integral control – Fundamentals of Linear Control: A Concise Approach

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.

Is a proportional controller right for you? Ask your control engineer! Part III

In Part I and Part II of this post we looked into the problem of finding a suitable discrete-time controller when the system being controlled is fast to reach steady-state so that it can be modeled as the single delay

$$y(t) = G u(t – \tau), \quad \tau > 0.$$

In Part I we showed that a proportional controller is not a good choice and in Part II we found out that, surprisingly, an integral only controller is an excellent choice but requires the use of a gain $\hat{G}$ that has to match the gain of the system $G$. In the present post we will revisit the design of a dynamic controller with the goal of showing that:

the Smith predictor from Part II also had a zero;
the integral controller is indeed an excellent choice;
the mismatch $\hat{G} \neq G$ is not necessarily catastrophic.

Is a proportional controller right for you? Ask your control engineer! Part II

Let’s now take another look at the problem we introduced here in this post. The problem was that of finding a suitable discrete-time controller when the system being controlled is fast to reach steady-state so that it can be modeled as the single delay

$$y(t) = G u(t – \tau), \quad \tau > 0.$$

As seen before, a proportional control is not a good solution in this case. So what is the “simplest” controller one could think of in a situation like that? Of course it will be a dynamic controller! We will go about constructing one such dynamic controller in the rest of this post.