In this paper, the robustness properties of sliding mode control (SMC) which is designed to produce a dynamic output feedback controller to achieve robustness for trajectory tracking of the nonlinear human swing leg system is presented. The human swing leg represents the support of human leg or the humanoid robot leg which is usually modeled as a double pendulum. The thigh and shank of a human leg will respect the pendulum links, hip and knee will connect the upper body to thigh and then shank respectively. The total moments required to move the muscles of thigh and shank are denoted by two external (servomotors) torques applied at the hip and knee joints. The mathematical model of the system is developed. The results show that the proposed controller can robustly stabilize the system and achieve a desirable time response specification.

In this paper, the H-infinity Sliding Mode Control (HSMC) is designed to produce a new dynamic output feedback controller for trajectory tracking of the nonlinear human swing leg system. The human swing leg system represents the support of human leg or the humanoid robot leg which is usually modeled as a double pendulum. The thigh and shank of a human leg is represented by two pendulum links and the hip joint will connect the upper body to the thigh and the knee joint will connect the thigh to the shank. The external torques (servo motors) are applied at the hip and knee joints to move the muscles of thigh and shank. The results show that the HSMC can robustly stabilize the system and achieve a desirable time response specification better than if only H-infinity or SMC is used. This controller achieves the following specifications:  sec,  for hip joint and sec, for knee joint.

In this paper, the robustness properties of H-infinity control to produce a dynamic output feedback controller is applied to a human swing leg system. The double pendulum structure is usually used to model this system. The pendulum links will represent the thigh and shank of a human leg. The upper body will be connected to the thigh and then the shank via hip and knee joints. The muscles of thigh and shank are moved by applied two external (servomotor) torques at the hip and knee joints. The mathematical model of the system is developed. The results show that the proposed controller can robustly stabilize the system and achieve a desirable time response specification. The results are obtained by using Matlab program and the achieved time response specifications are rise time tr=0.18 seconds, settling time ts=0.25 seconds and maximum over shoot Mp=0.03 for hip joint and tr=0.13 seconds, ts=0.21 seconds and Mp=0.01 for knee joint.

In this work, the design procedure of a hybrid robust controller for crane system is presented. The proposed hybrid controller combines the linear quadratic regulator (LQR) properties with the sliding mode control (SMC) to obtain an optimal and robust LQR/SMC controller. The crane system which is represented by pendulum and cart is used to verify the effectiveness of the proposed controller. The crane system is considered one of the highly nonlinear and uncertain systems in addition to the under-actuating properties. The parameters of the proposed LQR/SMC are selected using Particle Swarm Optimization (PSO) method. The results show that the proposed LQR/SMC controller can achieve a better performance if only SMC controller is used. The robustness of the proposed controller is examined by considering a  variation in system parameters with applying an external disturbance input. Finally, the superiority of the proposed LQR/SMC controller over the SMC controller is shown in this work.