Sliding Mode Control of a Two-Degree-of-Freedom Helicopter via Linear Quadratic Regulator

2006 ◽  
Author(s):  
Gwo-Ruey Yu ◽  
Hsuan-Tsung Liu
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Degree Of Freedom ◽  
Linear Quadratic ◽  
Mode Control ◽  
Two Degree Of Freedom

Optimality of Synergetic Controllers

2006 ◽  
Author(s):  
Antonius Nusawardhana ◽  
Stanislaw H. Zak
Keyword(s):  
Sliding Mode Control ◽  
Control Strategy ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Variable Structure ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Control Approach ◽  
Mode Control ◽  
Synergetic Control

Optimality properties of synergetic controllers are analyzed using the Euler-Lagrange conditions and the Hamilton-Jacobi-Bellman equation. First, a synergetic control strategy is compared with the variable structure sliding mode control. The synergetic control design methodology turns out to be closely related to the methods of variable structure sliding mode control. In fact, the method of sliding surface design from the sliding mode control are essential for designing similar manifolds in the synergetic control approach. It is shown that the synergetic control strategy can be derived using tools from the calculus of variations. The synergetic control laws have simple structure because they are derived from the associated first-order differential equation. It is also shown that the synergetic controller for a certain class of linear quadratic optimal control problems has the same structure as the one generated using the linear quadratic regulator (LQR) approach by solving the associated Riccati equation.

Multi-Objective Design of Optimal Sliding Mode Control for Trajectory Tracking of SCARA Robot Based on Genetic Algorithm

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Wafa Boukadida ◽  
Anouar Benamor ◽  
Hassani Messaoud
Keyword(s):  
Genetic Algorithm ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Linear Time ◽  
Linear Quadratic Regulator ◽  
Second Phase ◽  
Robot Arm ◽  
Linear Quadratic ◽  
Multi Objective ◽  
Mode Control

This paper focuses on robust optimal sliding mode control (SMC) law for uncertain discrete robotic systems, which are known by their highly nonlinearities, unmodeled dynamics, and uncertainties. The main results of this paper are divided into three phases. In the first phase, in order to design an optimal control law, based on the linear quadratic regulator (LQR), the robotic system is described as a linear time-varying (LTV) model. In the second phase, as the performances of the SMC greatly depend on the choice of the sliding surface, a novel method based on the resolution of a Sylvester equation is proposed. The compensation of both disturbances and uncertainties is ensured by the integral sliding mode control. Finally, to solve the problem accompanying the LQR synthesis, genetic algorithm (GA) is used as an offline tool to search the two weighting matrices. The main contribution of this paper is to consider a multi-objective optimization problem, which aims to minimize not only the chattering phenomenon but also other control performances. A novel dynamically aggregated objective function is proposed in such a way that the designer is provided, once the optimization is achieved, by a set of nondominated solutions and then he selects the most preferable alternative. To show the performance of the new controller, a selective compliance assembly robot arm robot (SCARA) is considered. The results show that the manipulator tracing performance is considerably improved with the proposed control scheme.

Sliding Mode Control for Two-Degree-Of-Freedom Fractional Zener Oscillator

2021 ◽  
Author(s):  
Jian Yuan ◽  
Song Gao ◽  
Liying Wang ◽  
Guozhong Xiu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Mode Control ◽  
Fractional Oscillator ◽  
Total Mechanical Energy ◽  
Two Degree Of Freedom

Abstract Fractional-order derivatives provide a powerful tool for the characterization of mechanical properties of viscoelastic materials. A fractional oscillator refers to mechanical model of viscoelastically damped structures, of which the viscoelastic damping is described by constitutive equations involving fractional-order derivatives. This paper proposes active control of vibration in a two-degree-of-freedom fractional Zener oscillator utilizing sliding mode technique. Firstly, with a state transformation, the fractional differential equations of motion are equivalently transformed into a relatively simple form. Meanwhile, a virtual fractional oscillator is generated, which is further used to analyze the original oscillator. Then, the stored energy in the two fractional derivative terms is derived based on the diffusive model of fractional integrator. Thus, the total mechanical energy in the virtual oscillator is determined as the sum of the kinetic energy, the potential energy and the fractional energy. Furthermore, sliding mode control of vibration in the fractional Zener oscillator is designed, of which the Lyapunov function is chosen as the total mechanical energy. Finally, numerical simulations are conducted to validate the effectiveness of the proposed controllers.

Sign in / Sign up

Export Citation Format

Share Document