Root Locus Approach Research Articles

A Generic Robust Model-Based Estimator for Active Damping of Single-Phase GridTied Inverters

This paper presents the design and analysis of a signal estimator with improved robustness applied in the active damping (AD) of a single-phase grid-tied inverter with LCL low-pass filter. The proposed estimator is based on the mathematical model of the LCL filter, with resistors in series with the converter-side inductor and capacitor for improving robustness. The implementation method is also capable of estimate multiple filter signals. The control strategy presented uses a virtual resistor based AD, that suppresses the resonance ensuring stability and robustness, helping comply with power quality standards, such as IEEE 1547 and IEC 61727. The signal necessary for achieving the AD is obtained through the estimator, dismissing the use of additional sensors. The current control structure uses grid-side current feedback with proportional-resonant controller and harmonic compensation. The system is designed by the root locus approach to achieve stability despite grid parameter variance. The estimator and overall system is analyzed through mathematical modeling, computational simulation and experimental setup. The results show that the estimator presented is capable of providing the necessary AD feedback signal, even with grid inductance variation.

Root locus approach in design of PID controller for cruise control application

The Proportional Integral Derivative (PID) controller is an effective and common feedback control design used in closed loop control systems. One such best consideration of closed loop control system would be cruise control system. This is a system that automatically controls the speed of an electric vehicle despite external disturbances. In this paper, the goal is to design a PID controller using root locus technique for a closed loop cruise control system. By root locus approach, the controller constants and controller design is finalized. Simulation results through MATLAB environment validate the effectiveness of controller design.

Feedback Control Design for VCM

A design of PD feedback control law for a class of the second order system to satisfy the desired performance requirements is presented. It is achieved by using root-locus approach. The desired specifications of the step-input system response are first transformed into a required region for the poles of the PD control closed-loop system. Ranges of the corresponding PD control gains are then derived to guarantee the poles of the closed-loop system lie within the targeted region. Besides, the proposed control law is also applied to the feedback control of Voice Coil Motor (VCM) to support the function of the so-called “Optical Image Stabilization (OIS).” Numerical results by using a referenced VCM model have demonstrated the success of the proposed design.

Desain Kompensator Motor Servo Dc 734 Pada Laboratorium Dasar Sistem Kendali

Compensation is the arrangement of a system in order to meet the desired specifications. The approach used in designing the compensator for the DC servo motor control system 734 series in the Basic Control System Laboratory is the root locus approach. In designing an electronic compensator, the physical realization or implementation should be done carefully so that an electronic circuit is produced that can represent the desired specifications. Lead compensator will generally speed up system response and increase system stability; while the lag compensator will increase the steady-state accuracy of the system, but tends to slow down the response of the system. If you want to develop a control system that has good specifications for both transient response and steady-state response, the combination of these two compensator principles is a pretty good choice.

Design performance of lead and lag compensator using OPAMP and root locus approach through simulation tool

The design objective behind lead and lag compensator is to meet the relative stability as well as to meet desired performance. Both in time domain or frequency domain, the compensator design can be carried out. Absolute stability of a system can be predicted from root locus approach. Simulation tool like tinkercad and wolfram alpha can provide easy access of different control engineering design performance, so that it helps all under graduate, post graduate and researchers can able to apply their knowledge to engineering application from any computing environment. And they can perform it at any time. By this passive learning is also possible with active engagement in the learning related to practical and theory. To judgment and easily understand on simulation, student can modify their design specification and get deeper knowledge on control system design engineering. one can also use opamp circuit to understand the compensator design performance.

Modular approach for control design of an autonomous two-wheeled inverted pendulum

Modular design of systems is an important tool to subdivide complex problems into smaller parts (sub-systems) that are easier to analyze and design. The scope of this paper is to present a methodology for modularizing the design of a mechatronic system through the adequate decoupling of its main subcomponents. The proposed approach is applied in the design of an automatically guided two-wheeled inverted pendulum that works by following a specified acceleration/velocity profile in a longitudinal trajectory. With this purpose, the approach considers the relations among the different parts of the platform belonging to multiple physical domains such as the mechanical platform and wheels, DC motors, power system drivers, gearboxes and controllers. The control design was derived carefully based on a linearized model using a cascade architecture by appropriately choosing the main variables and the control loop structures. Each compensator transfer function was then designed using Root Locus approach. The complete designed system was simulated such that its response to a previously established sequence of position input commands could be verified. The final simulation behavior of the platform succeeded to reach the proposed maximum speed of 20km/h in less than 30s while following the position trajectory. Results showed that the method is applicable as a tool to facilitate independent design by decoupling the influence of a subpart on another, which also ensures reconfigurability and variety in the design of mechatronic products.

