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In controller design, it is essential to achieve stability of the closed-loop system and various performance specifications. Frequency domain criteria such as gain margin, phase margin and H8 norms of the closed-loop transfer functions as well as time domain criteria such as settling time, rise time and overshoot can be counted among important performance specifications. Most of the controllers used in the practical world are low order controllers such as P, PI and PID controllers. It is possible to see that methods for finding stabilizing low order compensators can be considered in three main categories: methods based on Nyquist theorem, methods based on a generalized version of the Hermite- Biehler theorem, and methods based on parameter space and the concept of singular frequencies. Robust stabilization of continuous time single-input single-output (SISO) linear time invariant (LTI) systems with multiplicative uncertainties is considered in this study. In particular, it has been shown that all P and PI controllers that robustly stabilize a given uncertain SISO LTI system can be found by utilizing a generalization of the Nyquist theorem and the parameter space approach, respectively. The generalization of Nyquist stability criterion suggests to determine the number of the unstable poles for gain intervals obtained by calculating the location and direction of the crossing of the Nyquist plot with the real axis. A stable characteristic polynomial, whose roots are in the left half plane, becomes unstable if and only if at least one root crosses the imaginary axis. The parameter values of the root crossing form the stability boundaries in the parameter space, which can be classified into three cases: the real root boundary, where a root crosses the imaginary axis at the origin (substitute s= jw and w = 0 in the characteristic polynomial), the infinite root boundary, where a root leaves the left half plane at infinity (for w → ∞ ) and the complex root boundary, where a pair of conjugate complex roots crosses the imaginary axes (for 0< w<∞). These stability boundaries separate regions in which the number of closed loop system unstable poles do not change in the parameter space. Sometimes, it is not possible to represent uncertainties in a system model with parametric uncertainties. Such uncertainties are usually encapsulated in a norm bounded system block that acts on a nominal system in an additive or multiplicative manner. Although it is possible to find robust controllers that can stabilize systems with such uncertainties by the help of H∞ control theory, the resulting compensators are usually of high order (at least as high as the order of the plant) and therefore impractical in many cases. Several attempts exist to put constraints on the order of H∞ controllers in the literature. However, many of these approaches suffer from computational intractability.… [ABSTRACT FROM AUTHOR]

In this study, Sliding Mode Control (SMC) and High Order Sliding Mode Control (HOSMC) methods are applied to a single Flexible Link Robot Arm (FLA) with payload. A sliding mode and high order sliding mode controllers are designed to achieve set point precision positioning control and trajectory tracking control for a FLA. Flexible robot arms have structural flexibilities and resulting high number of passive degrees-of-freedom. They cannot be decoupled due to the highly nonlinear structure. Since the flexible systems have highly nonlinear structure and coupled dynamics, the sliding mode based control approach is chosen a powerful method to overcome the unmodeled and parametric uncertainties. One of the proposed controllers is 2nd order HOSMC method is compared with classical SMC method. Comparison of the methods is experimentally fulfilled using HIL simulator, and additionally torque ripple analysis is made to evaluate of the methods aspect from system harmonics. Direct drive motors are used as actuator in controlled systems. Of all system dynamics affect system harmonics via motor shaft due to the direct drive system that is no gear box. Therefore, harmonics analysis is crucial to investigate of designed controllers effects on system harmonics. To precise set-point and trajectory tracking control of 1-DOF DD FLA has been derived SMC and HOSMC. Sliding Mode Controllers (SMCs) have the robustness properties, while also increasing accuracy by reducing chattering effects. The performance of the designed control methods are tested for the precise position and targeting control of a 1- DOF-DD-FLA system under heavy uncertainties. Comparative results of both methods have been evaluated in real-time using a Hardware-in-the- Loop (HIL) simulator designed for robotics. Especially, HIL simulator for this system includes DD motors and obtained results can be evaluated more realistically according to pure computer simulations Additionally, torque ripples of whole system with HIL simulator have been determined and their eliminations using for both methods are introduced. HIL simulator is used to implement designed controller for a flexible-link arm. Direct drive joint motors are important parts of the direct drive underactuated robot manipulators. Therefore two DD motors take part in HIL simulator and couple through their shaft. One of the motors represents joint actuator, while the other motor is used for generation of the dynamics of the controlled system via the torque applied to the shaft. The two motors acting as "actuator" and "load torque simulator" are driven separately by a high performance controller board. HIL Simulator is expressed briefly as software that is modeled control algorithm and system dynamic model via controller board is integrated with hardware. HIL simulation differs from computer simulation as it involves actual hardware and is not limited with a software-based representation of the system.… [ABSTRACT FROM AUTHOR]

In a hard disk drive with a dual-stage actuator the standard rotary actuation of the voice coil motor (VCM) is combined with an additional micro- or milli-actuation to accomplish high-bandwidth and highly accurate track following. For extremely high density recording, the servo control algorithm designed for a specific dual-stage actuator needs to maintain high performance track following in lieu of external disturbances and uncertainties in the dynamic response induced by product manufacturing tolerances. Essential in the robust design of a servo control algorithm is to bound these uncertainties and design a robust track following servos accordingly. In this paper, we present an experiment based methodology to characterize and bound the uncertainties in the dynamic response of a dual-stage actuator in the form of an uncertainty model. Subsequently, the uncertainty model is used for the analysis and synthesis of a robust dual-stage servo controller that is able to optimize position error variance in the presence of uncertainty information. [ABSTRACT FROM AUTHOR]