Shubhobrata Rudra

An FPGA based implementation of a flexible digital PID controller for a motion control system

Implementation of digital controllers in embedded environment suffers from the inherent problems associated with analog-digital signals interfacing in hard real-time, therefore, the control algorithms are invariantly subjected to approximations. This paper presents a novel technique for implementation of an efficient FPGA based digital Proportional-Integral-Derivative (PID) controller for the motion control of a permanent magnet DC motor. The implementation technique circumnavigates the problem of interfacing analog and digital systems in real-time. The controller is used in a speed control loop. The hardware implementation has been done on a Xilinx Spartan 3 FPGA chip. A novel technique has been adopted for the generation of the control input as a PWM signal for controlling the motor driver circuit and decoding the optical encoder data for using it for the speed feedback in the PID control loop. The VHDL algorithm for the proposed implementation has also been presented in this paper. A comparison of the experimental results with the Matlab® based simulation shows the effectiveness of the proposed method.

Nonlinear state feedback controller design for underactuated mechanical system: A modified block backstepping approach

This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for a generalized nonlinear underactuated mechanical system. For the convenience of compact design, first, the state model of the underactuated system has been converted into the block-strict feedback form. Next, we have incorporated backstepping control action to derive the expression of the control input for the generic nonlinear underactuated system. The proposed block backstepping technique has further been enriched by incorporating an integral action additionally for enhancing the steady state performance of the overall system. Asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Subsequently, the stability of the zero dynamics has also been analyzed to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. The proposed control algorithm has been applied for the stabilization of a benchmarked underactuated mechanical system to verify the effectiveness of the proposed control law in real-time environment.

Global stabilization of a flat underactuated inertia wheel: A block backstepping approach

This paper presents the formulation of a novel block-backstepping based control algorithm to address the global stabilization problem of a flat underactuated inertia wheel system. The ideas behind the method are as follows. At first, state model of the inertia wheel system has been converted into block-strict feedback form. Then the control Lyapunov function has been designed for each cascaded dynamic block to derive the expression of the control input for the overall nonlinear system. The overall asymptotic stability of the inertia wheel system has been analyzed using Lyapunov Stability Criteria. Finally, the effectiveness of the proposed control algorithm has been verified in the simulation environment.

Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems

This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The mathematical derivations are described using well-known notations and simple algebra, without the need for any special previous background in higher mathematics. The chapters are lucidly described in a systematic manner, starting with control system preliminaries and moving on to a generalized description of the block backstepping method, before turning to several case studies. Simulation and experimental results are also provided to aid in reader comprehension.

Stabilization of Furuta Pendulum: A backstepping based hierarchical sliding Mode approach with disturbance estimation

An adaptive backstepping sliding mode controller, which combines both the merits of adaptive backstepping control and sliding mode control, is proposed to address the control problem of the Furuta Pendulum in the presence of external disturbances. At first, the underactuated state model of the Furuta Pendulum has been divided into two separate subsystems. Then a pair of first layer sliding surfaces is defined for each second-order subsystem. Two separate adaptive backstepping based control law is designed for each of the subsystem to ensure the states of each subsystem approach to their own sliding mode surface. Based on this two first layer sliding surfaces, a second layer sliding surface is defined correspondingly, through which a total control law is derivedto make sure that all states can converge to their desired value via Lyapunov stability theorem. The asymptotic stability of all the sliding surfaces has proven theoretically, and simulation results show the controllers validity and its adaptive abilities for all kinds of extraneous disturbances.

Design of block backstepping based nonlinear state feedback controller for pendubot

Design of a novel block-backstepping based nonlinear stabilizing control law of a pendubot is presented in this paper. It is a 2-DOF underactuated with unactuated shape variable and second order nonholonomic constraint. At the onset of the design, state model of the pendubot has been transformed into the block-strict feedback form. Thereafter, a systematic approach has been utilized to devise a backstepping control law for the pendubot system, which eventually yields a control law that is more conducive to practical applications. Lyapunov stability criteria has been used to analyze the stability of the overall system. Furthermore, stability of the zero dynamics has also been investigated to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. Finally, performance of the proposed control law has been studied in simulation environment. Indeed, main novelty of the proposed approach lies in the fact that a systematic block backstepping control approach has been proposed to yield a solution for the control problem of pendubot.

Design of nonlinear state feedback control law for underactuated TORA system: A block backstepping approach

This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for the well-known nonlinear benchmark TORA system. The ideas behind the method are as follows. At first, state model of the TORA system has been converted into block-strict feedback form. Then the control Lyapunov function has been designed for each cascaded dynamic block to derive the expression of the control input for the overall nonlinear system. The overall asymptotic stability of the TORA system has been analyzed using Lyapunov Stability Criteria. Finally, the effectiveness of the proposed control algorithm has been verified in the simulation environment.

Design of Nonlinear State Feedback Control Law for Underactuated Two-Link Planar Robot: A Block Backstepping Approach

This paper presents the formulation of a novel block-backstepping based control algorithm to address the control problem of the well-known nonlinear benchmark two-link planar robot (acrobot) system. For the convenience and compact design, first the state model of the two-link robot has been transformed into a block-strict feedback form. Then the control Lyapunov function has been designed for each cascaded dynamic block to derive the expression of the control input for the overall two-link system. The overall asymptotic stability of the robot system has been analyzed using Lyapunov stability criteria. Finally, the effectiveness of the proposed control algorithm has been verified in the simulation environment.