Design and Simulation of a PID Controller for Motion Control Systems

Motion control system plays important role in many industrial applications among which are in robot system, missile launching, positioning systems etc. However, the performance requirement for these applications in terms of high accuracy, high speed, insignificant or no overshoot and robustness have generated continuous challenges in the field of motion control system design and implementation. To compensate this challenge, a PID controller was design using mathematical model of a DC motor based on classical root-locus approach. The reason for adopting root locus design is to remodel the closed-loop response by putting the closed-loop poles of the system at desired points. Adding poles and zeros to the initial open-loop transfer function through the controller provide a way to transform the root locus in order to place the closed-loop poles at the required points. This process can also be used for discrete-time models. The Advantages of root locus over other methods is that, it gives the better way of pinpointing the parameters and can easily predict the fulfilment of the whole system. The controller performance was simulated using MATLAB code and a reasonable degree of accuracy was obtained. Implementation of the proposed model was conducted using-Simulink and the result obtained shows that the PID controller met the transient performance specifications with both settling time and overshoot less than 0.1s and 5% respectively. In terms of steady state error, the PID controller gave good response for both step input and ramp.

Diseño de Herramientas Didácticas Enfocadas al Aprendizaje de Sistemas de Control Utilizando Instrumentación Virtual

This paper describes the design of three didactic tools focused on learning of control systems implemented in LabVIEW virtual instruments software. These tools are dedicated to stability analysis in control systems, compensator design using root locus approach and Bode diagrams in the frequency domain. Each of them has a friendly interface with the user. The advantage of these didactic tools is the several options to simulate some characteristics referent to control in contrast with others teaching tools.

Towards Robust Non-Fragile Control in Wind Energy Engineering

<p>Blade Pitch Controller (BPC) that can cope system uncertainties is one of the most interesting topics in wind energy engineering. Therefore, this paper presents a step towards the design of robust non-fragile BPC for wind energy conversion system. The proposed approach presents all boundaries of stability region that can guarantee robust stability (RS) over a wide range of operating conditions. The proposed technique results from the complementarity of both Root-Locus and Routh-Hurwitz (RL/RH) approach. Continuous variation in the operating conditions is tackled through a new hybrid control technique based on the referential integrity of both RL/RH and Kharitonov (Kh) theorem. Simulation results confirm the effectiveness of the proposed designing approach in computing the most resilient and robust controller.</p>

Realizing the dynamics of a non-Markovian quantum system by Markovian coupled oscillators: a Green’s function-based root locus approach

In this paper, we develop a Green's function-based root locus approach to realizing a Lorentzian-noise-disturbed non-Markovian quantum system by Markovian coupled oscillators in an extended Hilbert space. By using a Green's function-based root locus method, we design an ancillary oscillator for Markovian coupled oscillators to be a Lorentzian noise generator. Thus a principal oscillator coupled to the ancillary oscillator via a direct interaction can capture the dynamics of a Lorentzian-noise-disturbed non-Markovian quantum system. By matching the root locus in the frequency domain, conditions for the realization are obtained and a critical transition in the non-Markovian quantum system can also be observed in the Markovian coupled oscillators.

IJIREEICE - Electrical, Electronics, Instrumentation and Control

Magnetic Levitation System (MLS) is an example of a non-linear and inherently unstable system. To overcome this instability an electromagnet will have to be constructed. The current in the electromagnetic coil is to be varied suitably using a compensator to generate varying magnetic field and hence a varying force to be exerted on any object in its vicinity. Two approaches were followed to design compensator. Firstly Root locus approach where in the pole in unstable region is moved to stable region. Another approach is Inward approach where in the poles are placed at desired location & co-efficient of compensator are obtained.

On Near-Controllability, Nearly Controllable Subspaces, and Near-Controllability Index of a Class of Discrete-Time Bilinear Systems: A Root Locus Approach

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 class of discrete-time bilinear systems are fully characterized. Finally, examples are provided to demonstrate the results of the paper.

A root locus approach to near-controllability of a class of discrete-time bilinear systems with applications to Hermitian matrices

In this paper, a root locus approach is developed to investigate near-controllability of a class of discrete-time bilinear systems and new representations of Hermitian matrices are derived. The root locus approach has three merits: firstly, it makes the proof of near-controllability of the systems more simple; secondly, the control inputs that achieve the state transition can be computed in an explicit way and, meanwhile, the number of the required control inputs can be fixed; and thirdly, it leads to a more general conclusion on near-controllability. A numerical example is given to demonstrate the effectiveness of the root locus approach. Finally, the more general conclusion yields new representations of Hermitian matrices.

