Adaptive Frequency Shaped Linear Quadratic Control of Mechanical Systems: Theory and Experiment

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
An-Chyau Huang ◽  
Ting-Kai Jhuang
Keyword(s):  
Frequency Domain ◽  
Function Approximation ◽  
Design Procedure ◽  
Adaptive Controller ◽  
Optimal Performance ◽  
Approximation Technique ◽  
Linear Quadratic ◽  
System Output ◽  
Dual Stage ◽  
The Time Domain

The traditional linear quadratic (LQ) controller can give optimal performance to a known linear system with weightings in the time domain, while the frequency shaped LQ (FSLQ) controller is able to provide optimal performance to the same class of systems with weightings in the frequency domain. When the system contains uncertainties, both of these two approaches fail. In this paper, an adaptive controller is proposed to an uncertain mechanical system such that LQ performance can be achieved with weightings in the frequency domain. The function approximation technique is applied to represent the uncertainties into a finite combination of a set of known basis functions. This allows the system to be with various nonlinearities and uncertainties without significant impact on the design procedure. The Lyapunovlike analysis is used to ensure convergence of the system output and boundedness of the internal signals. A dual stage is built to evaluate the performance of the proposed scheme experimentally.

A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 205-210 ◽  
Author(s):  
An-Chyau Huang ◽  
Shi-Chang Wu ◽  
Wen-Fa Ting
Keyword(s):  
Function Approximation ◽  
Matrix Theory ◽  
Robot Manipulator ◽  
Nonlinear Differential Equations ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Approximation Technique ◽  
Control Scheme ◽  
Approximation Errors ◽  
Theory And Experiments

In this paper, an adaptive control scheme is proposed for an n-link rigid robot manipulator without using the regressor. The robot is firstly modeled as a set of second-order nonlinear differential equations with the assumption that all of the matrices in that model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique (FAT) is used here to represent uncertainties in some finite linear combinations of orthonormal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. Experiments are also performed on a 2-D robot to test the efficacy of the proposed scheme.

A regressor-free adaptive controller for robot manipulators without Slotine and Li's modification

Robotica ◽  
2013 ◽  
Vol 31 (7) ◽  
pp. 1051-1058 ◽  
Author(s):  
Chen-Yu Kai ◽  
An-Chyau Huang
Keyword(s):  
Function Approximation ◽  
Closed Loop ◽  
Controller Design ◽  
Robot Manipulators ◽  
Adaptive Controller ◽  
Approximation Technique ◽  
Simple Method ◽  
Acceleration Vector ◽  
Acceleration Feedback ◽  
Joint Acceleration

SUMMARYSimilar to the traditional adaptive strategies for robot manipulators, the regressor-free adaptive controller design also requires applying Slotine and Li's modification to avoid the feedback of joint accelerations. In this paper, a simple method is proposed to construct a regressor-free adaptive controller for robot manipulators without Slotine and Li's modification. In the new design, the joint acceleration vector is lumped into an unknown time-varying function and the function approximation technique is utilized to cover its effect; therefore, its implementation is free from joint acceleration feedback. The closed-loop stability and boundedness of internal signals are justified by the Lyapunov-like technique. Both simulation and experimental results for a two-link robot are presented to show the effectiveness of the proposed design.

Frequency Domain Design for Maximal Rejection of Persistent Bounded Disturbances

1991 ◽  
Vol 113 (2) ◽  
pp. 195-205 ◽  
Author(s):  
S. Jayasuriya ◽  
M. A. Franchek
Keyword(s):  
Frequency Domain ◽  
Transfer Functions ◽  
Design Method ◽  
Design Procedure ◽  
Loop Shaping ◽  
Trade Offs ◽  
Control Objective ◽  
Bounded Disturbances ◽  
The Time Domain ◽  
Domain Constraints

A frequency domain methodology for synthesizing controllers for SISO systems under persistent bounded disturbances is presented. The control objective is to maximize the disturbance magnitude without violating prespecified state, control and bandwidth constraints. These constraints are treated explicitly in the design process. State and control constraints expressed in the time domain are first mapped into a set of equivalent frequency domain design specifications. The latter specifications define a set of frequency domain constraints on admissible loop transfer functions. These constraints are then displayed on a Nichols chart highlighting the dependency of the loop gains on phase and frequency. The final step in the process is to follow a loop shaping procedure to satisfy the frequency domain constraints. In the proposed methodology, the structure of the controller emerges naturally as a consequence of loop shaping and is not preconceived. The design procedure is semi-graphical and clearly demonstrates the design trade-offs at each frequency of interest. The effectiveness of the design method is illustrated by synthesizing a controller for a third order boiler-turbine set.

