scholarly journals PID Control Design for SISO Strictly Metzlerian Linear Systems

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1979
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Pid Control ◽  
Linear Time ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Control Law ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Parameter Constraints ◽  
Structural Influence

For linear time-invariant Metzlerian systems, this paper proposes an original approach reflecting specific structural system constraints and positiveness in solving the problem of PID control. Refining parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with the control law representation and is formulated as a linear matrix inequality feasibility problem. Taking into account structural restriction of Metzlerian positive systems, a characterization of PID control law parameters is permitted, to highlight dynamical properties of the closed-loop system solutions and the significant structural influence of derivative gain value of the control law parameters in design.

scholarly journals On PID Design Constraints in Relation to Control of Strictly Metzler Linear MIMO Systems

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1589
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Pid Control ◽  
Mimo Systems ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Control Law ◽  
Matching Conditions ◽  
Time Invariant ◽  
Parameter Constraints ◽  
The Given ◽  
First Time

For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the controller and system parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with PID control law parameter representation and is formulated as a linear matrix inequality feasibility problem. Characterization of the PID control law parameters is permitted to highlight dynamical properties of the closed-loop system and the structural influence of the control derivative gain value in the design step. For the first time, the paper comprehensively sets the synthesis standard for PID control of MIMO Metzler systems because others for the given task have not been created at present.

Computing Impulse Response of Room Acoustics Using the Ray-Tracing Method in Time Domain

2010 ◽  
Vol 35 (4) ◽  
pp. 505-519 ◽  
Author(s):  
Adil Alpkocak ◽  
Malik Sis
Keyword(s):  
Impulse Response ◽  
Linear Time ◽  
Simulation Software ◽  
Room Acoustics ◽  
New Approach ◽  
Linear Time Invariant ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Time Invariant System

AbstractThis paper proposes a new approach for calculating the impulse response of room acoustics. Impulse response provides unique characterization of any discrete lineartime invariant (LTI) systems. We assume that the room is a linear time-invariant system and the impulse response is calculated simply by sending a Dirac Impulse into the system as input and getting the response from the output. Then, the output of the system is represented as a sum of time-shifted weighted impulse responses. Both mathematical justifications for the proposed method and results from simulation software developed to evaluate the proposed approach are presented in detail.

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.

scholarly journals A multi-model approach to Saint-Venant equations: A stability study by LMIs

2012 ◽  
Vol 22 (3) ◽  
pp. 539-550 ◽  
Author(s):  
Valérie Dos Santos Martins ◽  
Mickael Rodrigues ◽  
Mamadou Diagne
Keyword(s):  
Linear Time ◽  
Dimensional Space ◽  
Stability Study ◽  
Linear Matrix ◽  
Model Concept ◽  
Infinite Dimensional ◽  
Linear Time Invariant ◽  
Saint Venant Equations ◽  
The Stability ◽  
Time Invariant

Abstract This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

scholarly journals Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Xie
Keyword(s):  
Controller Design ◽  
Linear Time ◽  
Admissible Solution ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lpv Control ◽  
Lpv System ◽  
Time Invariant ◽  
Iterative Linear Matrix Inequality

A linear time-invariant (LTI) output feedback controller is designed for a linear parameter-varying (LPV) control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI) formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

An Optimal Control Approach for Consensus of General Linear Time-Invariant Multi-Agent Systems

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Poorya Shobeiry ◽  
Ming Xin
Keyword(s):  
Optimal Control ◽  
Cooperative Control ◽  
Linear Time ◽  
General Linear ◽  
Control Law ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Linear Time Invariant ◽  
Multi Agent ◽  
Time Invariant

Abstract In this paper, the consensus problem for general linear time-invariant (LTI) multi-agent systems (MASs) with a single input is studied in a new optimal control framework. The optimal cooperative control law is designed from a modified linear quadratic regulator (LQR) method and an inverse optimal control formulation. Three cost function terms are constructed to address the consensus, control effort, and cooperative tracking, respectively. Three distinct features of this approach can be achieved. First, the optimal feedback control law is derived analytically without involving any numerical solution. Second, this formulation guarantees both asymptotic stability and optimality. Third, the cooperative control law is distributed and only requires local information based on the communication topology to enable the agents to achieve consensus and track a desired trajectory. The performance of this optimal cooperative control method is demonstrated through an example of attitude synchronization of multiple satellites.

Determination of Different Polytopic Models of the Prototypical Aeroelastic Wing Section by TP Model Transformation

2006 ◽  
Vol 10 (4) ◽  
pp. 486-493 ◽  
Author(s):  
Péter Baranyi ◽  
◽  
Zoltán Petres ◽  
Péter L. Várkonyi ◽  
Péter Korondi ◽  
...  
Keyword(s):  
Model Transformation ◽  
Linear Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Wing Section ◽  
Parameter Varying ◽  
Time Invariant

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting polytopic models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the type of the convex combination in the polytopic model. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

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