Vahid Azimi

STABLE ROBUST ADAPTIVE IMPEDANCE CONTROL OF A PROSTHETIC LEG

We propose a nonlinear robust model reference adaptive impedance controller for an active prosthetic leg for transfemoral amputees. We use an adaptive control term to consider the uncertain parameters of the system, and a robust control term so the system trajectories converge to a sliding mode boundary layer and exhibit robustness to variations of ground reaction force (GRF). The boundary layer not only compromises between control chattering and tracking performance, but also bounds the parameter adaptation to prevent unfavorable parameter drift. We also prove the stability of the controller for the robotic system in the case of non-scalar boundary layer trajectories using Lyapunov stability theory and Barbalat’s lemma. The acceleration-free regressor form of the system removes the need to measure the joint accelerations, which would otherwise introduce noise in the system. We use particle swarm optimization (PSO) to optimize the design parameters of the controller and the adaptation law. The PSO cost function is comprised of control signal magnitudes and tracking errors. PSO achieves a 8% improvement in the objective function. Finally, we present simulation results to validate the effectiveness of the controller. We achieve good tracking of joint displacements and velocities for both nominal and perturbed values of the system parameters. Variations of ±30% on the system parameters result in an increase of the cost function by only 3%, which confirms the robustness of the controller.Copyright

Robust multi-objective H2/H∞ tracking control based on the Takagi–Sugeno fuzzy model for a class of nonlinear uncertain drive systems

In this paper a robust H2/H∞ multi-objective state-feedback controller and tracking design are presented for a class of multiple input/multiple output nonlinear uncertain systems. First, some states (error of tracking) are augmented to the system in order to improve tracking control. Next, uncertain parameters and the quantification of uncertainty on physical parameters are defined by the affine parameter-dependent systems method. Then, to apply the H2/H∞ controller, the uncertain nonlinear system is approximated by the Takagi–Sugeno fuzzy model. After that, based on each local linear subsystem with augmented state, an H2/H∞ multi-objective state-feedback controller is designed by using a linear matrix inequalities approach. Finally, parallel distributed compensation is used to design the controller for the overall system and the total linear system is obtained by use of the weighted sum of the local linear subsystems. Several results show that the proposed method can effectively meet performance requirements such as robustness, good load disturbance rejection, good tracking and fast transient responses for a three-phase interior permanent magnet synchronous motor system.

Position and Current Control of an Interior Permanent-Magnet Synchronous Motor by Using Loop-Shaping Methodology: Blending of H∞ Mixed-Sensitivity Problem and T–S Fuzzy Model Scheme

This paper presents a robust mixed-sensitivity H1 controller design via loop-shaping methodology for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems. In order to design this controller, the nonlinear plant is first modeled as several linear subsystems by Takagi and Sugeno’s (T–S) fuzzy approach. Both loop-shaping methodology and mixed-sensitivity problem are then introduced to formulate frequency-domain specifications. Afterward for each linear subsystem, a regional pole-placement output-feedback H1 controller is employed by using linear matrix inequality (LMI) approach. The parallel distributed compensation (PDC) is then used to design the controller for the overall system. Several experimental results show that the proposed method can effectively meet the performance requirements like robustness, good load disturbance rejection, and both tracking and fast transient responses even in the presence of parameter variations and load disturbance for the three-phase interior permanent-magnet synchronous motor (IPMSM). Finally, the superiority of the proposed control scheme is approved in comparison with the input–output linearization (I/O linearization) and the H2/H1 controller methods. [DOI: 10.1115/1.4024200]

Ground reaction force estimation in prosthetic legs with an extended Kalman filter

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) prosthetic leg for transfemoral amputees, and includes four degrees of freedom (DOF): vertical hip displacement, thigh angle, knee angle, and ankle angle. We design a continuous-time extended Kalman filter (EKF) to estimate not only the states of the robot/prosthesis system, but also the GRFs that act on the prosthetic foot. The simulation results show that the average RMS estimation errors of the thigh, knee, and ankle angles are 0.007, 0.015, and 0.465 rad with the use of four, two, and one measurements respectively. The average GRF estimation errors are 2.914, 7.595, and 20.359 N with the use of four, two, and one measurements respectively. It is shown via simulation that the state estimates remain bounded if the initial estimation errors and the disturbances are sufficiently small.

Robust H 2 /H ∞ control for a robot manipulator fuzzy system

In this article we investigate on robust H2/H∞ control with regional Pole-Placement, for tool position control of a nonlinear uncertain flexible robot manipulator. First, to apply the H2/H∞ controller, the uncertain nonlinear system is approximated by Takagi and Sugenos (T-S) fuzzy model. Then, an extra state (error of tracking) is augmented to the T-S model in order to improve tracking control. Based on each local linear subsystem with augmented state, a regional pole-placement state feedback H2/H∞ controller by using linear matrix inequality (LMI) approach is employed. Parallel Distributed Compensation (PDC) is used to design the controller for the overall system and the total linear system is obtained by using the weighted sum of the local linear systems. A fuzzy weights online computation (FWOC) component is employed to update fuzzy weights in real time for different operating point of system. Simulation results are presented to validate the effectiveness of the proposed controller like robustness and good load disturbance attenuation and accurate tracking, even in the presence of parameter variations and load disturbances on motor and tool.

