In the paper (Mobayen et al., 2021), two continuous controls and two adaptive discontinuous controls are proposed for tracking of disturbed robotic manipulator. This paper points out four flaws making all the proposed controls therein untenable.

A simple nonlinear proportional-integral-derivative (PID) controller is proposed for global finite-time regulation of robot manipulators without velocity measurements. A Lyapunov-based stability argument is employ to prove global finite-time stabilization. The proposed control algorithm does not involve the model parameters in the control law formulation and the control gains can be explicitly determined based on some well-known bounds extracted from the robot dynamics, and thus permits easy implementation. Simulations are included to demonstrate the expected properties of the proposed approach.

A simple nonlinear proportional-integral-derivative (PID) controller is proposed to solve the finite-time regulation of uncertain robot manipulators. The semiglobal finite-time stabilization is shown by using Lyapunov theory and finite-time stability theory. The proposed control algorithm does not involve the modeling information in the control law formulation and the control gains can be explicitly determined based on some well-known bounds extracted from the robot dynamics, and thus permits easy implementation. Simulations preformed on a two degrees-of-freedom (DOF) manipulator demonstrate the expected properties of the proposed approach.

A simple continuous output feedback proportional-derivative (PD) plus desired gravity compensation controller is proposed to solve the global finite-time regulation of robot manipulators with position measurements only. The global finite-time convergence is proved by using Lyapunov theory and finite-time stability theory. Simulations preformed on a two degrees-of-freedom (DOF) manipulator demonstrate the expected properties of the proposed approach.

In this paper, we provide an answer to the long-standing question of designing global asymptotically stable proportional-integral-derivative (PID) regulators with only position feedback for uncertain robots. Our main contribution is to establish the global asymptotic stability of the controlled system by using Lyapunov direct method and LaSalle's invariance principle. We provide explicit conditions on the regulator gains to ensure global asymptotic stability. The proposed controller does not utilize the modeling information in the control formulation, and thus permits easy implementation. Simulations performed on a planar two degrees-of-freedom robot manipulator demonstrate the effectiveness of the proposed approach.

High-quality low speed motion control calls for precise position and velocity signals. However, velocity estimation based on simple numerical differentiation from the only position measurement may be very erroneous, especially in the low-speed regions. A simple linear velocity estimator is proposed based for high-quality instantaneous velocity estimation, on position measurements only. The proposed estimator is constructed based on the fact that velocity belongs to the chain of kinematic quantities: position and velocity, and numerical integration can provide more stable and accurate results than numerical differentiation in the presence of noise. The main attraction of the new algorithm is that it is very effective as well as in low-speed ranges, high robustness against noise, and easy to implement with simple computation. Both extensive simulations and experimental tests have been performed to verify the effectiveness and efficiency of the proposed approach.

This paper presents a simple and globally stable nonlinear proportional-integral-derivative (N-PID) controller incorporated with a saturated function design. The proposed controller is formulated by using a new class of saturated function derived from quasi-natural potential function to shape the position and velocity errors. The global asymptotic stability of the controlled system for the setpoint position control is proven. Experiments are performed on an industrial robot manipulator to demonstrate the improved performance of the proposed approach over conventional linear PID controller

High-precision motion of parallel manipulators depends not only on the position accuracy of each actuator, but also on the position synchronization of all actuators. This paper presents a simple synchronized control algorithm for the setpoint position control of parallel manipulators, by incorporating cross-coupling technology into a common proportional-derivative (PD) control architecture. An integrated controller is developed, consisting of a PD control and a saturated proportional-integral (S-PI) control with feedback of the differential position errors amongst actuators (defined as the synchronization errors). The controller can stabilize the motion of each actuator, and meanwhile synchronize all actuators' motions so that both position and synchronization errors converge to zero. The control algorithm does not use the modeling parameters in the controller formulation, and thus permits easy implementation in practice. It is proved that the proposed method can guarantee global asymptotical stability of the system. Experiments conducted on a planar three-degree-of-freedom parallel manipulator demonstrate the effectiveness of the proposed approach.

A simple synchronized control algorithm is proposed, by incorporating cross-coupling technology into a common PD control architecture, for control of parallel manipulators. A saturated proportional (S-P) control and a linear proportional derivative (PD) control plus gravity force compensation is implemented for synchronization and position control, respectively. The proposed control law is easy to implement and is able to stabilize motion of each actuator while synchronizing all actuators’ motions, so that differential position errors amongst actuators converge to zero. It is shown that the proposed method guarantees global asymptotical stability of the closed-loop system. Experiments performed on a three-DOF parallel manipulator demonstrate the effectiveness of the proposed approach.

In this paper, an enhanced hybrid control algorithm is proposed to control the rotation of a flexible beam while suppressing the beam's vibration. The control law combines an enhanced PD feedback with nonlinear differentiator to derive high-quality velocity signal to control gross motion of the beam, and a vibration control by PZT actuators bonded on the surface of the beam. The significance of the proposed method are threefold: i) The enhanced PD control is a non-model based control, and appears to be more robust against the noise; ii) The linear velocity in contrast the angular velocity is used in the PZT actuator control, a signal which is easily available; iii) A unique solution is provided for examination of actuator placement, based on the analysis of mode shape functions. Experimental results validate these theoretical analyses.

The square kilometer array (SKA) is an ambitious world cooperation project to develop the next generation large radiotelescope. In Chinese engineering concept, the feed-supporting system is comprised of two parallel manipulators to realize the high precision tracking, which can be viewed as macro-micro manipulators. An independent tracking control strategy of the feed-supporting system is proposed, the dynamic coupling between the two comprising subsystems is considered as an external disturbance to the micro-system, and a high robust model reference learning controller (FMRLC) in joint space is designed to reject this coupling effect, along with any other disturbances, so that a higher tracking precision can be obtained. The effectiveness of this FMRLC is verified by numerical simulations, which has laid a solid base for the engineering accomplishment of high precision tracking for the SKA.

A new singularity analysis method for a general 6 degree-of-freedom (DOF) Stewart platform using genetic algorithm (GA) is proposed in the paper. The Jacobian matrix of the Stewart platform is first deduced, then the square of determinant of the Jacobian matrix is selected as the objective function, and the minimum of this objective function is searched in the workspace of the Stewart platform by a real-coded GA. The singularity of the Stewart platform depends on this minimum objective function, if this value is zero, the singularity of Stewart platform will happen, otherwise, the Stewart platform is singularity-free. The effectiveness of this new genetic singularity analysis method is validated by numerical simulation.