For those seeking to optimize performance, this chapter introduces optimal control theory, including design by maximum principle and optimal linear digital regulator design.

Kuo does not skip steps. Every derivation, from the pulse transfer function to the discrete Riccati equation, is laid out logically.

). Kuo emphasizes the , which states that the sampling frequency ( ) must be at least twice the highest frequency component ( fmaxf sub m a x end-sub ) contained in the signal to prevent aliasing: fs>2fmaxf sub s is greater than 2 f sub m a x end-sub

The derivations provided by Kuo ensure that engineers understand why a system behaves a certain way, preventing reliance on trial-and-error tuning.

The text features real-world problems, from controlling the read-write head of a hard disk drive to stabilizing complex industrial DC motors.

-plane. Kuo outlines specific stability tests adapted for digital systems, including:

An algebraic method analogous to the Routh-Hurwitz criterion used in analog control.

Sampling is the process of converting a continuous signal into discrete samples at uniform intervals, denoted as the sampling period (

Canonical forms (controllable, observable, and diagonal forms).

Under this mapping:

Analog control relies on differential equations. Digital control, however, operates on data sampled at specific time intervals. Kuo introduces the concept of sampling, the sampler, and the hold device (most commonly the Zero-Order Hold, or ZOH). The ZOH converts the digital output from a computer back into a continuous physical signal to drive actuators. 2. The z-Transform Just as the Laplace transform (

Unlike continuous-time (analog) control systems, which process signals continuously, digital control systems operate on discrete-time signals. These systems use digital computers, microcontrollers, or digital signal processors (DSPs) to compute the control actions. Core Components A typical digital control loop consists of: