Short Course on Principles of System Identification

This 3-day short course is intended to provide the industrial practitioner with a comprehensive survey of the various methods and procedures for performing system identification in the process industries. Emphasis is given to identification topics that have the most impact in practice. The course will provide the course participant with:

  • A better understanding of the fundamentals of system identification which in turn will enable the participant to make judicious, intelligent choices of methods and design variables in system identification. The user will get a feeling for the possibilities and limitations of various system identification techniques. The differences between linear and nonlinear system identification will also be addressed.
  • Increased experience with system identification technology via a comprehensive series of computer lab exercises that will give students a "hands-on" feel for the course topics. At the conclusion of the course, the student should feel comfortable using the System Identification Toolbox in MATLAB to apply and test the course topics.
  • Knowledge of system identification research efforts at Arizona State University and other academic programs, and how these can impact industrial operations.

The course material is presented in six modules over the three day period (an additional module focusing on nonlinear identification issues is available in a 3.5 day version of the course). Each module is scheduled for four hours and is devoted 50% to lecture and 50% to laboratory exercises via MATLAB with SIMULINK. Labs involve simulated plant models and real process data, although students may be able to use some of their own data sets if so desired. Significant emphasis is given to the use of the graphical user interface which is available in the System Identification toolbox (ver. 4). Each student will be provided with a set of course notes containing copies of all viewgraphs and a collection of MATLAB m-files used in the laboratory exercises. These will remain as reference to the course participant for continued study at the conclusion of the course.

Course Organization:

Day 1:

  • Module 1: Course Overview, Signals and Systems Concepts
  • Module 2: Input Signal Design and Nonparametric Estimation

Day 2:

  • Module 3: Parametric Model Estimation and Validation
  • Module 4: Control-Relevant Identification

Day 3:

  • Module 5: Closed-loop Identification
  • Module 6: Multivariable System Identification

An additional module (Issues in Nonlinear and Semiphysical System Identification) is also available; with the additional module, the course extends to 3.5 days.

Module Description:

  1. Signals and Systems Overview: Background material on signals and systems concepts which are the key to successful system identification is discussed. The material in this session is revisited (within the context of specific model structures and techniques) throughout the remainder of the course. Specific topics include: differential equations, Laplace transforms, frequency responses, difference equations, stationarity, autocorrelation, crosscorrelation, power spectra.

  2. Input Signal Design and Implementation; Nonparametric model estimation: The use and design of random and deterministic signals as inputs for system identification is presented. Among the signals presented are pulse, step, Random Binary Sequence (RBS), Pseudo Random Binary (PRBS), and m-level Pseudo Random (m-PRS) inputs. Emphasis is given to the systematic design of "plant-friendly" input signals (i.e., signals that can be introduced while the plant is in normal operation), the effective use of a priori information in input signal design, and real-time implementation aspects.

    Nonparametric estimation considers the use of correlation and spectral analysis to obtain estimates of the plant impulse, step and frequency responses from identification data. The effectiveness of these methods as a means for getting useful precursor models for parametric system identification is discussed.

  3. Prediction-Error Model Structures, Parameter Estimation and Classical Model Validation: Fundamental requirements for parametric estimation, particularly with regards to identifiability and requirements for consistent (asymptotically unbiased) estimation, are presented. Parametric estimation using one-step ahead prediction error model structures and estimation techniques (ARX, ARMAX, Box-Jenkins, FIR, Output Error) is described. These methods rely on regression (both linear and nonlinear) to compute the model parameters; all are supported by the functionality of the System Identification toolbox in MATLAB. The validation portion of the module presents the myriad of classical techniques (simulation, crossvalidation, residual analysis, etc.) for determining adequacy of the estimated models.
  4. Control-Relevant Identification: This portion of the course emphasizes techniques that incorporate closed-loop performance requirements in the identification procedure (control-relevant identification). Topics in the control-relevant identification discussion include control-relevant parameter estimation using prefiltering, control-relevant input signals (e.g., Schroeder-phased inputs), uncertainty estimation for robust control, and integrated identification with PID and digital controller design.

