Practical Techniques in Control Engineering (2 days; June 6 & 7, 2005)

Dennis S. Bernstein, University of Michigan
Carl R. Knospe, University of Virginia

Course Description (short version)

Provides a bridge between recent developments in control theory and their practical application in the laboratory and industry. Fundamental tradeoffs, modeling and identification, linear and nonlinear controller synthesis, saturation, and adaptive tuning will be discussed. The course is suitable for students, instructors, and researchers in control theory who wish to obtain a broad perspective of the control engineering enterprise as well as control engineers from all industrial applications seeking a coherent, self-contained overview of recent developments relevant to control practice.

Course Description (long version) See PDF Description

This course will provide a bridge between recent developments in control theory and their practical application in the laboratory and industry. Beginning with an overview of fundamental tradeoffs and issues that affect control-system performance, the course will systematically cover topics in linear and nonlinear modeling, linear and nonlinear controller synthesis, and robust and adaptive tuning. Controller implementation issues such as saturation, quantization, and state constraints will also be discussed. The theoretical foundation of each topic will be reviewed along with a discussion of practical ramifications and limitations. The course is suitable for students, instructors, and researchers who wish to obtain a broad perspective of the control engineering enterprise as well as control engineers from all industrial applications seeking a coherent, self-contained overview of recent developments relevant to control practice.

Schedule

Monday, June 6, 2005

1. . DEFINING THE ISSUES AND CHALLENGES IN CONTROL ENGINEERING
1.1. Course Overview (8:30-8:45)
1.2. Control-System Design: Strategy, Physics, Architecture, and Hardware (8:45-9:30)
1.3. Plant Properties and Achievable Performance (9:30-10:30)

Break (10:30-10:45)

2. DEVELOPING LINEAR MODELS FOR CONTROL
2.1. Linear Plant Modeling: Representation and Properties (10:45-11:30)
2.2. Empirical Linear Modeling: System Identification (11:30-12:30)

Break (12:30-1:30)

3. SYNTHESIZING LINEAR CONTROLLERS FOR PERFORMANCE AND ROBUSTNESS
3.1. Uncertainty Measures and Robust Synthesis (1:30-3:15)

Break (3:15-3:30)

4. REDUCING MODEL DEPENDENCE IN CONTROLLER SYNTHESIS
4.1. Minimal-Information Control: The Art and Science of PID Tuning (3:30-4:15)
4.2. Adaptive Control: What Do You Need to Know, and How Well Do You Need to Know It? (4:15-4:45)
4.3. Adaptive Stabilization and Command Following (4:45-5:30)

Tuesday, June 7, 2005

5. DEVELOPING NONLINEAR MODELS FOR CONTROL
5.1. Nonlinear Plant Modeling: Model Properties and Structure (8:30-9:00)
5.2. Nonlinear Identification Methods for Block-Structured Models (9:00-10:00)

6. INEXACT APPROACHES TO NONLINEARITY
6.1. Treating Nonlinearity as Uncertainty: Absolute Stability, LMIs, and IQCs (10:00-10:30)

Break (10:30-10:45)

6. INEXACT APPROACHES TO NONLINEARITY (continued)
6.2. Treating Nonlinearity as Linearity: Gain Scheduling, LPVs, and Frozen Linear Methods (10:45-12:15)

Break (12:15-1:15)

7. EXACT APPROACHES TO NONLINEARITY Part I (1:15-2:15)
7.1. Feedback Linearization: Methods and Pitfalls

8. EXACT APPROACHES TO NONLINEARITY
8.1. Backstepping: A Constructive Nonlinear Approach (2:15-2:45)

9. IMPLEMENTING REAL CONTROL SYSTEMS IN REAL HARDWARE
9.1. Facing the Reality of Constraints: Traditional and Modern Approaches (2:45-3:15)

Break (3:15-3:30)

10. FITTING THE PIECES TOGETHER
10.1. Adaptive Disturbance Rejection with Applications to Noise and Vibration Control (3:30-4:30)
10.2. A Case Study for Controller Design and Implementation: Active Chatter Control (4:30-5:30)

Engineering Applications in Genomics (2 days; June 6 & 7, 2005)

Aniruddha Datta, Texas A & M University

Course Description
Genomics concerns the study of large sets of genes with the goal of understanding collective function, rather than that of individual genes. Such a study is important since cellular control and its failure in disease result from multivariate activity among cohorts of genes. Very recent research indicates that engineering approaches for prediction, signal processing and control are quite well suited for studying this kind of multivariate interaction. The aim of this workshop will be to provide the attendees with a state of the art account of the research that has been accomplished in this field thus far and
to make them aware of some of the open research challenges.

