Time-Domain Input-Output Transient Performance Validation for Modular Control Systems: Method and Examples

2010 ◽  
Author(s):  
Deepak Sharma ◽  
D. M. Tilbury ◽  
Lucia Seno
Keyword(s):  
Control Systems ◽  
Time Domain ◽  
Convex Sets ◽  
Mimo Systems ◽  
Transient Performance ◽  
Input Output ◽  
Modular Control ◽  
Input And Output ◽  
The Time Domain ◽  
Performance Validation

This paper presents results that can be used to validate input-output transient performance for modular control systems. If bounds in the time-domain are specified for inputs of an LTI SISO system, the techniques in this paper can determine the minimum set containing all possible outputs. If both input and output bounds are given, they can determine whether these specifications are met. Network delay affecting the input of the system is also considered. Finally, this paper extends the techniques for MIMO systems. The results are derived using the theory of convex sets. Several examples are presented to illustrate the results and demonstrate their application.

A Multiple Harmonic Open-Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings

2002 ◽  
Vol 124 (4) ◽  
pp. 827-834 ◽  
Author(s):  
D. O. Baun ◽  
E. H. Maslen ◽  
C. R. Knospe ◽  
R. D. Flack
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Open Loop ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Rotor Vibration ◽  
Aerodynamic Forces ◽  
Analog Input ◽  
Input And Output ◽  
The Time Domain

Inherent in the construction of many experimental apparatus designed to measure the hydro/aerodynamic forces of rotating machinery are features that contribute undesirable parasitic forces to the measured or test forces. Typically, these parasitic forces are due to seals, drive couplings, and hydraulic and/or inertial unbalance. To obtain accurate and sensitive measurement of the hydro/aerodynamic forces in these situations, it is necessary to subtract the parasitic forces from the test forces. In general, both the test forces and the parasitic forces will be dependent on the system operating conditions including the specific motion of the rotor. Therefore, to properly remove the parasitic forces the vibration orbits and operating conditions must be the same in tests for determining the hydro/aerodynamic forces and tests for determining the parasitic forces. This, in turn, necessitates a means by which the test rotor’s motion can be accurately controlled to an arbitrarily defined trajectory. Here in, an interrupt-driven multiple harmonic open-loop controller was developed and implemented on a laboratory centrifugal pump rotor supported in magnetic bearings (active load cells) for this purpose. This allowed the simultaneous control of subharmonic, synchronous, and superharmonic rotor vibration frequencies with each frequency independently forced to some user defined orbital path. The open-loop controller was implemented on a standard PC using commercially available analog input and output cards. All analog input and output functions, transformation of the position signals from the time domain to the frequency domain, and transformation of the open-loop control signals from the frequency domain to the time domain were performed in an interrupt service routine. Rotor vibration was attenuated to the noise floor, vibration amplitude ≈0.2 μm, or forced to a user specified orbital trajectory. Between the whirl frequencies of 14 and 2 times running speed, the orbit semi-major and semi-minor axis magnitudes were controlled to within 0.5% of the requested axis magnitudes. The ellipse angles and amplitude phase angles of the imposed orbits were within 0.3 deg and 1.0 deg, respectively, of their requested counterparts.

A Deep Neural Network Model for Learning Runtime Frequency Response Function Using Sensor Measurements

2021 ◽  
Author(s):  
Yongzhi Qu ◽  
Gregory W. Vogl ◽  
Zechao Wang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fourier Transform ◽  
Time Domain ◽  
Frequency Response Function ◽  
Frequency Component ◽  
Operating Conditions ◽  
Input Output ◽  
The Fourier Transform ◽  
The Time Domain

