即時控制系統設計 Design of Real-Time Control Systems

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1 SPRING 2010 即時控制系統設計 Design of Real-Time Control Systems Outline Design of Digital Control Systems Transfer Function Design Methods NTUEE-RTCS24-DTDesign-2 Lecture 24 Controller Design of Digital Control Systems Feng-Li Lian NTU-EE Feb10 Jun10 > > Introduction NTUEE-RTCS24-DTDesign-3 NTUEE-RTCS24-DTDesign-4 Two basic digital controller design techniques: 1. Emulation: Design a continuous compensation D(s) by using any CT controller design methods Approximate that D(s) by using any approximation methods such as Tustin s Method 2. : Model in DT (difference equations) Design in DT (z-transform) Design by emulation: 1. Design a continuous compensation 2. Digitalize the continuous compensation 3. Use discrete analysis, simulation, or experimentation Design techniques: 1. Tustin s Method or bilinear approximation 2. Matched Pole-Zero method (MPZ) 3. Modified Matched Pole-Zero method (MMPZ)

2 NTUEE-RTCS24-DTDesign-5 NTUEE-RTCS24-DTDesign-6 Tustin s method: Tustin s method: NTUEE-RTCS24-DTDesign-7 NTUEE-RTCS24-DTDesign-8 Tustin s method: Tustin s method: sysds = tf( 10*[0.5 1], [0.1 1] ); sysdd = c2d( sysdc, 0.025, tustin );

3 NTUEE-RTCS24-DTDesign-9 NTUEE-RTCS24-DTDesign-10 Case 1: 1. Map poles and zeros according to the relation 2. If the numerator is of lower order than the denominator, add powers of (z+1) to the numerator until numerator and denominator are of equal order 3. Set the DC or low-frequency gain of D(z) = that of D(s) NTUEE-RTCS24-DTDesign-11 NTUEE-RTCS24-DTDesign-12 Case 2: The same power of z in the num & den of D(z):

4 NTUEE-RTCS24-DTDesign-13 NTUEE-RTCS24-DTDesign-14 Space station attitude digital controller Space station attitude digital controller NTUEE-RTCS24-DTDesign-15 NTUEE-RTCS24-DTDesign-16 Space station attitude digital controller Modified Matched Pole-Zero (MMPZ) method: u[k+1] depends only on e[k], but not e[k+1]

5 Comparison of Digital Approximation Methods: NTUEE-RTCS24-DTDesign-17 Outline Design of Digital Control Systems NTUEE-RTCS24-DTDesign-18 Transfer Function Design Methods > > NTUEE-RTCS24-DTDesign-19 NTUEE-RTCS24-DTDesign-20 The Exact Discrete Equivalent: Discrete Root Locus:

6 NTUEE-RTCS24-DTDesign-21 NTUEE-RTCS24-DTDesign-22 Feedback Properties: Proportional: Space Station Digital Controller example: Derivative: Integral: Lead Compensation: NTUEE-RTCS24-DTDesign-23 NTUEE-RTCS24-DTDesign-24 Space Station Digital Controller example: P + D feedback Space Station Digital Controller example: P + D feedback

NTUEE-RTCS24-DTDesign-26 Transfer Function Design Methods

7 NTUEE-RTCS24-DTDesign-25 Step Response of the continuous & digital systems: Outline Design of Digital Control Systems NTUEE-RTCS24-DTDesign-26 Transfer Function Design Methods NTUEE-RTCS24-DTDesign-27 NTUEE-RTCS24-DTDesign-28 State-Space Model: State-Space Model:

8 NTUEE-RTCS24-DTDesign-29 NTUEE-RTCS24-DTDesign-30 Discrete Transfer Function: Discrete SS Model of 1/s^2: NTUEE-RTCS24-DTDesign-31 NTUEE-RTCS24-DTDesign-32 Discrete SS Model of 1/s^2: Pole Placement by State Feedback:

9 NTUEE-RTCS24-DTDesign-33 Hardware Characteristics NTUEE-RTCS24-DTDesign-34 Discrete Full-Order Estimator: Hardware Characteristics: A/D Converters D/A Converters Anti-Alias Prefilters The Computer Word-Size Effects Sample-Rate Selection

CHAPTER 9 FEEDBACK. NTUEE Electronics L.H. Lu 9-1

CHAPTER 9 FEEDBACK. NTUEE Electronics L.H. Lu 9-1 CHAPTER 9 FEEDBACK Chapter Outline 9.1 The General Feedback Structure 9.2 Some Properties of Negative Feedback 9.3 The Four Basic Feedback Topologies 9.4 The Feedback Voltage Amplifier (Series-Shunt) 9.5