Discrete-time L2 loop-shaping control of a Maglev System using the LPV framework

2020 ◽  
Author(s):  
Luiz Benicio Degli Esposte Rosa ◽  
Renan Lima Pereira
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Practical Application ◽  
Closed Loop System ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Maglev System ◽  
Loop Shaping ◽  
And Performance ◽  
Time Invariant

This paper presents a practical application of discrete-time L2 loop-shaping control to a Maglev system using the linear parameter-varying (LPV) framework. LMI-based conditions are obtained for the synthesis of an output-feedback LPV controller that guarantees robust stability and performance to the closed-loop system. Guidelines to design such controller are given in a simple and transparent manner. In addition, detailed modeling of the didactic plant manufactured by Quanser is carried out and the process of embedding the nonlinear equations into a discretized quasi-LPV (qLPV) model is described. Simulations and experimental results show that the proposed procedure can be an advantageous alternative to handle nonlinear systems in comparison to its linear time-invariant (LTI) version.

Deterministic Continuous-Time Signals and Systems

2021 ◽  
pp. 562-598
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Continuous Variable ◽  
Linear Time Invariant ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
Linear Time Invariant Systems ◽  
Definition Of ◽  
Time Invariant

Due to the importance of the concept of independent variable modification, the definition of linear-time-invariant system, and their implications for discrete-time signal processing, Chapter 11 presents basic deterministic continuous-time signals and systems. These signals, expressed in the form of functions and functionals such as the Dirac delta function, are used throughout the book for deterministic and stochastic signal analysis, in both the continuous-time and the discrete-time domains. The definition of the autocorrelation function, and an explanation of the convolution procedure in linear-time-invariant systems, are presented in detail, due to their importance in communication systems analysis and synthesis. A linear modification of the independent continuous variable is presented for specific cases, like time shift, time reversal, and time and amplitude scaling.

scholarly journals Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming

2020 ◽  
Vol 42 (16) ◽  
pp. 3168-3182
Author(s):  
Okan Demir ◽  
Hitay Özbay
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Mixed Integer ◽  
Static Output Feedback ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Linear ◽  
Static Output

This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

Modal Control of Linear Time-Invariant Discrete-Time Systems

1969 ◽  
Vol 2 (8) ◽  
pp. T133-T136 ◽  
Author(s):  
B. Porter ◽  
T. R. Crossley
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Feedback Loops ◽  
Modal Control ◽  
Discrete Time System ◽  
Linear Time Invariant ◽  
Modal Theory ◽  
Discrete Time Systems ◽  
Time Invariant ◽  
Time Systems

Modal control theory is applied to the design of feedback loops for linear time-invariant discrete-time systems. Modal theory is also used to demonstrate the explicit relationship which exists between the controllability of a mode of a discrete-time system and the possibility of assigning an arbitrary value to the eigenvalue of that mode.

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.

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