Z Transformation
Provides a mathematical foundation for
representing the discrete nature of
computer control systems
Z Transformation
Builds on the Laplace transformation and
transforms a sampled function of time t
into a function of new complex variabl
Digital to Analog Conversion
Interfaces are needed that convert
computed manipulations to voltages
Digital to Analog Conversion
Digital to analog converters (DACs)
accept a binary value as input and
produce a proportional voltage
Both positive and nega
Feedforward Control
In some cases, it is possible to replace a
higher-performance closed-loop control
with the combination of feedforward
control and a lower-performance closedloop control.
Feedforward Control
Feedforward control is similar to openloop
Control Analysis and Design
Extensive calculations and plotting are at
the heart of control systems engineering
MATLAB Basics for
Control System Engineering
Before1990s (hours or days of work):
Calculate and plot response by hand
Write computer progra
Matlab Controls Toolbox
Builds on MATLABs basic functionality
Implements common controls calculations
MATLAB Control System
Toolbox Basics
Continuous process representation
Discrete process model calculation
Transfer function algebra
Response calcul
Optical Angle Encoder
control
computer
Position Sensing Using
Optical Shaft Angle Encoders
ENC(v,c)
encoder
interface
A
B optical
Z encoder
signals
v = BRU
c = channel #
Encoder interface decodes A & B signals,
and counts angle increments (Basic
Rotation
Sample Period Selection
Selection of the sample period is an
important step in controller design
Sample Period Selection
Rapid sampling is needed when
Rapid response (high performance) is
needed in closed-loop control
Sampled signals contain higher fr
Stability
A control system must be stable and
well-behaved to function productively
Stability
Stability is not a function of the input a
system is given; rather, it is an intrinsic
property of the system
Stability can be accessed by examining
the roots
Utility of Block Diagrams
Visualization of control systems
Reflect physical structure of system
Block Diagrams
Show transfer functions of components
Show input-output relationships
Convenient analysis of control systems
straightforward manipulation
Chapter 4 Homework Solutions Spring 2012
Problem 4.1
dc(t )
= 5m (t )
dt
For sample period T = 0.1, the discrete transfer function for the process is
0.5z !1
Gp (z) =
1 ! z !1
From item #3 of Table 2.1, the desired transfer function for a gain of 1 and a
Manipulation of Block Diagrams
Convenient tool in analysis of control
systems
Block Diagram Manipulation Examples
based on transfer functions and algebra
simplify of block diagrams
obtain closed-loop system transfer functions
Summing points and pick-
Analog to Digital Conversion
Interfaces are needed that sample sensor
feedback voltages
Analog to Digital Conversion
Analog to digital converters (ADCs)
accept a voltage as their input and
produce a proportional binary word
Both positive and negative f
Discrete Process Transfer Functions
The discrete transfer function defining
the relationship between process
feedback and manipulation combines the
Transfer Functions
from Laplace Transform
continuous transfer function of the hold
continuous transfer f