May 2019 – Fundamentals of Linear Control: A Concise Approach

Step-by-step Bode plot example. Part II

In a previous post we have gone step-by-step over how to sketch straight-line approximations for the magnitude diagram of the Bode plot for a simple rational transfer-function. In this post we cover the sketch of the phase diagram. See Section 7.1 for details on the approximations.

Step-by-step Bode plot example. Part I

In this post we will go over the process of sketching the straight-line Bode plot approximations for a simple rational transfer-function in a step-by-step fashion. See Section 7.1 for details on the approximations. We will start with the magnitude plot and cover the phase plot in a future post.

Aliasing and the brain

I am a long-time subscriber of Wired magazine, which I obviously think is a fine publication otherwise I would no longer be a subscriber, but every now and then there will be some “sciency” article that is misleading. The latest one is here.

Asymptotic tracking a constant reference without a pole at zero?

On a previous post we have discussed how by invoking stability one can solve problems without having to worry about particular inputs. The contrast between a solution that holds for a particular input versus a solution that holds for a class of inputs is highlighted in the present post by revisiting the problem of asymptotic tracking for a simple example.

Balance scales and integral action. Part II

In a previous post we discussed how the principles of operation of a balance scale could be understood as a feedback loop with integral action. We left off after analyzing the impact of measurement disturbances in the loop and mentioned that input disturbances could be used to model “operator errors.”

Balance scales and integral action. Part I

You can find many accounts of the history of feedback control in books, articles, and online. Some will go back to Greek and Arab antiquity to identify proportional feedback in water clocks, wind mills, advancing to the industrial revolution and the Watt governor. In virtually all of those accounts the feedback loop involves continuous-time signals. So I find it interesting that there is device that man has been using for millennia that requires a discrete-time feedback algorithm and integral action for its operation. That device is a balance scale.

Let your inputs go!

As one learns more about feedback and control systems, at some point, comes an important realization that a variety of distinct problems can be answered if we know how to answer the question: “is some closed-loop system asymptotically stable?” Indeed, the study of stability dominates Chapters 6 and 7, arguably the densest chapters in the book. Many students, when asked what they remember from their undergraduate control class, will quickly point at the root-locus or at the Nyquist stability criterion. Yet, in the beginning, it might seem that stability is a side dish and not the main attraction.

Controllers gone unstable

In order to obtain asymptotic tracking, we need $S(0)=0$, which means we’d need one of the poles of $G K$ to be zero. If $G$ has no poles at zero, then $K$ must be the transfer-function to have the pole at zero. But in order to be asymptotically stable, we need the real parts of the poles to be less than zero, correct? So does it matter if our controller is not asymptotically stable? Is there a way to design a controller that is both asymptotically stable AND provides asymptotic tracking?
Anonymous

The challenges of position control

On our daily lives we interact with devices (some engineered) that can steer toward a desired position. That could be a linear position, in a cart, in a valve or lock, angular position, in a motor or rotary system, or some more complicated 3D task, such as a robot or human arm. For their ubiquity, some may believe that position control is a simple, almost trivial task. They are up for surprises.

Root-locus angle of departure and arrival

I have previously discussed about why I kept the number of root-locus “rules” at a minimum in this post. One popular “rule” that I have omitted is the calculation of departure or arrival angles at complex poles or zeros.