Design of an optimal preview controller for linear time-varying discrete systems in a multirate setting

2015 ◽  
Vol 13 (06) ◽  
pp. 1550050 ◽  
Author(s):  
Fucheng Liao ◽  
Yujian Guo ◽  
Yuan Yan Tang
Keyword(s):  
Optimal Control ◽  
Discrete System ◽  
Control Method ◽  
Linear Time ◽  
Discrete Systems ◽  
Control Input ◽  
Time Varying ◽  
Preview Control ◽  
Rate System ◽  
Error System

This paper is concerned with preview control problems for linear time-varying discrete systems in a multirate setting. First, by using the discrete lifting technique, the multirate time-varying discrete system is converted to a formal single-rate system. Then, by applying the standard linear quadratic (LQ) preview control method, we construct the expanded error system, and the optimal preview control model of the common time-varying discrete system is obtained. The optimal control input of the expanded error system is obtained by using the outcome of optimal control theory on time-varying systems. The controller with preview action is obtained when we transfer our conclusion into the original system. Finally, a numerical example is included to illustrate the validity of the proposed method.

Vibration Control of Rope-Sway of Elevator for High-Rise Building

2001 ◽  
Author(s):  
Masatsugu Otsuki ◽  
Ryohsuke Nakada ◽  
Kazuo Yoshida ◽  
Kosoku Nagata ◽  
Shigeru Fujimoto ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Synthesis Method ◽  
Optimal Controller ◽  
Control Input ◽  
Time Varying ◽  
Object A ◽  
High Rise ◽  
High Rise Building ◽  
Kobe Earthquake

Abstract This study presents a synthesis method of a nonstationary optimal controller with a time-varying criterion function for reducing vibration of a time-varying object such as rope of elevator and crane. For time-varying object a stationary optimal control is little effective in reducing vibration. Hence, a nonstationary optimal control method with time-varying weightings on a control input and state values is applied to the time-varying object. As an illustration, the performance of reducing vibration with respect to the rope-sway problem on a high-rise building is examined through numerical calculation. Moreover, from the viewpoint of wave propagation, we propose a method of reducing vibration with wave-absorbing controller to remove the reflected waves. Finally, the performance of these nonstationary optimal and wave-absorbing controllers are compared with that of the stationary optimal controller for case that the structure is subjected to Kobe earthquake.

scholarly journals On the existence of a solution for some distributed optimal control hyperbolic system

2000 ◽  
Vol 23 (5) ◽  
pp. 297-311 ◽  
Author(s):  
Dariusz Idczak ◽  
Stanislaw Walczak
Keyword(s):  
Optimal Control ◽  
Hyperbolic System ◽  
Convex Set ◽  
Linear Time ◽  
Time Varying ◽  
Optimal Process ◽  
Existence Of A Solution ◽  
Distributed Optimal Control ◽  
Absolutely Continuous ◽  
State Variable

We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

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.

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