scholarly journals On Parametrizations of State Feedbacks and Static Output Feedbacks and Their Applications

2021 ◽  
Author(s):  
Yossi Peretz
Keyword(s):  
Linear Time ◽  
Linear Constraint ◽  
Pole Placement ◽  
Space Representation ◽  
Static State ◽  
Linear Time Invariant ◽  
State Space Representation ◽  
Time Invariant ◽  
Time Linear ◽  
Static Output

In this chapter, we provide an explicit free parametrization of all the stabilizing static state feedbacks for continuous-time Linear-Time-Invariant (LTI) systems, which are given in their state-space representation. The parametrization of the set of all the stabilizing static output feedbacks is next derived by imposing a linear constraint on the stabilizing static state feedbacks of a related system. The parametrizations are utilized for optimal control problems and for pole-placement and exact pole-assignment problems.

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.

Multivariable Control of an Over-Head Crane System Based on Entire Eigen-Structure Assignment

2010 ◽  
Author(s):  
Hamed Moradi ◽  
K. Haji Hajikolaei ◽  
Firooz Bakhtiari-Nejad ◽  
Aria Alasty
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Control Strategies ◽  
Control Signal ◽  
Space Representation ◽  
Linear Time Invariant ◽  
State Space Representation ◽  
Stabilization Control ◽  
Structure Assignment ◽  
Time Invariant

Motion and stabilization control strategies are required to improve positioning accuracy, transportation time and swing angle of an overhead crane system. In this paper, a controller is designed to enhance both efficiency and safety and to extend the system application to other engineering fields. An over-head crane is modeled as a linear time invariant (LTI) system with two degrees of freedom. Trolley position and cable angle are the controlled outputs while the force exerted on trolley and torque on the load are the control inputs of the system. After state-space representation of the problem, feedback control is designed for tracking objective. An increase in the overall speed of the system time response corresponds to an increase in the control signal and leads to additional cost. Therefore, developing a code in MATLAB, eigenvalues and eigenvectors of the system are chosen optimally until an appropriate response is achieved; while the gains of control signal remain small.

Periodic controller for guaranteed simultaneous stabilization of two plants with robust zero error tracking

2018 ◽  
Vol 233 (5) ◽  
pp. 480-490
Author(s):  
Arindam Chakraborty ◽  
Jayati Dey
Keyword(s):  
Design Methodology ◽  
Linear Time ◽  
Pole Placement ◽  
Control Input ◽  
Efficient Design ◽  
Simultaneous Stabilization ◽  
Bounded Control ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Periodic

The guaranteed simultaneous stabilization of two linear time-invariant plants is achieved by continuous-time periodic controller with high controller frequency. Simultaneous stabilization is accomplished by means of pole-placement along with robust zero error tracking to either of two plants. The present work also proposes an efficient design methodology for the same. The periodic controller designed and synthesized for realizable bounded control input with the proposed methodology is always possible to implement with guaranteed simultaneous stabilization for two plants. Simulation and experimental results establish the veracity of the claim.

Proportional–integral–derivative controller family for pole placement

2016 ◽  
Vol 231 (20) ◽  
pp. 3791-3797 ◽  
Author(s):  
Chimpalthradi R Ashokkumar ◽  
George WP York ◽  
Scott F Gruber
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Generalized Eigenvalue ◽  
Square Systems ◽  
Time Invariant

In this paper, linear time-invariant square systems are considered. A procedure to design infinitely many proportional–integral–derivative controllers, all of them assigning closed-loop poles (or closed-loop eigenvalues), at desired locations fixed in the open left half plane of the complex plane is presented. The formulation accommodates partial pole placement features. The state-space realization of the linear system incorporated with a proportional–integral–derivative controller boils down to the generalized eigenvalue problem. The generalized eigenvalue-eigenvector constraint is transformed into a system of underdetermined linear homogenous set of equations whose unknowns include proportional–integral–derivative parameters. Hence, the proportional–integral–derivative solution sets are infinitely many for the chosen closed-loop eigenvalues in the eigenvalue-eigenvector constraint. The solution set is also useful to reduce the tracking errors and improve the performance. Three examples are illustrated.

New Results on Linear Time Invariant and Parameter Varying Static Output Feedback

2008 ◽  
Vol 31 (5) ◽  
pp. 1230-1238 ◽  
Author(s):  
Ricardo S. Sanchez-Pena ◽  
Phalguna Kumar Rachinayani ◽  
Dario H. Baldelli
Keyword(s):  
Output Feedback ◽  
Linear Time ◽  
Static Output Feedback ◽  
Linear Time Invariant ◽  
Parameter Varying ◽  
Time Invariant ◽  
Static Output
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