It’s all PID

Theorists and engineers have developed a number of servo compensation schemes over the years, but the overwhelming favorite is the PID loop. Several different implementations of the PID loop exist however, and it is not uncommon for different vendors to use different approaches.

Broadly speaking, PID controllers fall into two groups; the first is the “PID position loop,” and the second is the “cascaded position/velocity loop.” Figures 1A and 1B, on the following page, provide an overview of these two schemes.

The more common PID position loop requires us to determine three values, the position loop gain, (Kp) the Integral gain (Ki) and the derivative gain (Kd). Even for this “basic” servo system however, modern motion vendors provide a bevy of additional options. The most common of these are an integrator limit, feed-forward gains, motor bias, and frequency-domain filtering such as notch filters or band-pass filters. Several of these concepts will be discussed in later sections of this article.

Cascaded position/velocity loops are tuned inside-out, and either four or five parameters are set by the user. The inner velocity loop (usually a PI controller) is tuned first, and then the outer position loop (generally either a PI or PID controller) is tuned. While we will not focus on the cascaded position/velocity loop in this article, it shouldn't be hard to adapt some of the techniques presented to this type of loop. Note also that if you are using an external amplifier that provides velocity control, you already are, in effect, utilizing a cascaded position velocity loop. Generally speaking the type of amplifier you are using has an important effect on position loop tuning, so you should make sure that the complete system controller, including whatever control loops may exist in the amplifier, are taken into account.

Equations 1 & 2 below provide the basic form of the PID filter equation in both the continuous time domain and the discrete time domain. For anyone using a DSP or microprocessor to construct a servo loop, only the discrete time form applies. The continuous form is used in system modeling and analysis, and can be used as a representation of the discrete time form as long as the sampling rate is high compared to the system bandwidth.

PID position loop (1A); cascaded position/velocity loop (1B)