Classical Control Analysis - Root Loci

Parts of the real axis are nearly always on the root-loci and it can be very insightful to mark these domains. This video shows how this is done by inspection and reinforces with numerical examples.

Presents a number of worked examples illustrating the use of the rules and why sketching is a useful skill. Uses MATLAB to check results and reinforce how MATLAB can be used to plot root-loci.

This video gives a number of tutorial questions for students to try. Students are asked to sketch root-loci using he 5 basic rules introduced in videos 5-8. Worked solutions are included.

Indicates how root-loci can be used to indicate achieveable performance and to select the desired value of gain. The focus here is on simple paper and pen computations and estimation and it is shown how relatively crude estimation, based on root-loci sketches can give values of compensator gain very close to the ideal answer. Similar concepts were covered, but using MATLAB tools, in videos 2-4.

Tutorial questions on using root-loci sketches for gain selection to achieve specified performance. The focus is on simple paper and pen computations and estimation. Worked solutions are also provided.

Indicates how root-loci can be used to analyse the impact of lag compensators on achievable closed-loop poles positions. When is a lag design useful and when is it not?

Indicates how root-loci can be used to analyse the impact of lead compensators on achievable closed-loop poles positions. Includes some unstable open-loop examples.

This video discusses how the rules change for positive feedback as opposed to negative feedback - differences are subtle but importnat. Also demonstrates, through examples, occasions where a system connected with negative feedback still needs the positive feedback root-loci rules in order to generate the correct root-loci sketch.

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 and corresponding closed-loop behaviours can be computed and compared efficiently for various choices of gain.

Tutorial to consolidate introductory concepts covered in videos 1-3. Without recourse to formal or detailed analysis, gives questions on gain selection to achieve specified closed-loop pole positions. Students use MATLAB tools and trial and error to determine the solutions. Demonstrations are given in real time on MATLAB.

For strictly proper systems, as gain increases some closed-loop poles will tend to very large values in specified asymptotic directions. This video shows why that is the case and also how the asymptotes can be computed/sketched using just a few lines of elementary algebra. Numerical examples illustrate the required computations.

Gives an overview of the foundations for rules that are used for forming root-loci sketches. Main emphasis is introducing the underpinning closed-loop algebra that is used.

Shows how the start and end points for root-loci can be determined using relatively trivial computations. Numerical examples illustrate the required computations.

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 examples to demonstrate how root-loci could be computed analytically for simple examples.

Demonstrates how MATLAB tools can be used quickly and easily to select a suitable compensator gain to meet specified criteria on the cclosed-loop pole positions, assuming no changes in the open-loop poles and zeros.