Multiple-axis robot manipulators are widely used in industrial and space applications. The high accuracy of these robots is due to their rigidity, which makes them highly controllable. After the inception of harmonic drive in 1955, and its wide acceptance and use in the design of many electrically driven robots, the rigidity of robot manipulators was greatly affected. In the early 1980s researchers showed that the use of control algorithms developed based on rigid robot dynamics on real non-rigid robots is very limited and may even cause instability. Singular perturbation theory is used as the basic theory to model the dynamics of flexible joint robots (FJRs), in which, using two-time scale behavior, these systems are divided into fast and slow subsystems.As shown in the literature for a three-axis flexible robot the system is not feedback linearizable and the use of methods such as computed torque methods for flexible manipulators is not directly implementable. By neglecting the effects of link motion on the kinetic energy of the rotor, Spong derived a mathematical model for such systems in which the system is feedback linearizable. However, to linearize the system, acceleration and jerk feedback is required, whose measurement is very costly. To avoid the need for acceleration and jerk in this method the idea of an integral manifold is employed. In this method, instead of using the zero-order approximation of the model extracted from the singular perturbation theory, higher-order models can be used and, hence, a series of corrective terms is added to the control algorithm. Composite control scheme is called to such controller algorithms with corrective terms.

Canadarm 2 a sample of highly flexible joint robot

One of main drawbacks of composite PID controllers for FJR’s are the required high control effort. In this part of research we proposed composite controller structure as in previous research results but designing an H∞ controller for the slow subsystem. The main significance of this research is providing a systematic approach to use the control effort limitations directly into controller synthesis. The representation of the nonlinear dynamics of the system in terms of a linear model and multiplicative uncertainty is elaborated in this research, and an H∞- based robust controller is designed for the system. By analyzing the performance of the closed-loop system, it is observed that, the low frequency content reference inputs are well tracked, with a limited control effort, while the controller synthesis enables the designer to make a suitable compromise between the required bandwith and the control effort limitation. Moreover, in order to have the benefits of composite control law in addition to that of H∞ synthesis, these methods are combined and a composite H∞ controller is designed for the system. Through a simulation study it is shown that the composite H∞ controller provides significant improvement in control effort, while satisfying both stability and performance requirements.

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In this research nonlinear QFT approach is applied for controller design of FJR. It is first observed that the use of a stand alone QFT controller for the system causes large uncertainty templates, and hence, loop shaping within the bounds is infeasible. Hence, the use of a composite controller similar to that in previous research is proposed, but with a nonlinear QFT controller for slow subsystem. The structure of controller consists of three parts. A simple PD controller is used to stabilize the fast dynamics, and a QFT controller is used in addition to an integral manifold corrective term to perform on the slow dynamics. Because of the nonlinear dynamics of FJR and the proposed controller scheme, linear time invariant equivalent (LTIE) technique is used to assign a nominal model for the system with uncertainties templates. Design of the QFT controller, as slow part of the composite control law, is performed to compromise between the required bandwidth and the controller order. It is observed that this proposed structure is insensitive to structured variation of the plant, and only one design is sufficient for the full envelope. Moreover, any design limitations and the structure of the controller are apparent up front, and there is less development time for a full envelope design. Furthermore, one can determine what specifications are achievable early in the design process, and the changes in the specifications can be accomplished quickly in the redesign. The effectiveness of the proposed control topology is verified through various simulations.  The details of the contoller structure is given in the following presentation (CCA05).

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In this research the nonlinear H∞ controller design for the FJR is studied in detail. The nonlinear H∞ control theory is a newly emerging nonlinear design approach in practical applications. Since in most physical systems nonlinear nature is observed, one of main advantage of the nonlinear H∞ theory over the linear control theories is the systematic consideration of system nonlinearities and uncertainties together, and thus robust stability and performance can be analyzed over a large operating region. Therefore, the nonlinear H∞ controller provides better potential for handling uncertain nonlinear control problems. Since the nonlinear H∞ controller does not support tracking requirements, a combinational method is proposed to accommodate this requirement. Moreover, the minimization of the control effort that is needed for regulation as well as tracking, is systematically encountered into controller synthesis. In this   first the modeling procedure for an uncertain FJR is elaborated. Next through a short overview of nonlinear H∞ control methods, suitable controllers are designed and simulated for FJR. The obtained results show the effectiveness of the proposed controller in tracking performance, despite model uncertainties and external disturbances.  The details of the contoller structure is given in the following presentation (CCA05).

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In order to come up with an online implementable controller for FJRs, a new composite controller, combined with a fuzzy logic supervisory loop has been proposed. In this topology, the anti-saturation logic is set to be “out of the main loop”, at a supervisory level, at the aim of preventing actuator saturation, despite preserving the essential properties of the main controller. This idea in a general form has been first published by the authors and then has been modified to use for FJRs. In this structure a PD controller is used to stabilize the fast dynamics and a PID controller is proposed to robustly stabilize the slow dynamics of the FJR. Moreover, a supervisory control loop is added to the structure, in order to decrease the bandwidth of the fast controller during critical occasions. It is observed in various simulations that by including this supervisory loop into the controller structure, the steady state performance of the system is preserved, and moreover, the supervisory loop can remove instability caused by saturation. The robust stability of the overall system in presence of the modeling uncertainties is then analyzed in detail, and it is shown that UUB stability of the overall system is guaranteed, only if the PD gains of the fast controller and the PID gains are tuned to satisfy certain conditions. This stability analysis is essential for susceptible applications of the FJRs such as space robotics, where the stability is a main concern. The details of the contoller structure is given in the following presentation (CCA05).

Performance of Fuzzy Supervisory Loop

As the first step on the implementation phase, in this research, experimental identification of the 2DOF KNTU FJR is accomplished. In order to implement an H∞- based robust controller on the system, the nonlinear dynamics of the system is encapsulated in terms of a linear model and multiplicative uncertainty. The linear identification technique used in here is implemented using B&K Pulse analyzer platform. Design and implementation of composite H∞ controller is considered next. Implementation results shows the importance of correct phase identification in frequency response estimates. By this means a composite H_∞ controller results into suitable closed loop performance.

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