Suboptimal control synthesis for state and input delayed quadratic systems

2022 ◽  
pp. 095965182110674
Author(s):  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Chemical Reactor ◽  
Open Loop ◽  
Quadratic System ◽  
Least Square ◽  
Suboptimal Control ◽  
Control Synthesis ◽  
Least Square Problem ◽  
Linear State

In this article a suboptimal linear-state feedback controller for multi-delay quadratic system is investigated. Optimal state and input coefficients resulting from the expansion over a hybrid basis of block pulse and Legendre polynomials are first obtained by formulating a nonlinear programming problem. Afterwards, suboptimal control gains are found by solving a least square problem constructed with optimal coefficients of the open loop study. A sufficient condition for the exponential stability of the closed loop is obtained from generalized Grönwall–Bellman lemma. The Van de Vusse chemical reactor case is handled allowing to validate the proposed technique.

scholarly journals Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Time Delay ◽  
Polynomial Time ◽  
State Feedback ◽  
Open Loop ◽  
Least Square ◽  
Suboptimal Control ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Nonlinear Feedback ◽  
Loop Control

The aim of this paper is to determine the optimal open loop solution and a nonlinear delay-dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system’s states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.

scholarly journals Decentralized Suboptimal State Feedback Integral Tracking Control Design for Coupled Linear Time-Varying Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Mohamed Sadok Attia ◽  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Tracking Control ◽  
State Feedback ◽  
Linear Time ◽  
Least Square ◽  
Control Synthesis ◽  
Operational Matrices ◽  
Control Input ◽  
Time Varying ◽  
State Equations ◽  
Integral Control

In this paper, a suboptimal state feedback integral decentralized tracking control synthesis for interconnected linear time-variant systems is proposed by using orthogonal polynomials. Particularly, the use of operational matrices allows, by expanding the subsystem input states and outputs over a shifted Legendre polynomial basis, the conversion of time-varying parameter differential state equations to a set of time-independent algebraic ones. Hence, optimal open-loop state and control input coefficients are forwardly determined. These data are used to formulate a least-square problem, allowing the synthesis of decentralized state feedback integral control gains. Closed-loop asymptotic stability LMI conditions are given. The proposed approach effectiveness is proved by solving a nonconstant reference tracking problem for coupled inverted pendulums.

scholarly journals Iterative LQG Controller Design Through Closed-Loop Identification

1996 ◽  
Vol 118 (2) ◽  
pp. 366-372 ◽  
Author(s):  
Min-Hung Hsiao ◽  
Jen-Kuang Huang ◽  
David E. Cox
Keyword(s):  
Kalman Filter ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Open Loop ◽  
The State ◽  
Magnetic Suspension ◽  
Loop Model ◽  
Closed Loop Identification ◽  
Noise Statistics

This paper presents an iterative LQG controller design approach for a linear stochastic system with an uncertain openloop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQG controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.

scholarly journals Nonlinear/Linear Switched Control of Inverted Pendulum System: Stability Analysis and Real-Time Implementation

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Amira Tiga ◽  
Chekib Ghorbel ◽  
Naceur Benhadj Braiek
Keyword(s):  
Stability Analysis ◽  
Real Time ◽  
State Feedback ◽  
Inverted Pendulum ◽  
System Stability ◽  
Control Synthesis ◽  
Vertical Position ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Linear State

This paper treats the problems of stability analysis and control synthesis of the switched inverted pendulum system with nonlinear/linear controllers. The proposed control strategy consists of switching between backstepping and linear state feedback controllers on swing-up and stabilization zones, respectively. First, the backstepping controller is implemented to guarantee the rapid convergence of the pendulum to the desired rod angle from the vertical position. Next, the state feedback is employed to stabilize and maintain the system on the upright position inherently unstable. Based on the quadratic Lyapunov approach, the switching between the two zones is analyzed in order to determine a sufficient domain in which the stability of the desired equilibrium point is justified. A real-time experimentation shows a reduction of 84% of the samples below the classical scheme when using only the backstepping control in the entire operating region. Furthermore, the reduction percentage has become 92% in comparison with the composite linear/linear controller.

Dissipative Control of Singular Systems by Proportional Plus Derivative State Feedback

2012 ◽  
Vol 246-247 ◽  
pp. 826-831
Author(s):  
Shuang Yun Xing ◽  
Xin Jing ◽  
Yang Cao
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Uncertain System ◽  
Loop System ◽  
Descriptor Systems ◽  
Control Synthesis ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Derivative Matrix

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

scholarly journals A Novel Control-rod Drive Mechanism via Electromagnetic Levitation in MNSR

Nukleonika ◽  
2014 ◽  
Vol 59 (2) ◽  
pp. 73-79
Author(s):  
Mohammad Divandari ◽  
Mehdi Hashemi-Tilehnoee ◽  
Masoud Khaleghi ◽  
Mohammadreza Hosseinkhah
Keyword(s):  
Control System ◽  
State Feedback ◽  
Closed Loop ◽  
Research Reactor ◽  
Magnetic Levitation ◽  
Electromagnetic Levitation ◽  
Open Loop ◽  
Control Rod ◽  
Levitation System ◽  
Magnetic Levitation System

Abstract In this paper, an electromagnetic levitation system was used with a synchronous motor to navigate the control rod of a small-type research reactor. The result from this prototype magnetic levitation system was in agreement with simulation results. The control system was programmed in MATLAB through open-loop system, closed-loop with state feedback and closed-loop with state feedback integral tracking. The final control system showed the highest performance with a low positioning error. Our results showed that the developed control system has the potential to be used as a reliable actuator in nuclear reactors to satisfy higher performance and safety.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Comparison of Dc-Dc SEPIC, CUK and Flyback Converters Based LED Drivers

2020 ◽  
pp. 99-107
Author(s):  
Erdal Sehirli
Keyword(s):  
Integrated Circuit ◽  
Closed Loop ◽  
Input Voltage ◽  
Open Loop ◽  
Current Sensor ◽  
Switching Frequency ◽  
Led Driver ◽  
Advantages And Disadvantages ◽  
Led Drivers ◽  
Conduction Mode

This paper presents the comparison of LED driver topologies that include SEPIC, CUK and FLYBACK DC-DC converters. Both topologies are designed for 8W power and operated in discontinuous conduction mode (DCM) with 88 kHz switching frequency. Furthermore, inductors of SEPIC and CUK converters are wounded as coupled. Applications are realized by using SG3524 integrated circuit for open loop and PIC16F877 microcontroller for closed loop. Besides, ACS712 current sensor used to limit maximum LED current for closed loop applications. Finally, SEPIC, CUK and FLYBACK DC-DC LED drivers are compared with respect to LED current, LED voltage, input voltage and current. Also, advantages and disadvantages of all topologies are concluded.

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