Time-Domain Adaptive Higher Harmonic Control for Rejection of Sinusoidal Disturbances

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Mohammadreza Kamaldar ◽  
Jesse B. Hoagg
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Harmonic Control ◽  
Lti System ◽  
Higher Harmonic Control ◽  
Higher Harmonic ◽  
The Stability ◽  
Time Invariant

Abstract This paper presents two new time-domain feedback controllers that reject sinusoidal disturbances with known frequencies acting on an asymptotically stable linear time-invariant (LTI) system. The first controller is time-domain higher harmonic control (TD-HHC), which is effective for uncertain LTI systems. The second controller is time-domain adaptive higher harmonic control (TD-AHHC), which is effective for completely unknown LTI systems. TD-HHC requires an estimate of the control-to-performance transfer function evaluated at the disturbance frequencies. In contrast, TD-AHHC does not require any information regarding the LTI system. We analyze the stability and closed-loop performance of TD-HHC and TD-AHHC. For both TD-HHC and TD-AHHC, we show that the controller asymptotically rejects the disturbance. We present numerical simulations comparing TD-HHC and TD-AHHC with frequency-domain higher harmonic control (FD-HHC), which is an existing frequency-domain controller for rejection of sinusoidal disturbances. We also present results from acoustic disturbance rejection experiments, which demonstrate the practical effectiveness of both TD-HHC and TD-AHHC.

scholarly journals Active Unmatched Disturbance Cancellation and Estimation by State--Derivative Feedback for Plants Modeled as an LTI System

2018 ◽  
Vol 8 (2) ◽  
pp. 237-249
Author(s):  
Halil Ibrahim Basturk
Keyword(s):  
Linear Time ◽  
Position Information ◽  
Linear Time Invariant ◽  
Lti System ◽  
Disturbance Cancellation ◽  
Disturbance Model ◽  
The Stability ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Two Degree Of Freedom

We design adaptive algorithms for both cancellation and estimation of unknown periodic disturbance, by feedback of state--derivatives ( i.e.,} without position information for mechanical systems) for the plants which are modeled as a linear time invariant system. We consider a series of unmatched unknown sinusoidal signals as the disturbance.The first step of the design consists of the parametrization of the disturbance model and the development of observer filters.The result obtained in this step allows us to use adaptive control techniques for the solution of the problem.In order to handle the unmatched condition, a backstepping technique is employed. Since the partial measurement of the virtual inputs is not available, we design a state observer and the estimates of these signals are used in the backstepping design.Finally, the stability of the equilibrium of the adaptive closed loop system with the convergence of states is proven.As a numerical example, a two-degree of freedom system is considered and the effectiveness of the algorithms are shown.

scholarly journals A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yu Xiaodan ◽  
Jia Hongjie ◽  
Wang Chengshan ◽  
Jiang Yilang
Keyword(s):  
Linear Time ◽  
Oscillation Mode ◽  
Lambert W Function ◽  
Real Eigenvalue ◽  
Linear Time Invariant ◽  
Lti System ◽  
The Stability ◽  
Definition Of ◽  
Complex Phenomena ◽  
Time Invariant

One type of bifurcation named oscillation emergence bifurcation (OEB) found in time-delayed linear time invariant (abbr. LTI) systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge. Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim) time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.

Time-domain noise analysis of linear time-Invariant and linear time-variant systems using MATLAB and HSPICE

2005 ◽  
Vol 52 (3) ◽  
pp. 805-812 ◽  
Author(s):  
S.C. Terry ◽  
B.J. Blalock ◽  
J.M. Rochelle ◽  
M.N. Ericson ◽  
S.D. Caylor
Keyword(s):  
Time Domain ◽  
Linear Time ◽  
Noise Analysis ◽  
Linear Time Invariant ◽  
Time Invariant

scholarly journals Torsion Discriminance for Stability of Linear Time-Invariant Systems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 386
Author(s):  
Yuxin Wang ◽  
Huafei Sun ◽  
Yueqi Cao ◽  
Shiqiang Zhang
Keyword(s):  
Lebesgue Measure ◽  
Linear Time ◽  
Zero Solution ◽  
Positive Lebesgue Measure ◽  
Asymptotically Stable ◽  
Linear Time Invariant ◽  
Measurable Set ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

This paper extends the former approaches to describe the stability of n-dimensional linear time-invariant systems via the torsion τ ( t ) of the state trajectory. For a system r ˙ ( t ) = A r ( t ) where A is invertible, we show that (1) if there exists a measurable set E 1 with positive Lebesgue measure, such that r ( 0 ) ∈ E 1 implies that lim t → + ∞ τ ( t ) ≠ 0 or lim t → + ∞ τ ( t ) does not exist, then the zero solution of the system is stable; (2) if there exists a measurable set E 2 with positive Lebesgue measure, such that r ( 0 ) ∈ E 2 implies that lim t → + ∞ τ ( t ) = + ∞ , then the zero solution of the system is asymptotically stable. Furthermore, we establish a relationship between the ith curvature ( i = 1 , 2 , ⋯ ) of the trajectory and the stability of the zero solution when A is similar to a real diagonal matrix.

Admissible Range of Proportional Gain in Stabilizing PID Region

2014 ◽  
Vol 530-531 ◽  
pp. 1068-1077 ◽  
Author(s):  
Yu Dong
Keyword(s):  
Linear Time ◽  
Stability Boundary ◽  
Closed Loop System ◽  
Double Pole ◽  
Linear Time Invariant ◽  
Admissible Range ◽  
Boundary Locus ◽  
The Stability ◽  
Time Invariant ◽  
Integral Gain

This paper considers the problem of stabilizing linear time-invariant plants by a PID controller. If the proportional gain reaches the extreme value, the closed-loop system contains a double pole on the imaginary axis. Using this property, the admissible range of the proportional gain is derived, also the corresponding integral gain and derivative gain are obtained. If the proportional gain is fixed, the stability region in the plane with respect to the integral gain and the derivative gain is determined by plotting the stability boundary locus. The effectiveness of the method presented is illustrated by several examples.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)

2013 ◽  
Author(s):  
Qingbin Gao ◽  
Umut Zalluhoglu ◽  
Nejat Olgac
Keyword(s):  
Linear Time ◽  
Broad Class ◽  
Delay Systems ◽  
Multiple Delays ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Time In Literature ◽  
The Stability ◽  
Time Invariant ◽  
Delay Space

It has been shown that the stability of LTI time-delayed systems with respect to the delays can be analyzed in two equivalent domains: (i) delay space (DS) and (ii) spectral delay space (SDS). Considering a broad class of linear time-invariant time delay systems with multiple delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.

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