LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

Das, Saptarshi; Pan, Indranil; Halder, Kaushik; Das, Shantanu; Gupta, Amitava

doi:10.1016/j.apm.2012.09.022

Cited by 123 publications

(89 citation statements)

References 27 publications

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“…Substituting p 13 , p 23 and p 33 into the above equation, Rearranging (26), the expression for q 2 /r can be obtained as given below. (27) Likewise, the element available in third row and third column of ARE (10) …”

Section: Closed Loop Response Of the Systemmentioning

confidence: 99%

“…The general form of desired characteristic equation of the third order system is (14) Comparing Equations (13) and (14), the expressions for p 13 , p 23 From the element available at first row and first column of Equation (10) …”

Section: Closed Loop Response Of the Systemmentioning

confidence: 99%

“…According to direct substitution method for the pole placement controller design, the actual characteristic equation of the system is compared with the desired characteristic equation to obtain the expressions for p 13 , p 23 …”

Section: Closed Loop Response Of the Systemmentioning

confidence: 99%

“…One of the essential features of LQR is that Q should be a symmetric positive semidefinite matrix and R should be a positive definite matrix. So, the weighting matrices Q and R, and the solution of ARE are chosen as The elements of P matrix such as p 13 , p 23 and p 33 are obtained using the ARE given in (4). …”

Section: Analytical Approach For Weighting Matrices Selection Of Lqrmentioning

confidence: 99%

“…However, two main issues of the LQR problem have been the subject of investigation since the 1960s until the present day: the solution of ARE, and the choice of Q and R weighting matrices [13]. The two tasks are known to be strongly time dependent and based on certain operational conditions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Kumare¹,

Jerome²

2016

Archives of Electrical Engineering

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This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.

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Section: Closed Loop Response Of the Systemmentioning

confidence: 99%

Section: Closed Loop Response Of the Systemmentioning

confidence: 99%

Section: Closed Loop Response Of the Systemmentioning

confidence: 99%

Section: Analytical Approach For Weighting Matrices Selection Of Lqrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Kumare¹,

Jerome²

2016

Archives of Electrical Engineering

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Stabilization of Single‐Input LTI Systems by Proportional‐Derivative Feedback

Abdelaziz¹

2015

Asian Journal of Control

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This article presents an efficient solution to the stabilization pole placement problem for single-input linear time-invariant (LTI) systems by proportional-derivative (PD) feedback. For a controllable system, any arbitrary closed-loop poles can be placed in order to achieve the desired closed-loop system performance. Its derivation is based on the transformation of linear system into Hessenberg form by a special coordinate transformation before solving the pole placement problem. The available degrees of freedom offered by PD feedback are utilized to obtain closed-loop systems with small gains. So, the minimization problem for a suitably chosen cost function is formulated. Simulation results are included to show the effectiveness of the proposed approach.

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Distributed fault detection and isolation in time‐varying formation tracking UAV multi‐agent systems

Amirani

Bigdeli

Haeri

2022

Asian Journal of Control

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The problem of distributed fault detection and isolation (DFDI) in conjunction with time‐varying formation control of unmanned aerial vehicle (UAV) multi‐agent systems with multiple‐leader leader–follower structure is studied, in this paper. It is assumed that the communication data of the agents are noisy, and faults may occur in either leaders or followers. The followers are not aware of the main trajectory and just follow the leaders. The first step in this paper is to reduce the communication noise. Besides, if a fault occurs in one of the leaders causing to exit the leader from the main trajectory, the followers should be able to detect the fault, isolate the leader, use the other leaders' data, and keep the main trajectory. Tracking the trajectory by followers in such a case is the second step of this paper. Preserving the time‐varying formation despite a fault occurring in one of the followers is the next step. To reach these goals, a distributed array of Kalman filters is used for noise cancellation and data extraction. Next, the combination of state vector data fusion and some type of χ2 test are employed for DFDI, in agents. Besides, a controller is implemented in each agent for formation tracking. In this controller, estimated relative position and velocity vectors of the agents are employed to keep the time varying formation while tracking the leaders. The closed‐loop stability is studied via Lyapunov stability theorem, and various simulations are carried out to demonstrate the capability of the proposed strategy.

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LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

Cited by 123 publications

References 27 publications

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Stabilization of Single‐Input LTI Systems by Proportional‐Derivative Feedback

Distributed fault detection and isolation in time‐varying formation tracking UAV multi‐agent systems

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