Explore the vast range of titles available.

The root locus method is the classical method for analyzing the variation of the position of the poles of a closed-loop control system transfer function in the complex plane. It is also the basis for guiding the design of various controllers. Starting from the nature of the root locus, this paper takes a standard form of closed-loop feedback control system as an example, and analyzes in detail the internal logic of designing a controller and compensator by the root locus method. At the same time, software such as MATLAB/Simulink, and Octave are used. The working principles and properties of the PD controller; the lead and lag compensator, their interconnections, advantages, and characteristics, as well as the adjustment of parameters to better suit practical needs, are sorted out. The PD controller improves the system response, the lead compensator eliminates the PD controller’s defects, and the lag compensator reduces the steady-state error of the system. It provides help for understanding the essence of controller design and provides design ideas for control problems in actual engineering.

The doubly-fed induction generator (DFIG) based on the control strategy of constant parameter virtual synchronous generator (VSG) can cause problems of sharp frequency variations in the grid-connected system, long adjustment times, and large overshoot of the active power output from the DFIG. Aiming at dealing with the above-mentioned problems, a VSG control strategy with an independent flexible link (IFLVSG) is proposed in this paper without changing the parameters and structure of the VSG, so that the moment of inertia and damping coefficient can be flexibly adjusted according to the change of the system frequency, so as to improve the system frequency stability. To form a complete selection scheme for control parameters in IFL, the state space equation including IFLVSG control is established, and the advantages of exponential IFL are highlighted by using the sensitivity calculation method. At the same time, in order to improve the analysis efficiency, the main control parameters affecting the frequency stability of the system are selected according to the sensitivity value. Finally, the root locus analysis method is used to reveal the influence law of the main control parameters on the frequency stability of the system. The formed scheme provides a theoretical basis for the selection of control parameters.

An explicit unconditionally stable algorithm for hybrid tests, which is developed from the traditional HHT-α algorithm, is proposed. The unconditional stability is first proven by the spectral radius method for a linear system. If the value of α is selected within [-0.5, 0], then the algorithm is shown to be unconditionally stable. Next, the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system. The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening. To improve the stability of the proposed method, the structure stiffness is then identified and updated. Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.

This paper studies near-controllability of a class of discrete-time bilinear systems via a root locus approach. A necessary and sufficient criterion for the systems to be nearly controllable is given. In particular, by using the root locus approach, the control inputs which achieve the state transition for the nearly controllable systems can be computed. Furthermore, for the non-nearly-controllable systems, nearly controllable subspaces are derived and near-controllability index is defined. Accordingly, the controllability properties of such a class of discrete-time bilinear systems are fully characterized. Finally, examples are provided to demonstrate the results of the paper.

An Attitude control system plays the important role to maintain the satellite to desired attitude orientations. The intended application of NANO satellite in low earth orbits (LEO) helps find transient responses with and without controllers. LEO satellites typically orbit at an altitude ranging between160-2000 km. LEO satellites are widely used for remote sensing, navigation, and military surveillance applications. The Nano NPSAT-1 satellite attitude control systems (ACS) are described in this research work. The high pointing accuracy attitude estimation and feedback control systems are presented. The design specifications have been taken to meet the accuracy requirements (desired value ≤ 0.2 seconds) of Nano satellite attitude control. The feedback signal from on-board sensors compared with reference orbit trajectory and implementation of the Proportional Derivative (PD) controller is constructed. An algorithm of Nano satellite (NPSAT-1) attitude control is implemented using MATLAB Tools. In addition, the closed loop poles help find the gain of the system using Root Locus (RL) methods. The satellite control system is used to improve the transient response like overshoot and settling time of the system. Thus, the design of attitude control to improve the rise time, the settling time, the maximum overshoot, and no steady state error was carried out.

For a third-order complex polynomial with its roots bounded by a circle, Marden’s theorem provides a useful way to evaluate the locus of its critical points. We construct a fourth-order complex polynomial by restricting its roots to ellipse and hyperbola. The locus of its critical points can be expressed by a formula. In addition, if the roots of complex polynomials are not restricted, their critical points will not occupy some regions.

As an alternative to power system stabilizer, this paper presents a robust controller known as extended state observer (ESO) for synchronous machine connected to an infinite bus (SMIB) power system. The ESO-based control scheme is implemented with an automatic voltage regulator in order to enhance the damping of low frequency power system oscillations so that the deviations in terminal voltage are compensated. The proposed ESO provides the estimates of system state as well as disturbance state together in order to improve the damping as well as compensate system efficiently in presence of parameter uncertainties and external disturbances. The closed-loop poles (CLPs) of the system have been assigned by the symmetrical root locus technique, with the desired level of system damping provided by the dominant CLPs. The performance of the system is analysed through simulating at different operating conditions. The control method is not only capable of providing zero estimation error in steady-state, but also shows robustness in tracking the reference command under parametric variations and external disturbances. Illustrative examples have been provided to demonstrate the effectiveness of the developed methodology.

Context: This work shows a novel navigation approach based on images for an assistant hybrid robot composed by a humanoid and an omnidirectional platform. Method: This approach introduces a complex space analysis, using Zeros and Poles attraction-repulsion principle. In order to perform the algorithm, an integrated system is developed; this system includes: an external camera to take a global navigation surface view, the assistant robot, and communication devices. Navigation is supported by some digital image processing algorithms and performed using the root location technique. Results: An integrated system of global navigation with external sensors was successfully implemented for the proposed hybrid robot. Conclusions: Some simulation and experimental tests will be discussed in order to validate this proposal and the whole system. Additionally, some suggestions for future research are proposed.

Rotating machinery with high speed powered by industrial motors frequently suffers from instability by exhibiting non-linear jump phenomena, formally known as Sommerfeld effect. The drives whose excitation is a function of the system responses, referred to as non-ideal. The system dynamics of such systems exhibit a couple of complex and interesting features when the input power exceeds a critical value. The present research suggests a novel approach to study the efficacy of active magnetic bearing with fractional PD controller to suppress the instability caused by the Sommerfeld effect. The steady-state results obtained by solving the system characteristic equation numerically is compared with the transient analysis. Finally, root locus method is introduced to obtain the bifurcation points at which this kind of instability completely disappears.

The hunting phenomenon is an intrinsic swaying motion appearing in railway vehicles due to the vehicle’s forward speed and the wheel–rail contact forces. Hunting motion consists of wheelset and other vehicle’s components oscillations that arise above a certain vehicle’s speed known as critical or hunting speed. These oscillations are of unstable nature and represent a safety hazard as they could lead to the vehicle’s derailment. This article analyses the stability of a bogie nonlinear model for a Spanish high-speed train when this is travelling at speeds near the hunting speed. The vehicle’s stability is studied by means of root loci methods, and the value of the critical speed is found. In addition to this, the behaviour of the vehicle is studied in both stable and unstable regions and the existence of limit cycles is discussed in this work. Finally, a sensitivity analysis of the axle load and suspension parameters is performed. The results show that the axle load, the vertical stiffness of the primary suspension and the lateral damping of the secondary suspension have a significant influence on the value of the critical speed.