The workshop will provide a tutorial introduction to the current engineering research in genomics. The necessary Molecular Biology background will be presented and techniques from signal processing and control will be used to (i) unearth intergene relationships (ii) model genetic regulatory net-
works and (iii) alter (i.e. control) their dynamic behaviour. The workshop will be divided into two parts. On the first day, we will focus on building up the necessary molecular biology background. NO PRIOR EXPOSURE TO MOLECULAR BIOLOGY WILL BE ASSUMED. On the second day, we
will discuss the application of engineering approaches for attacking some of the challenging research problems that arise in genomics related research. A more detailed description of the material to be covered on each day follows.

Syllabus

Workshop Day 1
• 1. Review of Organic Chemistry: Sugars, Fatty Acids, Amino Acids and Nucleotides (1 hour 45 minutes)
• 2. DNA, RNA and Proteins: Transcription, Translation, the Genetic Code, Chromosomes and Gene Regulation (2 hours)
• 3. Genetic Variation, Genetic Engineering: Recombinant DNA Technology and Microarrays (1 hour 45 minutes)
• 4. Procaryotes, Eucaryotes, Eucaryotic Cell Structure, Cell Cycle, Mitosis, Meiosis, Apoptosis, Cancer as the breakdown of Cell Cycle control (2 hours)

Workshop Day 2
• 5. Analysis of cDNA Microarray Images (1 hour 45 minutes)
• 6. Unearthing Genomic Relationships using the Coefficient of Determination (2 hours)
• 7. Models of Genetic Regulatory Networks (1 hour 45 minutes)
• 8. Intervention and Control in Genetic Regulatory Networks (2 hours)

Workshop Materials
Detailed notes covering the material on the first day will be handed out at the workshop. The material for the second day will consist of the following journal articles, copies of which will be included in the workshop notes.

1. Chen, Y., Dougherty, E. R. & Bittner, M. L. (1997). Ratio-Based Decisions and the Quantitative Analysis of cDNA Microarray Images. Journal of Biomedical Optics, Vol. 2, No. 4, 364-374.
2. Kim, S., Dougherty, E. R., Bittner, M. L., Chen, Y., Sivakumar, K., Meltzer, P., & Trent, J. M. (2000). A General Framework for the Analysis of Multivariate Gene Interaction via Expression Arrays. Biomedical Optics, Vol. 4, No. 4, 411-424.
3. Shmulevich, I., Dougherty, E. R., Kim, S., & Zhang, W. (2002a). Probabilistic Boolean Networks: A Rule-based Uncertainty Model for Gene Regulatory Networks. Bioinformatics, 18, 261-274.
4. Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002c). Gene Perturbation and Intervention in Probabilistic Boolean Networks. Bioinformatics, 18, 1319-1331.
5. Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002d). Control of Stationary Behavior in Probabilistic Boolean Networks by Means of Structural Intervention. Biological Systems, Vol. 10., No. 4, 431-446.
6. Datta, A., Choudhary, A., Bittner, M. L., & Dougherty, E. R. (2003). External Control in Markovian Genetic Regulatory Networks. Machine Learning, Vol. 52, 169-191.
7. Datta, A., Choudhary, A., Bittner, M. L., & Dougherty, E. R. (2004). External Control in Markovian Genetic Regulatory Networks: The Imperfect Information Case. Bioinformatics, Vol. 20, No. 6, 924-930.

Recent Advances in Subspace System Identification: Linear, Nonlinear, Closed-Loop, and Optimal with Applications (2 days; June 6 & 7, 2005)

Wallace E. Larimore, Adaptics, Inc.