Robust mixed-sensitivity H∞ control for a class of MIMO uncertain nonlinear IPM synchronous motor via T-S fuzzy model

This article presents robust mixed-sensitivity H∞ output feedback controller by using loop shaping with regional Pole Placement for a class of MIMO uncertain nonlinear system. In order to design of controller first via Takagi and Sugenos (T-S) fuzzy approach the nonlinear dynamic is represented by several linear sub systems. After that, loop-shaping methodology and Mixed-sensitivity problem are introduced to formulate frequency-domain specifications and a systematic design of weighting matrices is presented. Then a regional pole-placement output feedback H∞ controller is employed by using linear matrix inequality (LMI) approach for each linear subsystem. Parallel Distributed Compensation (PDC) is used to design the controller for the overall system and the total linear system is obtained by using the weighted sum of the local linear system. Several results show that the proposed method can effectively meet the performance requirements like robustness, good load disturbance rejection responses, good tracking responses and fast transient responses for the 3-phase interior permanent magnet synchronous motor (IPMSM) system. In addition, the superiority of the proposed control scheme is indicated in comparison with the feedback linearization and the H2/H∞ controllers methods.

Robust Mixed-Sensitivity Gain-Scheduled H ∞ tracking control of a nonlinear Time-Varying IPMSM via a T-S fuzzy model

This article presents a robust Mixed-Sensitivity Gain-Scheduled H∞ controller based on the Loop-Shaping methodology for a class of MIMO uncertain nonlinear Time-Varying systems. In order to design this controller, the nonlinear parameter-dependent plant is first modeled as several linear sub systems by Takagi and Sugenos (T-S) fuzzy approach. Both Loop-Shaping methodology and Mixed-Sensitivity problem are then introduced to formulate frequency-domain specifications, which will be used to devise a systematic design for choosing properly the weighting matrices. Furthermore, for each linear subsystem a H∞ controller is designed by using linear matrix inequality(LMI) approach. Such controllers are said to be scheduled by the Time-Varying parameter measurements in real time. The Parallel Distributed Compensation (PDC) is then used to design the controller for the overall system and the total linear system is also obtained by using the weighted sum of the local linear subsystems. Several results show that the proposed method can effectively meet the performance requirements like robustness, good load disturbance rejection and tracking responses, and fast transient responses for the 3-phase interior permanent magnet synchronous motor (IPMSM). Finally, the superiority of the proposed control scheme is approved in comparison with the feedback linearization controller, the H2/H∞ Controller and the H∞ Mixed-Sensitivity controller methods.

Robust multi objective H 2 /H ∞ control of nonlinear uncertain systems using multiple linear model and ANFIS

This paper considers the multi objective robust control for nonlinear systems using multiple model and adaptive neuro fuzzy inference system (ANFIS). Nonlinear system divided to multiple linear model based on piecewise linearization around set points. For each linear model multi objective robust controller is designed to guarantee both system performance and robust stability. To design the robust controller for each linear model, nonlinearity part of system consider as uncertainty of linear system. The advantages of proposed method are that it can reduce the parameter perturbation and nonlinear uncertainty as well as increased the performance of the system. In this work ANFIS is used to make decision and combine the designed controller for each linear model. Simulation result on a nonlinear benchmark plant shows the effectiveness of the proposed method.

Robotics and Prosthetics at Cleveland State University: Modern Information, Communication, and Modeling Technologies

This chapter concentrates on the correlation between research-based education, government priorities and research funding. Special attention is paid to an analysis of the role of modern information and communication technology (ICT) in the education of engineering students. Successful cases with specific description of computer modeling methods for the implementation of prosthesis and robotics research projects are presented based on experiences in the Embedded Control Systems Research Laboratory of Cleveland State University.

Fuzzy robust control of MIMO nonlinear uncertain systems

This paper describes robust H2/H∞ multi-objective state feedback controller for nonlinear uncertain systems. To apply the H2/H∞ multi-objective state feedback method, the nonlinear dynamics is represented by a T-S fuzzy model. First, uncertain parameters and Quantification of uncertainty on physical parameters is defined by affine parameter-dependent systems method. Next, the Takagi and Sugenos fuzzy linear model is utilized to approximate uncertain nonlinear systems. Then, some states (error of tracking) are augmented to the system in order to improve tracking control. Finally, based on fuzzy linear model with augmented state, a H2/H∞ multi-objective state feedback controller is developed to achieve the robustness design of nonlinear uncertain systems. LMI (Linear Matrix Inequality) method and PDC (Parallel Distributed Compensation) are used to design the controller for the whole system. The results show that the proposed method can effectively meet the performance requirements like robustness, disturbance rejection and tracking for the 3-phase permanent magnet synchronous motor (PMSM).