Here is a presentation by one of industry's experts on the subject of autopilots - both the slides and associated audio-feed are in this folder (it is best to watch and listen concurrently):
https://www.dropbox.com/sh/6ru1dtrp2...1dHS_MPSrPJlra
The presentation starts with basic principles that most contributing to this thread will know but still, the distinctions between 3-axis, four-axis-analogue and four-axis-digital will be interesting for a number of contributors who have not yet been exposed to the latest incarnations. Where the presentation becomes more interesting is when discussing the reduction of complexity by integration and simplifying HMIs. It concludes with a view of what more should be done - not just in autopilot design and control laws, but holistically within the system (design, procedures, training, provision of information etc.).
One of the most interesting elements of the latest discussion here, is the point where redundancy and 'fail operative architecture' lead to a situation where elements becomes just a box in the 'conceptual model' and 'apparent' complexity reduces almost to zero. When that point is reached, we have moved from technology-led-design to human-centric-design. Perhaps the issue is that we are not yet at that point, are approaching the average pilot's knowledge saturation level and are having to discuss compensatory measures in the form of knowledge, training and procedures.
Jim