  5. Closed-Loop Identification: The discussion on closed-loop identification addresses fundamental limitations associated with the presence of feedback in the system. Students will understand why identification from plant normal plant operating records (failing to meet certain fundamental conditions on input design and model structure) is often unsucessful in providing useful models. Topics to be discussed include identifiability requirements for closed-loop identification, signal injection points for closed-loop identification, nonparametric closed-loop identification via correlation and spectral analysis, and considerations involved in using parametric estimation methods with closed-loop data (indirect and direct approaches). If time permits, control-relevant, closed-loop identification via iterative refinement will be discussed.

  6. Identification of Multivariable Systems: Many issues in multivariable identification extend naturally from single-input, single-output concepts. Additional issues involved in multivariable system identification include: 1). experimental /data generation issues: (multivariable Random Binary and Pseudo-Random Binary inputs, "zippered" Schroeder-phased inputs), 2) multivariable parameter estimation (MISO PEM, MIMO ARX, state-space models estimation, model reduction), and 3) integration of identification and control geared to popular industrial multivariable control algorithms, i.e., model predictive control. As before, emphasis will be given to methods that complement industrial practice. Case studies in this module include the Jacobsen-Skogestad high purity distillation column and the Shell Heavy Oil Fractionator benchmark problems.

  7. Issues in Nonlinear and Semiphysical System Identification: Similarities and differences from linear system identification is discussed. Many results from linear system identification still hold when things go nonlinear and, to some extent, this knowledge and intuition from linear system identification can be very useful. We will point out some of the most important changes and pitfalls. Some nonlinear black-box models which are generalizations of linear models (Volterra, NARX, Hammerstein) as well as "trendy" nonlinear identification techniques (neural network-based ID, Model-On-Demand) will be presented.

    The traditional black-box identification approach does not make use of any prior knowledge about the process. However, prior knowledge can be very valuable (i.e., do not estimate what you already know). Different ways to combine physical knowledge and black-box techniques will be discussed.

Course Availability:

On-site instruction is the most efficient and cost-effective way of receiving this course. The course has been taught both on the ASU campus and at a diverse number of academic and industrial sites in North and South America, Europe, and Asia since 1994.


Daniel E. Rivera is a Professor of Chemical Engineering in the School of Mechanical, Aerospace, Chemical, and Materials Engineering at Arizona State University and Program Director for the ASU Control Systems Engineering Laboratory. Prior to joining ASU he was an Associate Research Engineer in the Control Systems Section of Shell Development Company. He received his Ph.D. in chemical engineering from the California Institute of Technology in 1987, and holds B.S. and M.S. degrees from the University of Rochester and the University of Wisconsin-Madison, respectively.  He has been a visiting researcher with the Division of Automatic Control at Linköping University, Sweden, Honeywell Technology Center, the University "St. Cyril and Methodius" in Skopje, Macedonia, the National Distance Learning University (UNED) in Madrid, Spain, and the University of Almería in Andalucía, Spain.

 His research interests include the topics of robust process control, system identification, and the application of control engineering principles to problems in process systemssupply chain management, and prevention and treatment interventions in behavioral health. Dr. Rivera was chosen as 1994-1995 Outstanding Undergraduate Educator by the ASU student chapter of AIChE, and was a recipient of 1997-1998 Teaching Excellence Award awarded by the College of Engineering and Applied Sciences at ASU.  In 2007, Dr. Rivera was awarded a K25 Mentored Quantitative Research Career Development Award from the National Institutes of Health to study control systems approaches for fighting drug abuse.  Read an ASU news article describing the NIH grants funding this work and related research in optimized behavioral interventions.

For more information, please contact Professor Rivera at or at 480-965-9476.