In another undergraduate class I teach here at UCSD students develop hands on control projects and many of them have not taken a class in controls. They have to quickly design and implement controllers often using really cheap and noisy sensors and slow processing times. In that context, a proportional controller, which might be the first choice in a search for a suitable controller, is rarely adequate. I will deal with the issue of noisy sensors and how they severely limit the closed-loop bandwidth in another post. In this one I want to address the issue of large delays.
Continue reading “Is a proportional controller right for you? Ask your control engineer! Part I”Author: MdO
Simulating linear systems with non-zero initial conditions
I have discussed in another post how to work with state-space models to simulate the response of linear systems using Matlab’s lsim. It is however also possible to approach this problem from a transfer-function point of view without having to mess with state-space at all.
Simulating linear systems with non-zero initial conditions in state space
Matlab’s lsim function for simulating linear systems will give you the option to provide an initial condition if your system is in state-space but not for transfer-functions.
Simulating linear systems with Matlab’s lsim
In this post we will go over a couple of ways to simulate linear systems in Matlab.
Continue reading “Simulating linear systems with Matlab’s lsim”Routh-Hurwitz stability criterion
I am often asked why I chose not to cover the Routh-Hurwitz stability criterion in the book. Here are some of the reasons.
- First is space. I would need to develop a lot of ideas to be able to do a decent presentation of the Routh-Hurwitz criterion. That takes space.
- Second is lack of connection with other ideas in the book. The algebraic polynomial machinery that is behind the criterion is somewhat disconnected from the other topics covered.
- Third is utilitarian. For system with numeric coefficients the use of the criterion has been virtually made obsolete by numeric calculators. Finding the roots of high order polynomials in the 21st century is not as hard as it used to be in 1876! For symbolic coefficients, the algebraic rational inequalities produced by the application of the criterion are only useful for relatively small problems. They do not scale very well or are as universal as the root-locus method or the Nyquist criterion. In the end one still has to solve a set of rational inequalities in the system’s coefficients to assess stability.
- Fourth is the Pandora’s box effect. If I cover Routh-Hurwtiz, why not the Liénard–Chipart criterion? Or the Hermite criterion? Those are even nicer than the Routh-Hurwitz one!
What do you think?
New slides
To disturb or not to disturb?
So here is a recurrent question. You have some model that has a constant showing up on the differential equation and you’re not sure how to handle it. For example, your model looks like:
$$\dot{y}(t)=ay(t)+bu(t)+c$$
where $c$ is a constant. There are multiple ways you can handle this situation.
Continue reading “To disturb or not to disturb?”Welcome
Welcome to the new website for the book
Fundamentals of Linear Control: A Concise Approach
I will be using this space to post information that complements the contents of the book. I will cover theory and practice, some Matlab examples, and occasional random thoughts, mostly motivated by class discussion. I hope you find this information useful.