Design of optimal lighting control strategy based on multi-variable fractional-order extremum seeking method

The paper focuses on the numerical approximation of nabla fractional order systems with the conditions of nonzero initial instant and nonzero initial state. First, the inverse nabla Laplace transform is developed and the equivalent infinite dimensional frequency distributed models of discrete fractional order system are introduced. Then, resorting the nabla Laplace transform, the rationality of the finite dimensional frequency distributed model approaching the infinite one is illuminated. Based on this, an original algorithm to estimate the parameters of the approximate model is proposed with the help of vector fitting method. Additionally, the applicable object is extended from a sum operator to a general system. Three numerical examples are performed to illustrate the applicability and flexibility of the introduced methodology.

Section: Preliminariesmentioning

confidence: 99%

Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

Wei

Wang

Tse

et al. 2019

“…The comparative study highlights the advantages of using these fractional order PI λ D μ controllers over a conventional PID controller with reduced settling time and maximum peak overshoot . An energy saving control strategy with an extremum seeking control (ESC) optimization technique using fractional order multivariate performance function for a multi‐input single output (MISO) system has been developed in . The performance of this has been compared with integer order ESC to exhibit better control performance and reduced energy consumption for indoor lighting system with multiple lighting sources.…”

Section: Introductionmentioning

confidence: 99%

“…The performance of this has been compared with integer order ESC to exhibit better control performance and reduced energy consumption for indoor lighting system with multiple lighting sources. The conventional integer order Proportional‐Integral and Derivative (PID) control approach has been adopted in both the above mentioned literatures to realize the desired lighting level. A nonlinear fractional order controller for fractional order non‐linear system has been proposed in with fractional order exponential switching technique, the stability analysis of which has been performed relying on the stable region analysis of fractional order systems.…”

Section: Introductionmentioning

confidence: 99%

Optimal fractional order PI^λD^μ controller for stabilization of cart‐inverted pendulum system: Experimental results

Mondal

Chakraborty

Dey

et al. 2019

The cart-inverted pendulum is a non-minimum phase system having right half s-plane pole and zero in close vicinity to each other. Linear time invariant (LTI) classical controllers cannot achieve satisfactory loop robustness for such systems. Therefore, in the present work the fractional order PI λ D μ (FOPID) controller is addressed for robust stabilization of the system, since fractional order controller design allows more degrees of freedom compared to its integer order counterparts by virtue of its two parameters λ and μ. The controller parameters are tuned by three evolutionary optimization techniques. In order to select the controller parameters optimally, a novel non-linear fitness function using integral time square error (ITSE), settling-time, and rise time is proposed here. The control algorithm is implemented successfully in real-time. Moreover, stability analysis of the system compensated with a fractional order controller is presented using Riemann surface. Robustness of the physical cartinverted pendulum system towards multiplicative gain variations and plant parameter variations is verified. In this regard, it is shown that the fractional order controller provides satisfactory robust performance in both simulation and real-time system. KEYWORDS cart-inverted pendulum system, FOPID controller, gain margin (GM), non-minimum phase system, Riemann surface, robust stability

“…In recent years, there has been significant attention on the study of UAV amongst academics, including in relation to design of sensors, optimization of system structure, and the control algorithm [4,5]. As control theory is being developed and advanced control methods are being applied in the field of rotor craft, a considerable amount of typical control methods have been applied in this area, such as PID, backstepping control, and extremum seeking [6][7][8][9][10]. Manuscript The backstepping method is a recursive procedure under the Lyapunov stability.…”

Section: Introductionmentioning

confidence: 99%

Design of Fractional‐Order Backstepping Sliding Mode Control for Quadrotor UAV

Shi

Cheng

Yin

et al. 2018

Self Cite

This paper derives a nonlinear translational and rotational dynamic model of the quadrotor UAV. An original fractional-order backstepping sliding mode control method for a typical quadrotor UAV is presented. The new approach can decrease the chattering phenomenon and increase the robustness of control strategy. The strongly coupled characteristics of the under-actuated system are sought by the virtual controllers. The feasibility for different track trajectories are verified using MATLAB. The new control method can not only track the expected trajectory very well but also has a better robustness for different complex trajectory under disturbances, as the simulation results demonstrate.