Abstract The frequency response function (FRF), defined as the ratio between the Fourier transform of the time-domain output and the Fourier transform of the time-domain input, is a common tool to analyze the relationships between inputs and outputs of a mechanical system. Learning the FRF for mechanical systems can facilitate system identification, condition-based health monitoring, and improve performance metrics, by providing an input-output model that describes the system dynamics. Existing FRF identification assumes there is a one-to-one mapping between each input frequency component and output frequency component. However, during dynamic operations, the FRF can present complex dependencies with frequency cross-correlations due to modulation effects, nonlinearities, and mechanical noise. Furthermore, existing FRFs assume linearity between input-output spectrums with varying mechanical loads, while in practice FRFs can depend on the operating conditions and show high nonlinearities. Outputs of existing neural networks are typically low-dimensional labels rather than real-time high-dimensional measurements. This paper proposes a vector regression method based on deep neural networks for the learning of runtime FRFs from measurement data under different operating conditions. More specifically, a neural network based on an encoder-decoder with a symmetric compression structure is proposed. The deep encoder-decoder network features simultaneous learning of the regression relationship between input and output embeddings, as well as a discriminative model for output spectrum classification under different operating conditions. The learning model is validated using experimental data from a high-pressure hydraulic test rig. The results show that the proposed model can learn the FRF between sensor measurements under different operating conditions with high accuracy and denoising capability. The learned FRF model provides an estimation for sensor measurements when a physical sensor is not feasible and can be used for operating condition recognition.

scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

Frequency Constrained Adaptive PID Laws for Motion Control Systems

2017 ◽  
Author(s):  
Tesheng Hsiao ◽  
Chung-Chiang Cheng
Keyword(s):  
Frequency Domain ◽  
Control Systems ◽  
Motion Control ◽  
Time Domain ◽  
Pid Controller ◽  
Tracking Performance ◽  
Tracking Errors ◽  
Pid Tuning ◽  
The Time Domain ◽  
Tuning Methods

The proportional-integral-derivative (PID) controller is widely used in motion control systems due to its simplicity and effectiveness. To achieve satisfactory performance, the PID parameters must be properly tuned. Although numerous PID tuning methods were investigated in the past, most of them were based on either time-domain or frequency-domain responses, while integration of features in both domains for PID tuning was less addressed. However, many industrial practitioners still found it difficult to compromise multiple conflicting control objectives, such as fast responses, small overshoot and tracking errors, and good robustness, with PID controllers. Moreover, it is desirable to adjust PID parameters online such that plant variations and unexpected disturbances can be compensated for more efficiently. In view of these requirements, this paper proposes an adaptive PID control law that updates its parameters online by minimizing the time-domain tracking errors subject to frequency-domain constraints that are imposed for loop shaping. By combining optimization criteria in both time and frequency domains for online parameter adjustment, the proposed PID controller can achieve good tracking performance with adequate robustness margin. Then the proposed PID law is applied to control an XZ-table driven by AC servo motors. Experimental results show that the tracking performance of the proposed controller is superior to that of a constant-gain PID controller whose parameters were tuned by the commercial Matlab/Simulink PID tuner.

EFFICIENT DECIMATOR AND INTERPOLATOR ARRAY STRUCTURES

1995 ◽  
Vol 05 (02) ◽  
pp. 215-238
Author(s):  
ESAM ABDEL-RAHEEM ◽  
FAYEZ EL-GUIBALY ◽  
ANDREAS ANTONIOU
Keyword(s):  
Time Domain ◽  
Upper Bounds ◽  
Mapping Technique ◽  
Array Processor ◽  
Input Output ◽  
System Parameters ◽  
Control Signals ◽  
Compression And Expansion ◽  
Array Structures ◽  
The Time Domain

New and efficient array processor implementations of polyphase FIR and IIR decimators and interpolators, with integer compression and expansion factors, are derived using an algebraic mapping technique. The technique is based on the time-domain representation of the algorithms. It has the merit of being suitable for describing multirate algorithms. The control signals necessary to implement the polyphase structures are explicitly identified. Different array structures are derived in which the inputs are broadcast or pipelined and outputs are pipelined or added simultaneously. Upper bounds on the input/output processing rates are provided in terms of system parameters and hardware delays. The work is extended to map decimators/interpolators with fractional compression/expansion factors onto systolic hardware structures. The new structures have the advantages of being modular, regular, hierarchical, and pipelined.

