scholarly journals Frequency Weighted Controller Order Reduction (Part I)

2010 ◽  
Vol 61 (3) ◽  
pp. 141-148 ◽  
Author(s):  
Roozbeh Sadeghian ◽  
Paknosh Karimaghaee ◽  
Alireza Khayatian
Keyword(s):  
Model Reduction ◽  
Linear Time ◽  
Main Idea ◽  
Order Reduction ◽  
New Method ◽  
Frequency Model ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Output Characteristics ◽  
The Stability

Frequency Weighted Controller Order Reduction (Part I) In this paper, a new method for controller reduction of linear time invariant systems is presented. The method is based on newly defined controllability and observability grammians which are calculated from input to state and state to output characteristics of the controller in a certain frequency domain. These grammians are defined for the closed loop system to keep the performance of original controller. The main idea of this method is based on Moores model reduction. The relation of this method with weighted frequency model reduction of Enns will be described by a commutative diagram. The stability property of the new method is investigated. It is shown that the stability for two sided weights can be preserved under certain conditions. The simulation results show the effectiveness of this novel technique.

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.

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.

Active Control of Linear Time-Varying Structures by Confinement of Vibrations

2005 ◽  
Vol 11 (1) ◽  
pp. 89-102 ◽  
Author(s):  
S. Choura ◽  
A. S. Yigit
Keyword(s):  
Control Strategy ◽  
Linear Time ◽  
Steady States ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Slowing Down ◽  
Rapid Removal ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

We propose a control strategy for the simultaneous suppression and confinement of vibrations in linear time-varying structures. The proposed controller has time-varying gains and can also be used for linear time-invariant systems. The key idea is to alter the original modes by appropriate feedback forces to allow parts of the structure reach their steady states at faster rates. It is demonstrated that the convergence of these parts to zero is improved at the expense of slowing down the settling of the remaining parts to their steady states. The proposed control strategy can be applied for the rapid removal of vibration energy in sensitive parts of a flexible structure for safety or performance reasons. The stability of the closed-loop system is proven through a Lyapunov approach. An illustrative example of a five-link manipulator with a periodic follower force is given to demonstrate the effectiveness of the method for time-varying as well as time-invariant systems.

Model Reduction of Large-Scale Discrete Plants With Specified Frequency Domain Balanced Structure

2004 ◽  
Vol 127 (3) ◽  
pp. 486-498 ◽  
Author(s):  
Abbas H. Zadegan ◽  
Ali Zilouchian
Keyword(s):  
Model Reduction ◽  
Frequency Domain ◽  
Large Scale ◽  
Linear Time ◽  
Model Simulation ◽  
Large Scale Systems ◽  
Linear Time Invariant ◽  
Balanced Structure ◽  
Linear Time Invariant Systems ◽  
Model Reduction Technique

A new model reduction technique for linear time-invariant systems is proposed. A new method that reduces the order of large-scale systems by integrating singular perturbation with specified frequency domain balanced structure is proposed. Considering a frequency range at which the system actually operates guarantees a good approximation of the original full order model. Simulation experiments for model reduction of several large-scale systems demonstrate the effectiveness of the proposed technique.

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