Course Description (short version)

This workshop presents a first principles development of subspace system identification (ID) using a fundamental statistical approach. This includes basic concepts of reduced rank modeling of ill-conditioned data to obtain the most appropriate statistical model structure and order using optimal maximum likelihood methods. These principles are first applied to the well developed subspace ID of linear dynamic models; and using recent results, it is extended to closed-loop linear systems and then general nonlinear closed-loop systems.

Course Description (long version) See PDF Description

The fundamental statistical approach gives expressions of the multistep likelihood function for subspace identification of both linear and nonlinear systems. This leads to direct estimation of the parameters using singular value decomposition type methods that avoid iterative nonlinear parameter optimization. The result is statistically optimal maximum likelihood parameter estimates and likelihood ratio tests of hypotheses. The parameter estimates have optimal Cramer-Rao lower bound accuracy, and the likelihood ratio hypothesis tests on model structure, model change, and process faults produce optimal decisions.

The extension to general nonlinear systems determines optimal nonlinear functions of the past and future using the theory of maximal correlation. This gives the nonlinear canonical variate analysis. New results show that to avoid redundancy and obtain gaussian variables, it is necessary to determine independent canonical variables that are then used in the likelihood function evaluation. This gives a complete likelihood theory for general nonlinear stochastic system with continuous dynamics and possibly feedback.

These new results greatly extend the possible applications of subspace ID to closed-loop linear and nonlinear systems for monitoring, fault detection, control design, and robust and adaptive control. The precise statistical theory gives tight bounds on the model accuracy that can be used in robust control analysis and design. Also precise distribution theory is available for tests of hypotheses on model structure, process changes and faults. Potential applications include system fault detection for control reconfiguration, autonomous system monitoring and learning control, and highly nonlinear processes in emerging fields such as bioinformatics and nano technology. Applications are discussed to monitoring and fault detection in closed-loop chemical processes, identification of vibrating structures under feedback, online adaptive control of aircraft wing flutter, and identification of the chaotic Lorenz attractor.

The intended audience includes practitioners who are primarily interested in applying system identification techniques, engineers who desire an introduction to the concepts of subspace system identification, and faculty members and graduate students who wish to pursue research into some of the more advanced topics.

Syllabus

SCHEDULE - DAY ONE - LINEAR SYSTEMS WITH FEEDBACK

8:30-9:15 OVERVIEW OF SUBSPACE SYSTEM IDENTIFICATION
- Approaches and Algorithms
- Positivity, Stability, Accuracy, Computation
9:15-10:00 RANK OF A STOCHASTIC DYNAMIC SYSTEM
- Statistical Rank - Canonical Variate Analysis (CVA)
- Rank as Minimal State Order
Break
10:30-11:15 SUBSPACE MAXIMUM LIKELIHOOD ESTIMATION
- Multistep Likelihood Function
- State Space Regression Equations
11:15-12:00 STATISTICAL MODEL ORDER/STRUCTURE SELECTION
- Kullback Information and Akaike Information
- Accuracy of Estimated Model
Lunch Break
1:00-2:00 COMPARISON OF ALTERNATIVE SYSTEM IDENTIFICATION APPROACHES
- Model Structure Selection and Parameter Estimation
- Computational Issues and Software
2:00-2:45 OPTIMAL IDENTIFICATION OF I/O AND CLOSED-LOOP SYSTEMS
- Removing Effect of Future Inputs
- Model Nesting and Sufficient Statistics
3:15-4:00 PROCESS MONITORING USING CVA
- Low Rank Process Characterization by CVA
- Testing Hypotheses of Process Change
Break
4:00-4:45 PROCESS MONITORING APPLICATIONS
- Tennessee Eastman Challenge Problem
- Comparison with SPC and PCA Methods
4:45-5:30 IDENTIFICATION AND CONTROL APPLICATIONS
- Vibrating Structures
- On-line Adaptive Control of Aircraft Wing Flutter

