Vibration Control of a Two-Link Flexible Robot Arm with Time Delay through the Robust Receptance Method

This paper proposes a method for active vibration control to a two-link flexible robot arm in the presence of time delay, by means of robust pole placement. The issue is of practical and theoretical interest as time delay in vibration control can cause instability if not properly taken into account in the controller design. The controller design is performed through the receptance method to exactly assign a pair of pole and to achieve a given stability margin for ensuring robustness to uncertainty. The desired stability margin is achieved by solving an optimization problem based on the Nyquist stability criterion. The method is applied on a laboratory testbed that mimic a typical flexible robotic system employed for pick-and-place applications. The linearization assumption about an equilibrium configuration leads to the identification of the local receptances, holding for infinitesimal displacements about it, and hence applying the proposed control design technique. Nonlinear terms, due to the finite displacements, uncertainty, disturbances, and the coarse encoder quantization, are effectively handled by embedding the robustness requirement into the design. The experimental results, and the consistence with the numerical expectations, demonstrate the method effectiveness and ease of application.

Comparison of Star and String Offshore DC Collector Grid Topologies on the Aspect of Stability—An Impedance Approach

Offshore Direct Current (DC) collector grids are a promising technology for decreasing the installation and operation costs of offshore wind parks. Nevertheless, the stability properties and hence the design of such DC collector grids is not common or standardised. Hence, this paper describes an attempt to fill these gaps by analysing the stability of two different types of DC collector grids—star and string—by considering identical operating conditions. The approach follows a non-parametric formulation of the impedance based Nyquist Stability Criterion. The hyperbolic Π equivalent formulation of the telegraph equation is adopted for modelling the submarine cable due to high capacitance that is distributed and thus the conventional 50 Hz Π-model is not sufficient anymore. Furthermore, the paper shows how to integrate the complex dynamics of wind turbines into the overall stability assessment through an impedance building algorithm. Finally, it is shown how to stabilise the collector grids by means of active control parameter changes and it has been observed that the star configuration of wind turbines is more favourable on account of stability and controllability.

Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion

Stability of the rotor motion is the precondition for the reliable operation of magnetically levitated slice motors (MLSMs). However, with gyroscopic effect and non-collocated structure existing simultaneously, its stability analysis faces a tremendous challenge, because the torsional motions couple with the radial translational ones, making MLSM a multiple-input and multiple-output (MIMO) system with high order. Therefore, in this paper, we first establish a novel MIMO rotor dynamics closed-loop model and further convert it into an equivalent single-input and single-out (SISO) feedback control system by constructing complex variables, meanwhile reducing the system order by half. Beneficial from the equivalence between the MIMO and SISO systems, the sufficient and necessary conditions of the absolute stability of MLSM are derived by the extended inverse Nyquist stability criterion in the complex domain. Additionally, the effectiveness of the proposed modelling and stability analysis method is evaluated by simulation and experimental results. Thus, apart from PID parameters, this paper demonstrates that the stability of MLSM is also affected by the coupling of gyroscopic effect and non-collocated structure, which should serve as an essential guideline for system regulation of MLSM.

Stabilization of Unstable Second-Order Delay Plants under PID Control: A Nyquist Curve Analysis

Time delays arise in various components of control systems, including actuators, sensors, control algorithms, and communication links. If not properly taken into consideration, time delays will degrade the closed-loop performance and may even result in instability. This paper studies the stabilization problem of the second-order delay plants with two unstable real poles. Stabilization conditions under PD and PID control are derived using the Nyquist stability criterion. Algorithms for computing feasible PD and PID parameter regions are proposed. In some special cases, the maximal range of delay for stabilization under PD control is also given.

Stability of negative feedback

“Stability of negative feedback” discusses the measures that must be taken to guarantee that a negative-feedback system is stable. Examples are given of frequency dependences using Bode and Nyquist plots. Safety margins are quantified by means of gain margins and phase margins; the desirability of a minimum-phase-lag network. A design procedure is formulated. There is discussion of Nyquist (conditional) stability, and how it may be achieved by judicious introduction of a non-linearity. A demonstration circuit shows that these measures can yield Nyquist stability with safety.

Study of Dynamic Modes of Current Stabilization Systems of Powerful Electromagnets with Pulse-Width Modulation

This study is devoted to the consideration of a method for assessing the stability of systems with pulse-width modulation, based on the linearization of its equivalent system with pulse-width modulation. An approximate study of the dynamic modes of operation of systems with pulse-width modulation, taking into account the stability for the system of automatic control of the supply current of electromagnets under the conditions of external and internal interference, is carried out. Variants of execution of schemes of pulse-width regulators for the power supply of an electromagnet based on a unipolar and bipolar element with pulse-width modulation are presented. The possibility of linearization of systems with pulse-width modulation for the subsequent detailed assessment of the stability of such systems is shown. The prospects of using functional differential equations for stability analysis of automatic systems with pulse-width modulation are shown. The frequency characteristics of an equivalent pulse system are analyzed using the example of a current stabilization system of high-power electromagnets with a pulse-width regulator, taking into account the replacement of the latitude modulation by the amplitude one. Based on the analysis of the resulting transfer function, which is a stable linearized equivalent open system, the ways of evaluating the stability of the original system with pulse-width modulation using the Nyquist stability criterion are proposed. The conclusion is made about the advantage of a system with PWM, in relation to a system with AIM, in terms of stability, and recommendations are given for the use of the obtained data in the analysis oftransients in such systems.

Impedance Reshaping Control Strategy for Improving Resonance Suppression Performance of a Series-Compensated Grid-Connected System

In the series-compensated grid-connected system (SCGCS), there is an impedance interaction between the inverter impedance and the grid impedance that is prone to cause resonance in the SCGCS. In this paper, firstly, considering the effects of the phase-locked loop (PLL), current-loop, and frequency coupling, the broadband impedance model of the SCGCS is established. The stability of the SCGCS is analyzed by the impedance-based Nyquist stability criterion. It is found from the stability analysis that the impedance interaction between the inverter impedance and the grid impedance is the leading cause of the resonance. An impedance reshaping based resonance suppression method is proposed to suppress the resonance. The phase characteristics of the inverter equivalent output impedance are reshaped from the perspective of impedance. The phase margin at the intersection frequency of the inverter impedance and the grid impedance is improved. The proposed resonance suppression approach mainly consists of reshaping the current loop impedance and the novel phase-locked loop impedance. Finally, simulations and experiments are used to verify the feasibility of the resonance analysis and the effectiveness of the proposed control strategy.