Optimal second order integral sliding mode control for a flexible joint robot manipulator

Improving High Efficiency and Reliability of Pump Systems using Optimal Fractional-order Integral Sliding-Mode Control Strategy

“…with e(t) = x(t) − x(t) ref the tracking error between the four actual states of the system and the desired references and E = ∆A+∆Bu+d is the unknown lumped uncertainties possesses un upper bound [20], [21], [22]. 4) Linear-Quadratic Regulator: The optimal gain matrix, K, is determined by using LQR which can be considered a powerful optimal control among various linear controllers to design the fractional-integral sliding mode control with a minimum cost [18], [19].…”

“…The quadratic cost function is expressed by [16], [17], [18], [20], [21] After using the linearization prototype model tool of Matlab to obtain linearized dynamic around the equilibrium operating point in state space, and applying an adaptive Genetic Algorithm optimization tool (GA), the optimal matrix gain K of the closed loop optimal control law defined by proper selection of weighting matrix Q and R for the state x (t) and the control input u (t) respectively. Replacing the tracking error dynamics ė (t) with its expression without taking into account the disturbances ẋ − ẋref = Ax + Bu eq − ẋref , and using the conditions S(t) = 0 with .…”

Practically Robust Fixed-Time Convergent Sliding Mode Control for Underactuated Aerial Flexible JointRobots Manipulators

“…Concerning friction nonlinearities; this is because the friction model in the motor drive side consists of viscous and Coulomb terms, for an example. To capture the nonlinear friction behavior, the total friction torque of the motor, along with a speed operation θ, is described by τ fric = B eq θ + F c sign( θ) (10) where B eq is the linear viscous friction coefficient as defined with the system parameters, and F c > 0 denotes the Coulomb friction coefficient associated with the nonlinear part, which is unknown. By defining the unknown friction nonlinearity F c sign( θ) as the nonlinear friction term O fric ( θ), the friction model (10) can be rewritten as…”

“…In the existing literature on the tracking controller design of the FJR system, there have been numerous attempts to address the above issues, including PID, passivity-based control, adaptive control, singular perturbation control, backstepping, and sliding mode control, etc. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Among them, the sliding mode control (SMC) has proven its reputation in control engineering society owing to its robust performance against system uncertainties and perturbations [14,15,20,21].…”

A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators

“…However, the hierarchical SMC revealed more effectiveness for vibration attenuation. 72 There are other controllers that were designed based on sliding mode technique such as a high-order SMC for a single-FLM, 73 a partially decentralized SMC for a two-FLM, 74 a back-stepping SMC with a DOB for a two-FLM, 75 an optimal second-order integral SMC, 76 and a super-twisting integral SMC 77 for a single-LFJM.…”