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ECE 483. Digital Control Systems Analysis and Design

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1 ECE 483. Digital Control Systems Analysis and Design
Instructor: Jianghai Hu Office: MSEE 220 Tel: Office Hours: Tu 4:15-5:15pm TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA

2 Lec. 1. Control Systems Overview
Reading: Chapter 1 What is control? Use of algorithms and feedback to affect the operation of physical objects of interest (systems) to achieve some desired performance Environmental Perturbations Controller Input Physical Objects: Plant, Process, System output

3 Examples of (Digital) Control Systems
Digital thermostat Digital DC servo control Digital Automated Flight Computer System (AFCS)

4 Continuous-Time (Analog) Control Systems
Plants and controllers are continuous-time systems continuous-time input and output signals modeled by differential equations, or transfer functions 𝐺(𝑠) Block diagram of a simple analog feedback control system: controller plant 𝑈(𝑠) + 𝑌(𝑠) 𝑠+2 𝑠+3 1 𝑠(𝑠+1) _

5 Example: Satellite 𝑓 𝜃 gas jet Suppose that the antenna of the satellite needs to point to the earth. Satellite is a system with: Input: force f generated by reaction of gas jet Output: orientation of the satellite as given by the angle 

6 Example: Satellite 𝑇=𝐽⋅ 𝜃 𝑇=𝑓⋅𝑙 𝑓 𝑙 Newton’s Second Law:
Torque generated by the thrust f: 𝑇=𝑓⋅𝑙 𝑓 gas jet 𝑙 𝜃 Newton’s Second Law: 𝑇=𝐽⋅ 𝜃 Total torque Moment of inertia Angular acceleration System model (time domain): System model (frequency domain): Θ(𝑠) 𝐹 𝑠 = 𝑙 𝐽 𝑠 2 𝑓 𝑡 ⋅𝑙=𝐽⋅ 𝜃 (𝑡) Laplace transform

7 Example: DC Motor System
armature resistance 𝑅 𝑎 torque 𝑇 Basic motor properties: 𝑖 + Generated torque proportional to current: 𝜃 + 𝑒 - 𝑒 𝑚 𝐽 𝑇= 𝐾 𝑇 ⋅𝑖 - Motor voltage proportional to shaft angular velocity: Friction 𝐵 𝑒 𝑚 = 𝐾 𝑏 ⋅ 𝜃 Electro-mechanical system Input: voltage source e(t) Output: shaft angular position 𝜃(𝑡) Basic circuit properties (KVL): Newton law: 𝑒 𝑡 = 𝑅 𝑎 ⋅𝑖 𝑡 + 𝑒 𝑚 (𝑡) 𝑇=𝐽 𝜃 +𝐵 𝜃

8 Example: DC Motor System
System model:

9 Digital Control Systems
A typical digital feedback control system: T r(t) A/D Computer D/A Data Hold Plant y(t) Sampling Sensor Idea: computers have enormous data processing power (intelligence) Sampling and data hold: Needed since computer’s clock is in discrete time and plants operate in continuous time A/D and D/A units: needed since computer can only process binary strings

10 Example: Digital Motor Control
𝑇 𝑢 A/D Digital Controller D/A + + - 𝑇 - 𝜃 𝑖 + 𝑒 𝑚 𝜃 𝐽 - Sensor

11 Diagram of Digital Motor Control
Digital Controller Motor 𝑇 𝑢(𝑡) 𝜃(𝑡) A/D D/A 𝑧+0.1 𝑧+0.6 𝐾 1 𝑠(𝑠+𝑎) + - Both continuous-time and discrete-time signals present Both Laplace transforms and Z-transform used

12 Example: Remote Antenna Control
Digital reference input signal Antenna Power Amplifier q Motor Receiver Decoder D/A 1 𝑠(𝑠+𝑎) K wireless communication channel Digital Filter Receiver Decoder Encoder Binary code

13 Other Forms of Digital Control Systems

14 Digital Control System Analysis
Plant: still modeled by a Laplace transfer function G(s) Computer as the digital controller Input and output are both discrete-time signals, hence a digital filter Modeled using a linear difference (recursion) equation Or through z-transform as a transfer function in z So a mixture of s-transfer functions and z-transfer functions What about the A/D, D/A, sampling, and data hold? They cannot be modeled as transfer functions! This is the key difficulty of analyzing digital control systems

15 Digital Controller Design
For a given system, design the digital controller for Reduced steady-state error Faster transient response Disturbance rejection Low sensitivity to modeling error Design methods Root locus design Frequency response design Direct design method

16 State-Variable Approach
Modern perspective Systems with different internal structures may have the same TF Internal variables are of interest as well: input/output no longer enough Intrinsic system model More powerful design methods Cellular biosynthesis process Automated flight control system

17 Summary of Course Content
Digital System Modeling How to construct math model of a digital controller/system? Digital Control System Analysis What is system output under an arbitrary input? Digital Controller Design How to design digital controller so that the system output behaves desirably?


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