Transfer Functions from Sampled Impulse Responses

1970 ◽  
Vol 3 (6) ◽  
pp. T101-T108 ◽  
Author(s):  
M. Zaman ◽  
A. W. J. Griffin
Keyword(s):  
Unique Feature ◽  
Transfer Functions ◽  
Mathematical Formulation ◽  
Impulse Responses ◽  
Linear Dynamical Systems ◽  
Frequency Responses ◽  
Straight Line ◽  
Dc Gain ◽  
Correlation Techniques ◽  
Established Technique

A mathematical formulation is developed for obtaining the frequency responses from known sampled impulse responses of linear dynamical systems. This is done by assuming a straight line approximation from one sampled point to the next and performing the usual Fourier Transformation for this interval. This is repeated for all sampled points and the results are summed together. In practice sampled impulse responses can be obtained using correlation techniques. The frequency responses as obtained above are then processed by a generalised method, developed by the authors, to determine the transfer functions. The unique feature of this method is that the transfer functions can be obtained from the frequency responses without any idea about the actual order of the system and its poles and zeroes. However, the actual principle employed, that of complex curve fitting, is already a well established technique. Finally, many examples are presented which show the validity of the methods where impulse responses are exact and also corrupted by errors. The treatment is restricted to systems which have a finite dc gain. The numerical calculations are processed on an ICT 1905 computer.

scholarly journals Approximation and Analysis of Single Band FIR Pass Integrator Centered around Mid-band Frequencies with Degree k = 1, 2, 3…

2020 ◽  
Vol 64 (4) ◽  
pp. 366-373
Author(s):  
Sumit Bhardwaj ◽  
Ashwni Kumar ◽  
Ram Lal Yadava
Keyword(s):  
Impulse Response ◽  
Transfer Functions ◽  
Finite Impulse Response ◽  
Graphical Analysis ◽  
Performance Comparison ◽  
Phase Response ◽  
Relative Percentage ◽  
Differentiation Method ◽  
Frequency Responses ◽  
The Ideal

In this paper, a modified Finite Impulse Response based linear Pass integrator for centered frequency, ranging between 0.1 π to 0.9 π has been realized. Both the cases have been considered i.e. for what values the phase response is of use and where the phase response has zero value. An iterative formula has been used to calculate the weights depending upon the Transfer Functions, and applying differentiation method. A flat output approximation for the desired frequency ω has been applied for which the results overlap with the ideal integrator. Performance comparison of the proposed integrator has been done with the previous one and relative percentage errors have been observed for both cases implemented. Graphical analysis has also been carried out for frequency responses having degree greater than one (i.e. k = 2, 3, 4) for both cases of proposed integrator and compared with the ideal integrator's response.

scholarly journals Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Yan Chen ◽  
Yingchun Deng ◽  
Shengjie Yue ◽  
Chao Deng
Keyword(s):  
Stochastic Control ◽  
Optimal Trajectory ◽  
Control Method ◽  
Dimensional Space ◽  
Target Position ◽  
Movement Trajectory ◽  
Linear Dynamical Systems ◽  
Reaching Movement ◽  
Optimal Velocity ◽  
Straight Line

This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.

Linear dynamic errors-in-variables models

1986 ◽  
Vol 23 (A) ◽  
pp. 23-39 ◽  
Author(s):  
M. Deistler
Keyword(s):  
Dynamical Systems ◽  
Transfer Functions ◽  
Errors In Variables ◽  
Linear Dynamical Systems ◽  
Linear Dynamic ◽  
Dynamic Errors ◽  
Non Gaussian ◽  
Inputs And Outputs

Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.

Conjugated-Order Differintegrals

2005 ◽  
Author(s):  
Tom T. Hartley ◽  
Carl F. Lorenzo ◽  
Jay L. Adams
Keyword(s):  
Real Time ◽  
Fractional Derivatives ◽  
Transfer Functions ◽  
Control Design ◽  
Frequency Responses ◽  
Complex Order

This paper introduces the concept of conjugated-order differintegrals. These are fractional derivatives whose orders are complex conjugates. These conjugate-order differintegrals allow the use of complex-order differintegrals while still resulting in real time-responses and real transfer-functions. Both frequency responses and time responses are developed. The conjugated differintegral is shown to be a useful representation for control design. An example is presented to demonstrate its utility.

scholarly journals A two-stage calibration method for industrial robots with joint and drive flexibilities

2015 ◽  
Vol 6 (2) ◽  
pp. 191-201 ◽  
Author(s):  
M. Neubauer ◽  
H. Gattringer ◽  
A. Müller ◽  
A. Steinhauser ◽  
W. Höbarth
Keyword(s):  
Transfer Functions ◽  
Geometric Model ◽  
Maximum Error ◽  
Industrial Robots ◽  
Robot Calibration ◽  
Two Stage ◽  
End Effector ◽  
The Real ◽  
Frequency Responses ◽  
Real Robot

Abstract. Dealing with robot calibration the neglection of joint and drive flexibilities limit the achievable positioning accuracy significantly. This problem is addressed in this paper. A two stage procedure is presented where elastic deflections are considered for the calculation of the geometric parameters. In the first stage, the unknown stiffness and damping parameters are identified. To this end the model based transfer functions of the linearized system are fitted to captured frequency responses of the real robot. The real frequency responses are determined by exciting the system with periodic multisine signals in the motor torques. In the second stage, the identified elasticity parameters in combination with the measurements of the motor positions are used to compute the real robot pose. On the basis of the estimated pose the geometric calibration is performed and the error between the estimated end-effector position and the real position measured with an external sensor (laser-tracker) is minimized. In the geometric model, joint offsets, axes misalignment, length errors and gear backlash are considered and identified. Experimental results are presented, where a maximum end-effector error (accuracy) of 0.32 mm and for 90 % of the poses a maximum error of 0.23 mm was determined (Stäubli TX90L).

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