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In the present contribution, a methodology to solve the tracking control problem of robot manipulators through the use of a Proportional Retarded plus Gravity (PR+G) compensation scheme is presented. The main advantage of the proposal is to avoid the necessity of velocity measurements or their estimation, which is commonly used in most control schemes, such as the proportional derivative-type controllers or the computed torque control. The design of the PR+G controller is addressed via σ-stability analysis and its performance is tested in an experimental platform that consists of 2 degrees of the freedom robot manipulator. The proposed controller is compared with a classic proportional derivative plus gravity compensation scheme. The results are analyzed from a frequency perspective and measured by a quadratic error index.

The goal of this work is to propose a new time-delay control law called the cascade proportional integral retarded controller, which is aimed at position control of DC servodrives. The proposed controller has a cascade inner loop-outer loop structure. The inner loop is endowed with an integral retarded algorithm, and regulates the servodrive angular velocity. A proportional controller closes the outer loop whose goal is to regulate the servodrive angular position. The tuning of the cascade proportional integral retarded controller is accomplished into two steps. In the first step, the velocity of the inner loop is tuned by assigning a triple dominant root. The second step tunes the outer position loop. It is also possible to modify the cascade proportional integral retarded controller to avoid velocity measurements without adding extra filters. Moreover, the cascade topology of the cascade proportional integral retarded controller makes it easy to introduce a nonlinear saturated gain in the outer loop. This controller termed as the cascade nonlinear proportional integral retarded controller prevents overshoots for large values of the set point, avoids excessive control effort, and maintains a prescribed value of the angular velocity. Experiments in real-time using a laboratory prototype allow assessing the performance of the proposed controllers. [ABSTRACT FROM AUTHOR]

A fuzzy proportional-integral-derivative (PID) controller is designed using time-delay estimation (TDE). In this paper, we show that, in a discrete-time domain, the fuzzy PID controller is a superset of a time-delay controller (TDC). In other words, with certain fuzzy parameter conditions, the discrete fuzzy PID controller is equivalent to the discrete TDC. Tuning the fuzzy PID controller can be started by exploiting the TDC: a simple, efficient and effective controller. The initial fuzzy parameters can be obtained with equivalence relationships between the fuzzy PID controller and the TDC. Furthermore, the performance of the fuzzy PID controller can be enhanced by using the non-linear control surface described by various fuzzy parameters. To this end, a fuzzy TDC is proposed using the TDE and the desired fuzzy error dynamics, and a conversion formula from the fuzzy TDC to the fuzzy PID controller is derived in a discrete-time domain. The effectiveness of the proposed method is verified through experiments on a PUMAtype robot manipulator. [ABSTRACT FROM AUTHOR]

A dual‐loop robust controller is proposed for precise position control of an autonomous underwater vehicle under uncertain hydrodynamics and unknown disturbances. In the inner‐loop, a time‐delay controller is presented in which a time‐delay estimator estimates uncertain hydrodynamics and unknown disturbances from its time‐delayed information and cancels these, thereby reducing control efforts on internal dynamics considerably. In the outer‐loop, the linear controller stabilises the position error of the AUV without prior knowledge on values of hydrodynamic parameters. The proposed dual‐loop controller features simple structure and easy implementation because it does not require real‐time estimation of hydrodynamics. [ABSTRACT FROM AUTHOR]