# Essentials of Control and Estimation Theory, Tools, and Applications

Control and estimation theory and their aerospace applications have been used for more than 50 years. Yet, this is the only single course that puts these two important and useful topics together and demonstrates their practical aspects in detail, as well as provides MATLAB/SIMULINK-related tools for real industrial problems. Instruction presents theories and related tools proven to be the ultimate analysis and synthesis tools and methodology to capture the issues of control and estimation fundamentals, implementations, and the essential trade-offs between them when applied to real-world problems.

The course covers three major topics with hands-on lab experience:** control basics, estimation basics, and advanced case studies**. The course provides numerous aerospace design examples, including spacecraft attitude control, supermaneuverable fighter flight control, large space structure vibration control, disk drive suspension servo control, spacecraft attitude determination covering Kalman filtering, and advanced filtering. GPS position estimation for spacecraft attitude control also is illustrated in detail.

Through the course’s control and estimation design tools and methodologies, participants gain the basic knowledge and powerful MATLAB tools to solve practical real-life problems.

##### Course Materials

Participants receive lecture notes and published papers on the first day of the course. These materials are for participants only and are not for sale.

##### Coordinator and Lecturer

**Richard Y. Chiang, PhD**, Boeing Technical Fellow, Flight and Control Engineering Department, Space and Intelligence Systems, Boeing, El Segundo, California. Dr. Chiang is a nationally and internationally recognized expert in robust control system design and system identification. He is the leading author on the MATLAB software, Robust Control Toolbox, of which nearly 25,000 copies have been sold worldwide across industries and academia for the last 15 years. His control design methodology has become a universal standard in the field. Dr. Chiang began his career 30 years ago as a control system analyst at Garrett AiResearch. During the 1990s, he also worked for Northrop Aircraft on F-18 supermaneuver flight control and at JPL on large space structure vibration control. Since joining Boeing in the late ’90s, he has designed attitude control systems for 10 satellites and analyzed system stability for 15 programs. He has taught senior control courses at USC and has given control seminars at DEC, Northrop, General Dynamics, and JPL in the 1990s and several at Boeing from 2002 to the present. He also has published 17 journal papers and 45 conference papers, and has three issued U.S. patents and seven patent applications pending related to spacecraft control system design.

##### Daily Schedule

*Day 1*

**Controls**

**The Big Picture of Control Design**

- What is a Control System?
- Control Design Objectives (Why are We Doing This?)
- Brief History of Classical/Modern/Robust Control Theory

**Classical Control Theory**

- Basic Modeling and Transfer Function: Mass-Spring-Damper Systems; Laplace Transform; Transfer Function (Poles/Zeros); Second-Order Systems
- Linearization for Linear Models
- Feedback Characteristics (Sensitivity Function) and Specifications
- Root Locus
- Nyquist, Bode, Nichols
- Analysis (Stability Margins)
- Synthesis (Lead/Lag, Notch, PID)
- Gain/Phase Stabilization
- Feedforward: Internal Model Principle
- Disturbance Feedfoward
- Tools and Examples
- Lab Exercises and References

**Sampled-Data Systems**

- Z-Transform and Bilnear Transform
- Discrete Transfer Function and State-Space Realization
- Aliasing and Nyquist Frequency
- Discrete Analysis and Synthesis
- Multi-Rate System Analysis (Kranc Operator)
- Delta-Operator
- Tools and Examples
- Lab Exercises and References

**State-Space Linear System Theory**

- Linear Algebra and Matrix Theory
- State-Space Representation and Descriptor Systems
- Lyapunov and Riccati Equations
- Controllability and Observability
- Observer
- Optimality (LQR, LQG, LQR/LTR)
- Analysis (Minimal Realization)
- Synthesis (Pole Placement)
- Tools and Examples
- Lab Exercises and References

**Nonlinear Control Theory**

- Nonlinearities: Saturation, Switching and Hysteresis, Deadzone and Compensation, Anti-Windup, Friction
- Circle Criterion
- Describing Function Analysis
- Bang-Bang and Phase Plane Control
- Tools and Examples
- Lab Exercises and References

**Multi-Variable Robust Control Theory**

- Basics
- Singular Values
- Uncertainty Modeling
- Model Reduction Methods (Balanced Truncation)
- (Mu) Robustness Analysis Methods
- Robust Synthesis Methods
- Feedback Limitations
- Tools and Examples
- Lab Exercises and References

**System Identification for Control**

- Basics
- Excitation Signals
- Frequency Domain Spectrum Analysis
- State-Space Model Realization
- System ID GUI
- Tools and Examples
- Lab Exercises and References

**Control of Large Space Structure**

- Colocated and Non-Colocated Control
- Two-Mass-Spring ACC Benchmark Problem
- Model Reduction
- Classical/Modern Methods
- Jitter Analysis
- Tools and Examples
- Lab Exercises and References

**Numerical Issues in Control**

- Floating Point Arithmetic (EPS)
- Coefficient Representation
- Frequency Response Sensitivity
- Round-Off Error/Noise
- Lyapunov and Riccati Equation Condition Number
- Tools and Examples
- Lab Exercises and References

*Day 2*

**Estimation**

**Introduction**

**Random Process and Noise Characteristics**

- Basics
- Tools and Examples
- Lab Exercises and References

**Least Squares Estimation**

- Parameter Estimation
- Weighted Least Squares
- Recursive Least Squares
- Wiener Filtering
- Tools and Examples
- Lab Exercises and References

**Propagation of States and Covariances**

- Tools and Examples
- Lab Exercises and References

**Linear System Driven by White Noise**

**State-Observers**

- Basics
- Tools and Examples
- Lab Exercises and References

**Kalman Filter Theory and Implementation**

- Discrete
- Continuous
- Fading Memory
- Constrained Kalman Filtering
- Tools and Examples
- Lab Exercises and References

**Nonlinear Kalman Filter**

- Linearized Kalman Filter
- Extended Kalman Filter
- Tools and Examples
- Lab Exercises and References

**H-Infinity Filtering**

- Introduction
- Constrained Optimization
- Game Theory Approach
- Tools and Examples
- Lab Exercises and References

**Unscented Kalman Filter**

- Unscented Transformations
- Unscented Kalman Filtering
- Tools and Examples
- Lab Exercises and References

**Particle Filters**

- Bayesian State Estimation
- Particle Filtering
- Implementation Issues
- Tools and Examples
- Lab Exercises and References

**Applications**

- GPS Position Estimation
- Spacecraft Attitude Determination
- Orbit Estimation
- Target Tracking of Aircraft
- Lab Exercises and References

*Day 3*

**Case Studies**

**Control-Related Cases Studies**

- Disk Drive Pointing Control
- F-18 HARV Supermaneuverable Fighter Flight Control
- Spacecraft Attitude Control
- Payload Friction Control
- Air Refueling Control

**Estimation-Related Case Studies**

- GPS
- Spacecraft Attitude Estimation: Gyros, Star Trackers, Earth/Sun Sensors, SIAD

**Advanced Topics**

- Fuzzy Logic, Neural Network Control
- Unfalsify Robust Adaptive Control
- Real-Time Software/Workshop

**For more information contact the Short Course Program Office: **

shortcourses@uclaextension.edu (310) 825-3858