Classical Control Analysis - Bode Diagrams

Gives a number of tutorial questions on finding the frequency response for a number of alternative transfer functions for students to try. Also provides quick worked solutions.

Introduces possible definitions and interpretations of bandwidth and illustrates how this can be estimated from Bode gain plots. Also, illustrates links between open-loop bandwidth and the expected bandwidth of the same system when connected with unity negative feedback.

Builds on analysis of the bode diagram of a lead compensator and properties of Bode diagrams to show how compensation with a Lead affects the Bode diagram ofa system, that is compares the Bode diagrams of G(s) and G(s)M(s). Uses very simple observations and computations so that the compensated sketch can be done by inspection.

Gives a detailed analysis of the bode diagram of a lead-lag compensator and emphasises key attributes and thus differences with a lead compensator. Also illustrates that a good sketch can be produced using just a few elementary observations at key corner frequencies.

Considers transfer functions which include complex poles, that is under-damped modes, and investigates the associated Bode diagrams. Shows that under-damped modes can lead to peaks in the gain plot; these peaks are evidence of resonance, that is frequencies where the gain is disproportionately high.

Gives a detailed analysis of the bode diagram of a lead compensator and how this is affected by the pole/zero ratio. [Warning: includes a minor verbal typo on penultimate slide where geometric mean is described as sqrt(2) rather than sqrt(1.5). ]

Builds on the previous video by showing how some asymptotic information in the Bode plot can be obtained with minimal or no computation. This asymptotic information can be used as the basis for suprisingly accurate Bode diagram sketching for systems with multiple simple poles and zeros and requires minimal extra computations.

Demonstrates, through several examples, how simple asymptotic information and a few explicit computations can capture a fairly accurate bode diagram which thus is useful for insight into any subsequent design. Also demonstrates the use of MATLAB to form exact plots and shows how these compare to the hand drawn sketches.

Builds on analysis of the bode diagram of a lag compensator and properties of Bode diagrams to show how compensation with a Lag affects the Bode diagram of a system, that is compares the Bode diagrams of G(s) and G(s)M(s). Uses very simple observations and computations so that the compensated sketch can be done by inspection. [Warning: includes a minor typo on slide 6 - high frequency gain should be K]

Develops Bode diagrams for systems comprising mutliple simple poles, zeros and integrators from first principles. Demonstrates how rules of logarithms allow simple insights into the construction of Bode diagrams, but recognises that albeit conceptually simple, the method is cumbersome.

Gives a detailed analysis of the bode diagram of a lag compensator. Core information is the ratio of pole to zero. [Warning: includes a minor typo on slide 9 - high frequency gain should be K]

Develops Bode diagrams for simple poles, zeros and integrators from first principles. Introduces the concept of approximation and known values at key frequencies.

Tackles the weaknesses of simple graphical displays of frequency response information and thus introduces the definition of a Bode diagram which uses logarithmic scales. Discusses some key logarithmic values which help with Bode diagram interpretation.

Introduces the concept of frequency response and uses examples to demonstrate how the gain and phase of the output change as the frequency of the input is changed. Gives definitions for gain and phase in terms of frequency response.

Demonstrates how to solve for the frequency response parameters of a system from atransfer function model and hence shows that the gain and phase have simple analytic dependence upon the system parameters.

Students often make silly mistakes when computing the frequency response of systems with RHP factors. This video presents a simple approach for avoiding simple errors and getting the answer right first time.

Building on the definition for system gain and phase in terms of transfer function parameters, this video shows how using a factorised version of the transfer function enables the user to write down insightful expressions for gain and phase by inspection. Focus is on factors with LHP roots.

Introduces the plotting of frequency response information and illustrates the use of MATLAB to do so. Indicates the weaknesses of using linear graph scales for these plots.