digplanet beta 1: Athena
Share digplanet:


Applied sciences






















Closed-loop poles are the positions of the poles (or eigenvalues) of a closed-loop transfer function in the s-plane. The open-loop transfer function is equal to the product of all transfer function blocks in the forward path in the block diagram. The closed-loop transfer function is obtained by dividing the open-loop transfer function by the sum of one (1) and the product of all transfer function blocks throughout the feedback loop. The closed-loop transfer function may also be obtained by algebraic or block diagram manipulation. Once the closed-loop transfer function is obtained for the system, the closed-loop poles are obtained by solving the characteristic equation.[disambiguation needed] The characteristic equation is nothing more than setting the denominator of the closed-loop transfer function to zero (0).

In control theory there are two main methods of analyzing feedback systems: the transfer function (or frequency domain) method and the state space method. When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function(the poles) or zero (the zeroes). Two different transfer functions are of interest to the designer. If the feedback loops in the system are opened (that is prevented from operating) one speaks of the open-loop transfer function, while if the feedback loops are operating normally one speaks of the closed-loop transfer function. For more on the relationship between the two see root-locus.

Closed-loop poles in control theory[edit]

The response of a linear and time invariant system to any input can be derived from its impulse response and step response. The eigenvalues of the system determine completely the natural response (unforced response). In control theory, the response to any input is a combination of a transient response and steady-state response. Therefore, a crucial design parameter is the location of the eigenvalues, or closed-loop poles.

In root-locus design, the gain, K, is usually parameterized. Each point on the locus satisfies the angle condition and magnitude condition and corresponds to a different value of K. For negative feedback systems, the closed-loop poles move along the root-locus from the open-loop poles to the open-loop zeroes as the gain is increased. For this reason, the root-locus is often used for design of proportional control, i.e. those for which \textbf{G}_c = K.

Finding closed-loop poles[edit]

Consider a simple feedback system with controller \textbf{G}_c = K, plant \textbf{G}(s) and transfer function \textbf{H}(s) in the feedback path. Note that a unity feedback system has \textbf{H}(s)=1 and the block is omitted. For this system, the open-loop transfer function is the product of the blocks in the forward path, \textbf{G}_c\textbf{G} = K\textbf{G}. The product of the blocks around the entire closed loop is \textbf{G}_c\textbf{G}\textbf{H} = K\textbf{G}\textbf{H}. Therefore, the closed-loop transfer function is


The closed-loop poles, or eigenvalues, are obtained by solving the characteristic equation {1+K\textbf{G}\textbf{H}}=0. In general, the solution will be n complex numbers where n is the order of the characteristic polynomial.

The preceding is valid for single input single output systems (SISO). An extension is possible for multiple input multiple output systems, that is for systems where \textbf{G}(s) and \textbf{K}(s) are matrices whose elements are made of transfer functions. In this case the poles are the solution of equation:


Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Closed-loop_pole — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
23849 videos foundNext > 

Lec-35 Closed-Loop Poles

Lecture Series on Control Engineering by Prof. S.D. Agashe, Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in.

Use of Matlab 10 - trial and error design for closed-loop poles

It can be useful for students to explore how changes in compensator affect closed-loop behaviour. This video illustrates how one can develop short code snippets that allow efficient iteration...

Root-loci 2 - The impact of changing compensator gain on closed-loop poles and behaviour

Builds on the concept of root-loci introduced in video 1, that is a picture showing how closed-loop pole positions vary as compensator gain is varied. Uses MATLAB to show how the pole positions...

Closed Loop Poles-Control Theory

Closed Loop Poles-Control Theory.

Nyquist Stability for two poles at origin and simple pole

Nyquist stability criterion is used to see if a closed loop systems with open loop gain G(s)H(s)=100/(s^2)(1+2s) is stable or not.

3.8 State Feedback | Control of Mobile Robots

3.8 State Feedback | Control of Mobile Robots state feedback (FSF), or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-deter...

Picking a pole/zero pair

How to pick pole/zero pair to place the closed loop poles at a specific point in the s-plane.

Root-loci 1 - What is a root-loci?

Introduces the concept of root-loci, that is a picture showing how closed-loop pole positions vary as compensator gain is varied assuming no changes in the loop poles and zeros. Uses numerical...

Low cost closed loop anti sway solution

Transforming a standard crane to a dynamic controlled system to reduce sway of a payload. The control is build using low budget components, for example a S7-1200 entry level PLC and low cost...

Generalised predictive control 2.4 - loop analysis and MATLAB

Demonstrates how the closed-loop control law parameters and associated pole polynomial can be computed for the SISO and MIMO cases. Illustrates simple (easy to edit) MATLAB code available for...

23849 videos foundNext > 

1 news items

PACE Today

PACE Today
Mon, 17 Nov 2014 19:00:00 -0800

Robust Control Toolbox provides a comprehensive set of tuning goals, including reference tracking, disturbance rejection, loop shaping, gain and phase margins, and closed-loop pole locations. For this example we use the following requirements:.

Oops, we seem to be having trouble contacting Twitter

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!

Searchlight Group

Digplanet also receives support from Searchlight Group. Visit Searchlight