Development of New Adaptive Control Strategies for a Two-Link Flexible Manipulator

Manipulators with thin and light weight arms or links are called as Flexible-Link Manipulators (FLMs). FLMs offer several advantages over rigid-link manipulators such as achieving highspeed operation, lower energy consumption, and increase in payload carrying capacity and find applications where manipulators are to be operated in large workspace like assembly of freeflying space structures, hazardous material management from safer distance, detection of flaws in large structure like airplane and submarines. However, designing a feedback control system for a flexible-link manipulator is challenging due the system being non-minimum phase, underactuated and non-collocated. Further difficulties are encountered when such manipulators handle unknown payloads. Overall deflection of the flexible manipulator are governed by the different vibrating modes (excited at different frequencies) present along the length of the link. Due to change in payload, the flexible modes (at higher frequencies) are excited giving rise to uncertainties in the dynamics of the FLM. To achieve effective tip trajectory tracking whilst quickly suppressing tip deflections when the FLM carries varying payloads adaptive control is necessary instead of fixed gain controller to cope up with the changing dynamics of the manipulator. Considerable research has been directed in the past to design adaptive controllers based on either linear identified model of a FLM or error signal driven intelligent supervised learning e.g. neural network, fuzzy logic and hybrid neuro-fuzzy. However, the dynamics of the FLM being nonlinear there is a scope of exploiting nonlinear modeling approach to design adaptive controllers. The objective of the thesis is to design advanced adaptive control strategies for a two-link flexible manipulator (TLFM) to control the tip trajectory tracking and its deflections while handling unknown payloads. To achieve tip trajectory control and simultaneously suppressing the tip deflection quickly when subjected to unknown payloads, first a direct adaptive control (DAC) is proposed. The proposed DAC uses a Lyapunov based nonlinear adaptive control scheme ensuring overall system stability for the control of TLFM. For the developed control laws, the stability proof of the closed-loop system is also presented. The design of this DAC involves choosing a control law with tunable TLFM parameters, and then an adaptation law is developed using the closed loop error dynamics. The performance of the developed controller is then compared with that of a fuzzy learning based adaptive controller (FLAC). The FLAC consists of three major components namely a fuzzy logic controller, a reference model and a learning mechanism. It utilizes a learning mechanism, which automatically adjusts the rule base of the fuzzy controller so that the closed loop performs according to the user defined reference model containing information of the desired behavior of the controlled system. Although the proposed DAC shows better performance compared to FLAC but it suffers from the complexity of formulating a multivariable regressor vector for the TLFM. Also, the adaptive mechanism for parameter updates of both the DAC and FLAC depend upon feedback error based supervised learning. Hence, a reinforcement learning (RL) technique is employed to derive an adaptive controller for the TLFM. The new reinforcement learning based adaptive control (RLAC) has an advantage that it attains optimal control adaptively in on-line. Also, the performance of the RLAC is compared with that of the DAC and FLAC. In the past, most of the indirect adaptive controls for a FLM are based on linear identified model. However, the considered TLFM dynamics is highly nonlinear. Hence, a nonlinear autoregressive moving average with exogenous input (NARMAX) model based new Self-Tuning Control (NMSTC) is proposed. The proposed adaptive controller uses a multivariable Proportional Integral Derivative (PID) self-tuning control strategy. The parameters of the PID are adapted online using a nonlinear autoregressive moving average with exogenous-input (NARMAX) model of the TLFM. Performance of the proposed NMSTC is compared with that of RLAC. The proposed NMSTC law suffers from over-parameterization of the controller. To overcome this a new nonlinear adaptive model predictive control using the NARMAX model of the TLFM (NMPC) developed next. For the proposed NMPC, the current control action is obtained by solving a finite horizon open loop optimal control problem on-line, at each sampling instant, using the future predicted model of the TLFM. NMPC is based on minimization of a set of predicted system errors based on available input-output data, with some constraints placed on the projected control signals resulting in an optimal control sequence. The performance of the proposed NMPC is also compared with that of the NMSTC. Performances of all the developed algorithms are assessed by numerical simulation in MATLAB/SIMULINK environment and also validated through experimental studies using a physical TLFM set-up available in Advanced Control and Robotics Research Laboratory, National Institute of Technology Rourkela. It is observed from the comparative assessment of the performances of the developed adaptive controllers that proposed NMPC exhibits superior 7performance in terms of accurate tip position tracking (steady state error ≈ 0.01°) while suppressing the tip deflections (maximum amplitude of the tip deflection ≈ 0.1 mm) when the manipulator handles variation in payload (increased payload of 0.3 kg). The adaptive control strategies proposed in this thesis can be applied to control of complex flexible space shuttle systems, long reach manipulators for hazardous waste management from safer distance and for damping of oscillations for similar vibration systems.