A Passivity-Based Regressor-Free Adaptive Controller for Robot Manipulators With Combined Regressor/Parameter Estimation

2018 ◽  
Author(s):  
Donald Ebeigbe ◽  
Dan Simon
Keyword(s):  
Function Approximation ◽  
Equations Of Motion ◽  
Adaptive Controller ◽  
Dynamics Simulation ◽  
Approximation Technique ◽  
Simultaneous Estimation ◽  
Robot Dynamics ◽  
Gravity Vector ◽  
Inertia Matrix ◽  
Function Approximation Technique

This paper develops a new function approximation technique (FAT)-based adaptive controller for the control of rigid robots called the adaptive passivity function approximation technique (APFAT) controller. This controller utilizes the passivity-based approach and simplifies the FAT controller design by eliminating the need for simultaneous estimation of the robot’s inertia matrix, Coriolis matrix, and gravity vector. The controller achieves its simplicity by treating the product of the regressor matrix and parameter vector as an unknown time-varying function to be approximated. The controller can be implemented in robots where the dynamic equations of motion are unknown. The stability of the controller is verified with Lyapunov functions by taking advantage of the passivity property of the robot dynamics. Simulation results on a three degree-of-freedom (DOF) PUMA500 robot demonstrate the ability to track reference trajectories using reasonable control signals when the inertia matrix, Coriolis matrix, and gravity vector are unavailable.

Digital Adaptive Flutter Suppression and Simulation Using Approximate Transonic Aerodynamics

1995 ◽  
Vol 1 (4) ◽  
pp. 363-388 ◽  
Author(s):  
Chan-Gi Pak ◽  
Peretz P. Friedmann ◽  
Eli Livne
Keyword(s):  
Moving Average ◽  
Arma Model ◽  
Adaptive Controller ◽  
Control Surface ◽  
Transition Matrices ◽  
Linear Quadratic ◽  
Time Step ◽  
Flutter Suppression ◽  
Time Marching ◽  
The Time Domain

A digital adaptive controller, using a trailing edge control surface, is introduced for the active flutter suppression of wings undergoing time varying flight conditions. The aeroservoelastic system is modeled in the time domain by a deterministic Auto Regressive Moving Average (ARMA) model together with a parameter estimator. Linear quadratic controller gains at each time step are obtained using an iterative Riccati solver. Aeroservoelastic transient response is obtained using Roger's approximation, state transition matrices, and an iterative time marching algorithm. Simulations of system performance for flights into the transonic speed regime are used to demonstrate suppression of flutter and divergence instabilities.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

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.

Time-Domain Nonlinear SSI Analysis of Foundation Sliding Using Frequency-Dependent Foundation Impedance Derived From SASSI

2008 ◽  
Author(s):  
Mansour Tabatabaie ◽  
Thomas Ballard
Keyword(s):  
Frequency Domain ◽  
Linear Systems ◽  
Time Domain ◽  
Soil Structure ◽  
Wave Radiation ◽  
Far Field ◽  
Frequency Dependent ◽  
Nonlinear Springs ◽  
Mat Foundation ◽  
The Time Domain

Dynamic soil-structure interaction (SSI) analysis of nuclear power plants is often performed in frequency domain using programs such as SASSI [1]. This enables the analyst to properly a) address the effects of wave radiation in an unbounded soil media, b) incorporate strain-compatible soil shear modulus and damping properties and c) specify input motion in the free field using the de-convolution method and/or spatially variable ground motions. For structures that exhibit nonlinearities such as potential base sliding and/or uplift, the frequency-domain procedure is not applicable as it is limited to linear systems. For such problems, it is necessary to solve the problem in the time domain using the direct integration method in programs such as ADINA [2]. The authors recently introduced a sub-structuring technique called distributed parameter foundation impedance (DPFI) model that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation soil is modeled using the frequency-domain procedure [3]. This procedure has been validated for linear systems. In this paper we have expanded the DPFI model to incorporate nonlinearities at the soil/structure interface by introducing nonlinear shear and normal springs arranged in series between the DPFI and structure model. This combination of the linear far-field impedance (DPFI) plus nonlinear near-field soil springs allows the foundation sliding and/or uplift behavior be analyzed in time domain while maintaining the frequency-dependent stiffness and radiation damping nature of the far-field foundation impedance. To check the accuracy of this procedure, a typical NPP foundation mat supported at the surface of a layered soil system and subjected to harmonic forced vibration was first analyzed in the frequency domain using SASSI to calculate the target linear response and derive a linear, far-field DPFI model. The target linear solution was then used to validate two linear time-domain ADINA models: Model 1 consisting of the mat foundation+DPFI derived from the linear SASSI model and Model 2 consisting of the total SSI system (mat foundation plus a soil block). After linear alignment, the nonlinear springs were added to both ADINA models and re-analyzed in time domain. Model 2 provided the target nonlinear solution while Model 1 provided the results using the DPFI+nonlinear springs. By increasing the amplitude of the vibration load, different levels of foundation sliding were simulated. Good agreement between the results of two models in terms of the displacement response of the mat and cyclic force-displacement behavior of the springs validates the accuracy of the procedure presented herein.

IDENTIFICATION OF INTERHARMONICS BASED ON WAVELET PACKET TRANSFORM

2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  
Keyword(s):  
Fourier Transform ◽  
Simulation Model ◽  
Frequency Domain ◽  
Time Domain ◽  
Wavelet Packet ◽  
High Accuracy ◽  
Wavelet Packet Transform ◽  
Mathematical Apparatus ◽  
Nonlinear Load ◽  
The Time Domain

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.

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