Computer Aided Design of Lead compensator using Root Locus Method (original) (raw)

A Review note on Compensator Design for Control Education and Engineering

2014

The compensators are one of the most important aspects in any undergraduate control engineering courses owing to their widespread industrial applications. The degree of convergence of the output waveform for any compensator depends upon proper selection and tuning of the compensator. In this paper the compensator parameters (α, β, τ) of the lead, lag and lag-lead compensators are tuned to their optimum values using the conventional root locus as well as frequency response approach. The compensator algorithm is studied using MATLAB and usefulness of these compensators for controlling process variables are demonstrated using proper tuning. The comparative studies showing promising results are discussed with suitable examples.

Design and Analysis of a Control System Using Root Locus and Frequency Response Methods

Control systems play a very important role in the domain of Electrical Engineering. Without them, it is impossible to comprehensively analyze and design electrical systems. This paper successfully attempts to model a practical real control system using root locus (time domain) and frequency response (Bode Plots) techniques. A brief review of root locus and Bode plots is given. Major focus has been placed on controller design and how the required goal criteria can be achieved. MATLAB has been used exclusively for simulation and design purpose.

Analysis of Correction in Automatic Control Systems with Root Locus

Deleted Journal, 2018

The article addresses the major challenges of automated control systems and solutions. One way is to choose the appropriate correction for the system and analyze parameters. For the synthesis of corrective device parameters, the article uses the root locus method.Root locus can be constructed by changing one or more parameter, which allows a thorough analysis of the stability of the system.In article one of the types the integrating corrective scheme with r, L, C source of an input signal is considered. The problem of synthesis of parameters of an integrated corrective scheme with root locus is is solved; The root locus is constructed, and with their help, the possibility of the approach of roots of the characteristic equation, to roots of the ideal transfer function is considered.

NEW SIMPLE ALGEBRAIC ROOT LOCUS METHOD FOR DESIGN OF FEEDBACK CONTROL SYSTEMS

consists of two decompositions. The first one, decomposition of the characteristic equation into two lower order equations, was performed in order to simplify the analysis and design of closed loop systems. The second is the decomposition of Laplace variable, s, into two variables, damping coefficient, ζ, and natural frequency,ω n . Those two decompositions reduce the design of any order feedback systems to setting of two complex dominant poles in the desired position. In the paper, we derived explicit equations for six cases: first, second and third order system with P and PI. We got the analytical solutions for the case of fourth and fifth order characteristic equations with the P and PI controller; one may obtain a complete analytical solution of controller gain as a function of the desired damping coefficient. The complete derivation is given for the third order equation with P and PI controller. We can extend the number of specified poles to the highest order of the characteristic equation working in a similar way, so we can specify the position of each pole. The concept is similar to the root locus but root locus is implicit, which makes it more complicated and this is simpler explicit root locus. Standard procedures, root locus and Bode diagrams or Nichol Charts, are neither algebraic nor explicit. We basically change controller parameters and observe the change of some function until we get the desired specifications. The derived method has three important advantage over the standard procedures. It is general, algebraic and explicit. Those are the best poles design results possible; it is not possible to get better controller design results.

Tuning of a Lag-Lead Compensator Used with a First Order Plus an Integrator Process

TJPRC, 2013

Lag-lead compensators are well known in automatic control engineering. They have 4 parameters to be adjusted (tuned) for proper operation. The frequency response of the control system or the root locus plot are traditionally used to tune the compensator in a lengthy procedure. A first order with an integrator process in a unity feedback loop of 67.3 % maximum overshoot and 12 seconds settling time is controlled using a lag-lead compensator (through simulation). The lag-lead compensator is tuned by minimizing the sum of absolute error of the control system using MATLAB. Four functional constrains are used to control the performance of the lag-lead compensated control system. The result was reducing the process oscillation to 2.438 % overshoot and an 0.648 seconds settling time. The performance of the lag-lead compensated system with the present tuning approach is compared with the classical tuning using the root locus technique. The comparison showed that the present tuning technique is superior.

Analytical and graphical design of lead–lag compensators

International Journal of Control, 2011

In this paper an approach based on inversion formulae is used for the design of lead-lag compensators which satisfy frequency domain specifications on phase margin, gain margin and phase (or gain) crossover frequency. An analytical and graphical procedure for the compensator design on the Nyquist and Nichols planes is presented with some numerical examples.

Design of lead-lag compensators for robust control

2011 9th IEEE International Conference on Control and Automation (ICCA), 2011

In this paper three different methods for the synthesis of lead-lag compensators that meet design specifications on the phase margin and the gain crossover frequency are presented. These numerical and graphical methods are based on the choice of a degree of freedom of the regulators. These procedures aim to satisfy an additional specification for robust control: the gain margin, the complementary modulus margin or a specification on the settling time of the controlled system.

Lead and lag compensators with complex poles and zeros design formulas for modeling and loop shaping

IEEE Control Systems Magazine, 2007

I n classical loop shaping, compensator structures are typically cascaded to modify the gain and phase characteristics of the open-loop frequency response. These alterations are used to achieve closed-loop performance specifications for disturbance rejection, reference following, noise rejection, and gain and phase margins. Lead and lag compensators are standard tools employed in the loop-shaping process.

Software for Comparative Studies of Phase Lead Compensator Design

IFAC Proceedings Volumes, 1997

The paper describes a new software package developed for designing phase lead / lag controllers for a given system. The package has been developed in the MAT-LAB environment with a powerful graphical user interface. It incorporates several phase lead / lag controller design methods based on the frequency domain technique some of which require a computational approach for a system of any complexity. Considerable education benefit can be obtained from studying the different design approaches which can be compared using loop frequency and closed loop step response plots. Two examples are given to demonstrate this.

Design of an Appropriate Lead Compensator for a Servomotor

2016

The present paper aims to designing the best controller of the servo motor. Servo motors feature a motion profile, which is a set of instructions programmed into the controller that defines the servo motor operation in terms of time, position, and velocity based on compensator modern control system. The control method is used to determine the gains of the controllers to apply the lead compensator The transfer equation of control system with required controller gains is established. The transfer functions for the servo motor system is obtained based on automatic control principles. The lead compensator for open loop is drawn and then gain margin values is .Finally the step responses of the closed loop system with servo motor system controller were drawn. The simulation results have proven the effectiveness of adding a lead compensator to a servomotor system on the overall gain margin value which is settable for the system under control.