Classical control analysis - Gain and phase margins & lead/lag compensation

Develops the previous two videos by giving a number of worked examples showing how to achieve a desired phase margin just by changes in gain. Uses analytic methods, Bode diagrams and MATLAB tools.

Shows how MATLAB tools can be used quickly and efficiently to implement, and illustrate, the mechanistic design procedure for a lag compensator. Designs are based on a target phase margin and desired steady-state gain recovery. Further fine tuning would be needed in practice.

Reviews the impact of a lead compensator on the Bode diagram and hence shows how this affects the margins. This insight is used to develop good and bad practice in lead compensator design. The video finishes with a mechanistic rule base for lead compensator design - something that is useful for very rapid rough tuning (but not necessarily a final design).

Shows how MATLAB tools can be used quickly and efficiently to implement, and illustrate, the mechanistic design procedure for a lead compensator. Designs are based on a target gain cross over frequency and a target phase margin. Further fine tuning would be needed in practice. [Two obvious typos: (i) on 5min 30 (author writes square root of beta instead of just beta) and (ii) around 13min 30 (author uses a cross over frequency of 9.75 in lead design as opposed to 9.43)].

Reviews the impact of lead and lag compensators and hence presents an argument for compensators which include both these components. This insight is used to propose and illustrate a simple mechanistic design procedure for lead-lag compensators, assuming that the specification includes three objectives: (i) gain cross over frequency; (ii) phase margin and (iii) low frequency gain characteristics.

Shows how MATLAB tools can be used quickly and efficiently to implement, and illustrate, the mechanistic design procedure for a lead-lag compensator. Designs are based on a target gain cross over frequency and a target phase margin. Further fine tuning would be needed in practice.

Presents analysis which explains the basis for the use of a 60 degree phase margin as a good target. Illustrates the limitations of this assumption through numerous examples.

Presents a typical examination questions for students to attempt. Covers basic analysis tools of Nyquist, Bode and root-loci and analysis of potential lead/lag compensators. Also gives a worked solution. [Silly typo in construction of Bode gain plot - asymptote drawn to w=root(3) rather than w=3.]

Presents a typical examination questions for students to attempt. Covers basic analysis tools of Nyquist, Bode and root-loci and analysis of potential lead/lag compensators. Also gives a worked solution.

Shows how change in compensator gain has a non-simple affect on the phase margin, but by using the Bode diagram, the affect is obvious. Uses the phase margin definition to show how it is very simple to specify the required gain to achieved a desired phase margin. Examples demonstrate this both analytically and using Bode diagrams, the latter being more pragmatic for many systems.

Reviews the impact of a lag compensator on the Bode diagram and hence shows how this affects the margins. This insight is used to develop good and bad practice in lag compensator design. The video finishes with a mechanistic rule base for lag compensator design - something that is useful for very rapid rough tuning (but not necessarily a final design).

Shows how gain and phase margins can be deduced directly from the Bode diagram and indeed can be estimated by inspection. Links margins to closed-loop stability to give visual insight into what from of Bode diagram is 'good' and what form is usually 'bad'. Demonstrates MATLAB tools which compute and illustrate gain and phase margins.

Shows how change in compensator gain has a very simple affect on the gain margin. Presents simple formulae for this effect and several illustrations. Emphasises the use of Bode diagrams for margin computation and also shows how to achieve a specified gain margin with an elementary computation.

Illustration of how the position of the Nyquist diagam relative to the -1 point tends to be directly related to the closed-loop behaviour. Uses several examples to show that being close to -1 tends to result in poor behaviour and also indicates that some formal measure of distance from -1 could be useful.

Introduces a definition of the distance of the Nyquist plot from the -1 point, that is the gain margin. Gives examples and pictures to help students understand this visually and a number of numerical examples to emphasise the procedure for computing the gain margin.

Introduces a definition of the distance of the Nyquist plot from the -1 point, that is the phase margin. Gives examples and pictures to help students understand this visually and a number of numerical examples to emphasise the procedure for computing the phase margin.

Goes through a number of examples, to demonstrate the computation of gain and phase margins. Some examples are analytic and some make use of Bode diagrams. [WARNING: minor typo at about 11min 40 sec where a superscript is wrong side of a bracket - should be (4-5.642)=-31.8 ]