A Concise Method of Pole Placement to Stabilize the Linear Time Invariant MIMO System

2019 ◽  
Author(s):  
Justin Jacob ◽  
Sreya Das ◽  
Navin Khaneja
Keyword(s):  
Linear Time ◽  
Mimo System ◽  
Pole Placement ◽  
Linear Time Invariant ◽  
Time Invariant

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.

Decentralized controller design by continuous pole placement for neutral time-delay systems

2016 ◽  
Vol 39 (3) ◽  
pp. 297-311 ◽  
Author(s):  
HE Erol ◽  
A İftar
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Linear Time ◽  
Pole Placement ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Linear Time Invariant ◽  
Assignment Algorithm ◽  
Placement Algorithm ◽  
Time Invariant

The stabilizing decentralized controller design problem for (possibly descriptor-type) linear time-invariant neutral time-delay systems is considered. A design approach, based on the continuous pole placement algorithm and the decentralized pole assignment algorithm, is proposed. A design example is also presented, to demonstrate the proposed approach.

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.

A Control Method for Non-Linear Time-Varying System Using Mixed H2/H∞ Control: Position and Force Control of 2-Link Manipulator

2001 ◽  
Author(s):  
Itsuro Kajiwara ◽  
Katsuhiro Yambe ◽  
Chiaki Nishidome
Keyword(s):  
Control Method ◽  
Linear Time ◽  
Gain Scheduling ◽  
Operating Conditions ◽  
Pole Placement ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Highly Nonlinear ◽  
Switching Controller ◽  
Time Invariant

Abstract Dynamics of multi-link manipulators are highly nonlinear and depend on the time varying configuration. This paper presents a method of gain scheduling which consists in designing a linear time invariant (LTI) controller for each operating point and in switching controller when the operating conditions change. Each LTI controller is designed based on LMI approach in which an optimization problem is defined as a mixed H2/H∞ control problem with pole placement. The performance of the force and the position controls is defined by the H2 norm, and the robust stability according to gain scheduling is evaluated with the H∞ norm and the pole placement of the closed-loop system. The effectiveness and the practicability of the proposed method are verified by both simulations and experiments with 2-link manipulator system.

A Static Anti-Windup Compensator Design Technique for Robust Regional Pole Placement

2006 ◽  
Author(s):  
Brandon Hencey ◽  
Andrew Alleyne
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Linear Matrix ◽  
Test Bed ◽  
Hydraulic Test ◽  
Linear Time Invariant ◽  
Loop Dynamics ◽  
Performance Deterioration ◽  
Time Invariant

This paper develops a new method of designing anti-windup compensators using the concept of robust pole placement using linear matrix inequality (LMI) regions. The anti-windup problem seeks to minimize the closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time-invariant plant and controller. Existing LMI-based anti-windup synthesis techniques do not explicitly provide a method to account for robust pole placement. This paper suggests a LMI-based method that not only attempts to minimize performance deterioration, but also explicitly restricts the anti-windup closed loop dynamics to an admissible set. Finally, the techniques discussed in this paper are demonstrated on a hydraulic test bed.

Analysis of an Error Integral Driven MIMO SM Regulator for LTI Systems

2016 ◽  
Author(s):  
Kerim Yunt
Keyword(s):  
Parameter Uncertainty ◽  
Sliding Mode ◽  
Linear Time ◽  
Pole Placement ◽  
Sliding Mode Controller ◽  
Minimum Phase ◽  
Linear Time Invariant ◽  
Luenberger Observer ◽  
Optimization Routine ◽  
Time Invariant

In this work an error-integral-driven sliding mode controller (EID-SMC) for multi-input multi-output (MIMO) minimum phase linear time-invariant (LTI) systems with feedthrough controls and output disturbance is analyzed. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within the boundary layer even if parameter uncertainty and unmatched input/output disturbances exist. The pole-placement is accomplished indirectly by an iterative optimization routine by considering limits on controls and state contrary to the existing practice in SMC where either direct pole placement or quadratic norm optimality of a performance is used. For the proposed controller framework the Luenberger observer is presented.

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