Discrete Shaper of Control Signals

2015 ◽  
Vol 18 ◽  
pp. 65-74
Author(s):  
Juraj Miček ◽  
Jozef Juríček
Keyword(s):  
Control Systems ◽  
Time Domain ◽  
Control Signal ◽  
Positioning Control ◽  
Digital Implementation ◽  
Positioning Systems ◽  
Fast Speed ◽  
Control Signals ◽  
Image Area ◽  
The Time Domain

Method of control signal shaping has been being used in the steering systems with flexible elements since the 1990s. Many useful applications were developed during the next 20 years, primarily in the field of the positioning control systems. Most of the applications were from the area of control systems in machinery industry (cranes, fast-speed lifts, positioning systems, etc.), many of published papers are based on the design of a proper sequence of pulses in the time domain. On the contrary, our approach describes the design of the discrete shaper in the image area and is focused on the digital implementation issues.

scholarly journals Frequency Domain System Identification With Instrumental Variable Based Subspace Algorithm

1997 ◽  
Author(s):  
Tomas McKelvey
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Instrumental Variable ◽  
Theoretical Discussion ◽  
Subspace Algorithm ◽  
Input And Output ◽  
Rank Constraint ◽  
The Fourier Transform ◽  
The Time Domain

Abstract In this paper we discuss how the time domain subspace based identification algorithms can be modified in order to be applicable when the primary measurements are given as samples of the Fourier transform of the input and output signals or alternatively samples of the transfer function. An instrumental variable (IV) based subspace algorithm is presented. We show that this method is consistent if a certain rank constraint is satisfied and the frequency domain noise is zero mean with bounded covariances. An example is presented which illuminates the theoretical discussion.

A Multiple Harmonic Open Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings

2001 ◽  
Author(s):  
Daniel O. Baun ◽  
Eric H. Maslen ◽  
Carl R. Knospe ◽  
Ronald D. Flack
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Open Loop ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Rotor Vibration ◽  
Aerodynamic Forces ◽  
Analog Input ◽  
Input And Output ◽  
The Time Domain

Inherent in the construction of many experimental apparatus designed to measure the hydro/aerodynamic forces of rotating machinery are features that contribute undesirable parasitic forces to the measured or test forces. Typically, these parasitic forces are due to seals, drive couplings, and hydraulic and/or inertial unbalance. To obtain accurate and sensitive measurement of the hydro/aerodynamic forces in these situations, it is necessary to subtract the parasitic forces from the test forces. In general, both the test forces and the parasitic forces will be dependent on the system operating conditions including the specific motion of the rotor. Therefore, to properly remove the parasitic forces the vibration orbits and operating conditions must be the same in tests for determining the hydro/aerodynamic forces and tests for determining the parasitic forces. This, in turn, necessitates a means by which the test rotor’s motion can be accurately controlled to an arbitrarily defined trajectory. Here in, an interrupt driven multiple harmonic open loop controller was developed and implemented on a laboratory centrifugal pump rotor supported in magnetic bearings (active load cells) for this purpose. This allowed the simultaneous control of sub-harmonic, synchronous and super-harmonic rotor vibration frequencies with each frequency independently forced to some user defined orbital path. The open loop controller was implemented on a standard PC using commercially available analog input and output cards. All analog input and output functions, transformation of the position signals from the time domain to the frequency domain, and transformation of the open loop control signals from the frequency domain to the time domain were performed in an interrupt service routine. Rotor vibration was attenuated to the noise floor, vibration amplitude ≈ 0.2 μm, or forced to a user specified orbital trajectory. Between the whirl frequencies of ¼ and 2 times running speed, the orbit semi-major and semi-minor axis magnitudes were controlled to within 0.5% of the requested axis magnitudes. The ellipse angles and amplitude phase angles of the imposed orbits were within 0.3° and 1.0°, respectively, of their requested counter parts.

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