 ◽

pp. 177-182 ◽

Cited By ~ 2

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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Robust Estimation of Linear State Space Models

SSRN Electronic Journal ◽

10.2139/ssrn.3068633 ◽

2017 ◽

Author(s):

Ruben Crevits ◽

Christophe Croux

Keyword(s):

State Space ◽

Robust Estimation ◽

State Space Models ◽

Linear State

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Optimal State-Space Control of a Gas Turbine Engine

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2906654 ◽

1992 ◽

Vol 114 (4) ◽

pp. 763-767 ◽

Cited By ~ 12

Author(s):

J. W. Watts ◽

T. E. Dwan ◽

C. G. Brockus

Keyword(s):

State Space ◽

Gas Turbine ◽

State Space Model ◽

Gas Turbine Engine ◽

The State ◽

Operating Conditions ◽

Turbine Engine ◽

Analog Control ◽

Linear State ◽

High Level

An analog fuel control for a gas turbine engine was compared with several state-space derived fuel controls. A single-spool, simple cycle gas turbine engine was modeled using ACSL (high level simulation language based on FORTRAN). The model included an analog fuel control representative of existing commercial fuel controls. The ACSL model was stripped of nonessential states to produce an eight-state linear state-space model of the engine. The A, B, and C matrices, derived from rated operating conditions, were used to obtain feedback control gains by the following methods: (1) state feedback; (2) LQR theory; (3) Bellman method; and (4) polygonal search. An off-load transient followed by an on-load transient was run for each of these fuel controls. The transient curves obtained were used to compare the state-space fuel controls with the analog fuel control. The state-space fuel controls did better than the analog control.

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Blind deconvolution of sparse but filtered pulses with linear state space models

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ◽

10.1109/icassp.2016.7472467 ◽

2016 ◽

Cited By ~ 4

Author(s):

Nour Zalmai ◽

Hampus Malmberg ◽

Hans-Andrea Loeliger

Keyword(s):

State Space ◽

Blind Deconvolution ◽

State Space Models ◽

Linear State

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Experience Rating of ARIMA Processes by the Kalman Filter

Astin Bulletin ◽

10.2143/ast.16.1.2015010 ◽

1986 ◽

Vol 16 (1) ◽

pp. 19-31 ◽

Cited By ~ 6

Author(s):

Jukka Rantala

Keyword(s):

Kalman Filter ◽

Time Delay ◽

State Space ◽

Theoretical Approach ◽

Space Form ◽

The State ◽

Experience Rating ◽

Filter Technique ◽

Main Emphasis ◽

Arima Processes

AbstractThis paper deals with experience rating of claims processes of ARIMA structures. By experience rating we mean that future premiums should be only a function of past values of the claims process. The main emphasis is on demonstrating the usefulness of the control-theoretical approach in the search for optimal rating rules. Optimality is here defined to mean as smooth a flow of premiums as possible when the variation in the accumulated profit is restricted to a certain amount. First it is shown how the underlying model in its simplest form can be transformed into the state-space form. Then the Kalman filter technique is used to find the optimal rules. Also a time delay in information is taken into account. The optimal rules are illustrated by examples.

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