Criteria for the Degree of Stability of the Linear Constant Systems

There are various applications of the stability theory of the first-order dynamical systems. And the stability of the non-linear control systems can be determined by its linear part. In practice, it is not enough to know the stability of the dynamical systems. Sometimes we must know the degree of stability of these systems. In this paper, we present some criteria for the degree of stability of the linear constant systems, by using the entries of the coefficient matrix A only.

A PID Tuning Approach for Inertial Systems Performance Optimization

In the practice of control the industrial processes, proportional-integral-derivative controller remains pivotal due to its simple structure and system performance-oriented tuning process. In this paper are presented two approaches for synthesis the proportional-integral-derivative controller to the models of objects with inertia, that offer the procedure of system performance optimization based on maximum stability degree criterion. The proposed algorithms of system performance optimization were elaborated for model of objects with inertia second and third order and offer simple analytical expressions for tuning the PID controller. Validation and verification are conducted through computer simulations using MATLAB, demonstrating successful performance optimization and showcasing the effectiveness PID controllers’ tuning. The proposed approaches contribute insights to the field of control, offering a pathway for optimizing the performance of second and third-order inertial systems through robust controller synthesis.

ROBUST STABILITY FOR A TYPE OF UNCERTAIN TIME-DELAY SYSTEMS

Some new results for stability of uncertain time-delay systems are derived and the stability degree is also discussed. Some previous results for stability and robust stability of time-delay systems are improved. Lastly, examples are included to illustrate our results.

A NUMERICAL METHOD ON ESTIMATION OF STABLE REGIONS OF ROTOR SYSTEMS SUPPORTED ON LUBRICATED BEARINGS

The stability degree of periodic solution of nonlinear nonautonomous system was defined by means of the Floquet theory. A method evaluating the stability degree of periodic solution based on transient response was presented by the aid of the concept of dynamic,systems or flows. The critical value of a system was determined by the condition, i.e., its stability degree equals zero. Stable regions of rotor systems with balanced and unbalanced disk supported on lubricated bearings were calculated. The study shows that stable region decreases with the increase of speed for a balanced rotor system and decreases with the increase of unbalance for an unbalanced rotor system. Stable regions of periodic solutions are less than that of equilibrium points under the same systematic conditions.

Augmented Virtual Stiffness Rendering of a Cable-driven SEA for Human-Robot Interaction

Human-robot interaction(HRI) is fundamental for human-centered robotics, and has been attracting intensive research for more than a decade. The series elastic actuator(SEA) provides inherent compliance, safety and further benefits for HRI, but the introduced elastic element also brings control difficulties. In this paper, we address the stiffness rendering problem for a cable-driven SEA system, to achieve either low stiffness for good transparency or high stiffness bigger than the physical spring constant, and to assess the rendering accuracy with quantified metrics. By taking a velocity-sourced model of the motor, a cascaded velocity-torque-impedance control structure is established. To achieve high fidelity torque control, the 2-DOF(degree of freedom) stabilizing control method together with a compensator has been used to handle the competing requirements on tracking performance, noise and disturbance rejection,and energy optimization in the cable-driven SEA system. The conventional passivity requirement for HRI usually leads to a conservative design of the impedance controller, and the rendered stiffness cannot go higher than the physical spring constant. By adding a phase-lead compensator into the impedance controller,the stiffness rendering capability was augmented with guaranteed relaxed passivity. Extensive simulations and experiments have been performed, and the virtual stiffness has been rendered in the extended range of 0.1 to 2.0 times of the physical spring constant with guaranteed relaxed passivity for physical humanrobot interaction below 5 Hz. Quantified metrics also verified good rendering accuracy.

Robust Stabilizing Regions of Fractional-order PI~λ Controllers for Fractional-order Systems with Time-delays

This study focuses on a graphical approach to determine the robust stabilizing regions of fractional-order PIλ（proportional integration） controllers for fractional-order systems with time-delays. By D-decomposition technique, the existence conditions and calculating method of the real root boundary（RRB） curves, complex root boundary（CRB） curves and infinite root boundary（IRB）lines are investigated for a given stability degree. The robust stabilizing regions in terms of the RRB curves, CRB curves and IRB lines are identified by the proposed criteria in this paper. Finally, two illustrative examples are given to verify the effectiveness of this graphical approach for different stability degrees.