A Study of RootLocus with Application to the Design of PD Controller for Linear Control Systems

In this paper, the break-away and break-in (BABI) condition used in root-locus approach for two-parameter linear control systemsis derived. The condition for one-parameter control system can also be obtained from those results, which agrees with the well-known results by using sensitivity function (e.g., Kuo, 2009). Based on those conditions, an algorithm is proposed to construct the PD control gains of linear control systems for meeting designed specifications of timing response. Compared with the conventional design by using root-contours, the proposed approach can give a guideline for choosing control gains instead of those obtained by trial-and-error from the root-contours scheme. An example of the 3rd-order linear systemwith PD control is also given to demonstrate the feasibility of the proposed design.

Design of a Discrete-Time Linear Control Strategy for a Multicell UPQC

A discrete-time linear control strategy for a multilevel three-phase unified power quality conditioner (UPQC) based on single-phase power cells is presented. The multi-variable, nonlinear, and coupled features of these topologies make the control strategy design a difficult task. Controlling this kind of system with single-variable linear controllers-as proposed in this work-presents significant advantages compared with other approaches as simplicity in the design steps due to the large amount of tools developed for this kind of schemes. Particularly, a classic design method based on the root locus approach is used to choose the controllers parameters in order to achieve a given dynamical behavior. Compensation of reactive power and fundamental frequency disturbances is presented in this paper as part of a general control strategy for multilevel active power filters. The proposed control strategy is implemented on the TMS320C6713 DSP-based system for a low-power laboratory prototype, and thus the controllers design is carried out on the discrete-time and -frequency domain. Also, due to the inherent asymmetries among the power cells in a modular topology, a dedicated local control strategy is proposed to ensure a symmetrical distribution of the power among the power cells. This feature allows the semiconductor devices of each module to operate under the same voltage and current ratings. Simulated and experimental results showing stationary and transient conditions demonstrate the feasibility of the control scheme.

Stability Analysis of Direct Integration Algorithms Applied to MDOF Nonlinear Structural Dynamics

Direct integration algorithms are typically used to solve temporally discretized equations of motion to evaluate the performance of structures under dynamic loading. The stability of these direct integration algorithms are usually investigated for linear elastic structures. However integration algorithms are often applied to structures with nonlinear behavior. This paper presents a procedure based on discrete control theory to investigate the stability of direct integration algorithms applied to multidegree-of-freedom (MDOF) nonlinear structures. The discrete root locus approach is used to investigate properties of the poles of the discrete transfer function matrix representing the nonlinear structural dynamics and to assess the stability of the integration algorithm. The procedure is illustrated using a nonlinear shear building MDOF system to investigate the stability of popular direct integration algorithms, including the Newmark family of integration algorithms, the Hilber-Hughes-Taylor α -method, and ...

On Kharitonov-type theorems for real polynomials: When is degree drop admissible?

A root-locus approach is adopted to show that extension of Kharitonov-type theorem for real interval polynomial with degree drop is not only applicable to the open left-half plane, but also other regions such as the left-shifted open left-half plane and the left sector.

Investigation ofthe Control System Behavior in Conditions of Its Parameters Variation within the Infinite Intervals

Investigation of the dynamic system described by the characteristic equation of the 3rd power in conditions of its parameters variation within the infinite intervals of values has been carried out. The root locus approach was applied for this purpose. A method has been worked out for finding values of the system characteristic equation co-efficients intervals ensuring its stable state for the cases when the initial system was found to be unstable. The corresponding root locus condition of the system stability has been formulated.

HIGH LEVEL PATH COORDINATION FOR MULTIPLE VEHICLES AND RECIPROCAL ROOT LOCUS

This paper presents a method based on the reciprocal root locus (RRL) approach for solving the multiple vehicle path coordination problem. A high level planning assigns the tasks to each vehicle, specifying each mission, inside a structured workspace with known obstacles. The problem is solved in two steps: first the given workspace is mapped onto a semicircle, using the theory of conformal mappings, then the RRL method is applied. Examples involving multiple vehicles illustrate the proposed technique and its effectiveness.

Robust pole placement versus root-locus approach in the context of damping interarea oscillations in power systems

The merits of a robust low-order pole-placement method of damping-control design over a conventional root-locus method are discussed: both being aimed at providing adequate damping against interarea oscillations. The design is based on a weighted and normalised eigenvalue-distance-minimisation method (WNEDM) to obtain damping controllers employing superconducting magnetic-energy-storage (SMES) devices in a study system. The WNEDM-based control guarantees adequate damping in the prefault and postfault cases. The damping performance of the controllers is compared with that obtained by the root-locus technique. The results show that the WNEDM-based control is preferred over root-locus-based control when the control efforts in each the same.