SCHEDULE - DAY TWO - NONLINEAR SYSTEMS

8:30-9:15 OVERVIEW OF NONLINEAR SYSTEM IDENTIFICATION METHODS
- Hammerstein and Wiener Systems
- Nonlinear State Space Models
9:15-10:00 NONLINEAR CANONICAL VARIATE ANALYSIS
- Nonlinear Functions of Past and Future
- Multivariate Reduction by Maximal Correlation
Break
10:30-11:15 MAXIMAL CORRELATION AND PROJECTION
- Definition and Properties
- Outline of Function Space Concepts
11:15-12:00 MINIMAL STATE RANK AND INDEPENDENT CVA
- Redundancy Problem with CVA
- Optimal Transformations to Gaussian Variables
Lunch Break
1:00-2:00 LIKELIHOOD FUNCTION FOR NONLINEAR SYSTEMS
- Multistep Likelihood
- Optimality of Independent CVA
2:00-2:45 OPTIMALITY IN CLOSED LOOP
- Remove Future Inputs with NARX
- Model Nesting and Nonlinear Regression

3:15-4:00 COMPARISON WITH OTHER METHODS
- Neural Networks, Statistical Learning
- Support Vector Machines
Break
4:00-4:45 COMPUTATIONAL METHODS
- Alternating Conditional Expectation (ACE)
- Kernel based Computation
4:45-5:30 LORENTZ ATTRACTOR IDENTIFICATION
- Nonlinear Dynamics and Noise
- Computation and Identification Accuracy

Real Time Optimization By Extremum Seeking Control (1 day; June 7, 2005)

Miroslav Krstic, University of California, San Diego
Kartik Ariyur, Honeywell Aerospace Electronic Systems
Andrzej Banaszuk, United Technologies Research Center
Dobrivoje Popovic, United Technologies Research Center
Eugenio Schuster, Lehigh University
Mario Rotea, Purdue University

Extremum seeking control, a popular tool in control applications in the 1940-50’s, has seen a resurgence in popularity as a real time optimization tool in aerospace and automotive engineering. This workshop will present the theoretical foundations and selected applications of extremum seeking.

In addition to being an optimization method, extremum seeking is a method of adaptive control, usable both for tuning set points in regulation/optimization problems and for tuning parameters of control laws. It is a non-model based method of adaptive control, and, as such, it solves, in a rigorous and practical way, some of the same problems as neural network and other intelligent control techniques.

The first half of the workshop will teach the attendees the extremum seeking algorithms, the basics of their stability analysis, the design guidelines. Both single-parameter and multivariable problems will be covered, as well as both the continuous and discrete time implementations. A novel “slope seeking” extension applicable to some unstable plants will be introduced. An application of extremum seeking to minimizing limit cycles caused by actuator limitation will be presented.

In the second half of the workshop, applications to aerospace and propulsion problems (formation flight, combustion instabilities, flow control, compressor rotating stall), automotive problems (anti-lock braking, engine mapping), bioreactors, and charged particle accelerators will be presented.

Presented by researchers who spearheaded the revival of extremum seeking, the workshop will be one well integrated mini-course, designed as such by organizers who have been working jointly on these problems since 1996, rather than patched up from distinct pieces of research by an ad hoc team.

The workshop will be of interest to a broad audience of ACC attendees interested in nonlinear and adaptive control (from IEEE CSS), in optimization (from SIAM and INFORMS), as well as to industrial control engineers working on applications in electrical, mechanical (ASME), aerospace (AIAA), chemical (AIChE), and biomedical engineering.

Syllabus

8:00-9:00 History of extremum seeking, introductory algorithm for a static map, elements of stability analysis (Krstic)
9:00-9:50 ES in the presence of plant dynamics, ES compensators
for performance improvement, ES with internal model principle for tracking parameter changes (Ariyur)
9:50-10:20 COFFEE
10:20-11:10 Multiparameter ES and slope seeking (Ariyur)
11:20-12:00 Limit cycle minimization via ES, discrete time ES (Krstic
and Ariyur)
12:00-13:30 LUNCH
13:30-13:45 Application to anti-lock braking (Ariyur)
13:45-14:05 Control of combustion instabilities (Banaszuk)
14:05-14:35 Control of flow separation in diffusers (Banaszuk)
14:35-15:00 Formation flight optimization via ES (Ariyur)
15:00-15:30 COFFEE
15:30-16:00 Compressor rotating stall control (Krstic and Ariyur)
16:00-16:30 Automotive engine mapping (Popovic)
16:30-16:45 Bioreactor optimization (Krstic and Ariyur)
16:45-17:00 Beam matching in particle accelerators (Schuster)