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Introduction to Feedback Control Systems
Published in Ramin S. Esfandiari, Bei Lu, Modeling and Analysis of Dynamic Systems, 2018
As presented in Section 10.2, the time-domain specifications, such as rise time tr, overshoot Mp, peak time tp, and settling time ts, are related to the natural frequency ωn and the damping ratio ζ, both of which can be used to express the pole locations of a second-order system in the s-plane. Thus, the dynamic response of a system can be influenced by changing the system’s pole locations. Root locus, developed by W. R. Evans in the late 1940s, is a graphical design technique that shows how changes in one of the system parameters will modify roots of the closed-loop characteristic equation, or the closed-loop poles, and thus change the dynamic response of the system. In this section, we first introduce the procedure to sketch the root locus of a feedback control system. Then, we discuss ways to analyze the stability and performance of the closed-loop system based on the root locus. Finally, we learn how to design a proportional feedback controller using the root locus technique.
Control of the Pulp and Paper Making Process
Published in William S. Levine, Control System Applications, 2018
Figure 4.15 shows the root locus plot for the case of λ = 2Td = 6 minutes. The root locus plot shows the Pade’ pole/zero pair approximation for deadtime at ±2/3, the reset zero at –1/9, and two poles at the origin. The closed poles are located on a root locus segment which moves quickly into the right halfplane (RHP), and the poles have a damping coefficient of only 0.69. Even more aggressive tuning speeds up the controller zero and increases the loop gain. This causes the root locus segment to bend towards the RHP earlier and reduce the damping coefficient.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
The root locus is defined as the locus (trajectory) of the roots of the characteristic equation of a feedback control system. Note that the above procedure is given only to get the concept of the root locus and the root locus for any general feedback control system is not obtained directly by finding the roots of the C.E. and then plotting or sketching the same in the s-plane as shown above, but is done indirectly by developing some rules/steps for constructing or sketching the root locus as given next.
Design of Temperature Controller for Irradiation Experiment in Nuclear Reactor
Published in IETE Journal of Research, 2023
Suman Saurav, P. K. Chaurasia, S. Murugan
The root-locus method is used to show the movement of the roots of the characteristics equation. It will plot root locus for all values of the system parameter on the “S-plane”. The position of poles and zero of the open-loop system decides the behaviour of the closed-loop system. Here, we construct the root locus plot of the open-loop TCIIC process system (3) for all the positive values of (zero to infinite) (Figure 3). Here, the delay term () is converted according to 1st order Pade approximation [35]. The root-locus plot on “S-plane” of the open system (3) and step response ( = 1) of the closed-loop system of (3) is shown in Figure 4. The rise time (Tr) and the settling time (Ts) of (3) are 21.2 and 39.8 s, respectively.
Evaluation of nonlinear control performance of air handling units under variable operation conditions using root distribution approach
Published in Science and Technology for the Built Environment, 2022
Zufen Wang, Rodney Hurt, Choon Yik Tang, Li Song, Gang Wang
The root locus technique can be used to analyze the control system performance when a parameter of interest is varied, such as component gain, time constant, or controller gain. To do so, however, the characteristic equation of the closed-loop transfer function in Eq. (4) should first be converted into the form of Eq. (1), with the interested parameter to be varied. The root locus (i.e., paths of the closed-loop poles) can then be hand-sketched using a standard procedure (Nise 2019) or drawn using the rlocus command in MATLAB. The control system stability and transient response under variable can subsequently be evaluated by examining the root locus on the s-plane.
A 3D-space vector modulation-based sensorless speed control of a fault-tolerant PMSMs fed by 27-level inverter
Published in International Journal of Electronics, 2021
The implementation of the above vector control structure in hardware is illustrated in the flow chart given in Figure 8 This flow chart shows what is done in each PWM period starting from reading the analog to digital converters of the Digital Signal Processor (DSP) to obtain both the stator currents and the stator dynamic current responses and ending of the generating the PWM signals. The stability analysis of the IRFO control topology that is given in Figure 7 is examined using root locus as shown in Figure 9. The root locus of the closed-loop system shows that the system is stable as the poles of the closed-loop system exist in the left half of the root locus.