In Digital Control, we will learn how to digitally implement the continuous dynamics synthesized by classical control or modern control to function as controllers, observers, filters, or phase-compensators. The implementation is finished in two stages: discrete equivalency and DSP programming. That is, the to-be-implemented continuous-dynamics is firstly transformed into a discrete-equivalent, which is then programmed into some microcontroller as a real-time processor. Unlike most of engineering curriculums that are computer-time technologies, Digital Control is a real-time technology.
The contents of the course are listed as follows.
Preface
Chapter1: Introduction to Digital Control
1-1 Discrete synthesis versus discrete equivalents
1-2 An example of classical control synthesis
1-3 Sampling and ZOH: sequence number
1-4 Discrete equivalent: trapezoidal approximation of integrator
1-5 Digital implementation of analog computer
Chapter 2: Z Transform
2-1 Take first-order dynamics as an introductory example
2-2 Long division
2-3 Unit-step response
2-4 Convolution
2-5 Unit pulse that defines transfer function
2-6 Z-transform of time-delay
2-7 Final-value theorem
2-8 Discrete state space
Chapter 3: Frequency Domain
3-1 Aliasing
3-2 Frequency response
3-3 Bode plots
3-4 Nyquist Criterion
3-5 Stability and robustness
3-6 Discrete modes
3-7 Discretization T/2 delay
3-8 Robustness and performance
Chapter 4: Discrete Equivalents
4-1 Tustin-1 method
4-2 Tustin-0 method
4-3 Euler-0 method
4-4 Euler-1 method
4-5 MPH approximation
4-6 Impulse-invariant approximation
4-7 Pre-warping Tustin
Chapter 5: Practice in Discrete Equivalence
5-1 Holder and sampler: dual structure
5-2 ZOH with T/2 embedded time-delay: demo in time and frequency domains
5-3 Linear holders: zero-order and first-order
5-3 Tustin-1 and Tustin-0 equivalents of integrator by convolution
5-5 Discrete equivalents of 1/s+1
5-6 Complete bases of linear interpolation
5-7 Different kinds of discrete equivalents in discrete Bode plots
5-8 Instability induced from the T/2 delay embedded in ZOH
Chapter 6: DSP Programming
6-1 IIR versus FIR
6-2 IIR-S: memorization of current state
6-3 IIR-P: memorization of past inputs and outputs (violates the principle of causality)
6-4 IIR-AC: iterative recursion of controllability canonical computer
6-5 IIR-AO: iterative recursion of observability canonical computer
6-6 IIR-S: Decomposition into a series of subsystems
6-7 FIR: finite impulse response
Chapter 7: Special Issue on Half-a-sample Delay Embedded in ZOH
7-1 Viewpoints from temporal signal
7-2 Frequency responses of equivalents
7-3 Nonlinear digital control: Tustin equivalent plus IIR-AC for van der Pol oscillators
Chapter 8: DSP-Programming into Microcontroller
8-1 Introduction to special-purpose and general-purpose microcontrollers
8-2 Overview of Microchip-dsPIC chips
8-3 Peripherals and interruption
8-4 Matlab-to/from-dsPIC
8-5 Coding of IIRs
8-6 Coding of signal generators
8-7 Example1: Firmware-based instruments
8-8 Example 2: Drivers/controllers of DC motors