17.1 Overview of Topics Covered in This Textbook

In the next few pages we attempt to concisely review the topics covered in this textbook. This summary should assist you in preparing for a final examination in a process control course, for example. It also serves the purpose of providing a quick way of helping you determine what topics you would like to understand better. In the next section these topics are reviewed in the chronological order presented in the text. In the subsequent section a concise review of the material presented in the modules is presented.

Chapters

Chapter 1 provided the motivation for process control, while Chapter 2 introduced fundamental models. Chapter 3 presented dynamic behavior, with a focus on transfer functions. Chapter 4 covered the development of empirical models, including continuous time step responses, as well as the identification of parameters for discrete-time models. Chapter 5 provided an introduction to the analysis of closed-loop control strategies, introducing the idea of a block diagram. Chapter 6 presented PID controller tuning techniques, followed by frequency response analysis in Chapter 7. Many advanced control techniques rely on the use of a process model embedded in the control strategy; Chapter 8 covers the Internal Model Control strategy. Internal model controllers can often be rearranged to form a PID controller, as shown in Chapter 9. Improved disturbance rejection is the main motivation of the cascade and feedforward techniques presented in Chapter 10. Enhancements to PID control, including autotuning, integral windup protection, and nonlinear approaches are discussed in Chapter 11. Ratio, split-range and selective controllers are presented in Chapter 12. The interaction of multiple SISO loops, with the RGA as the main analysis tool, is developed in Chapter 13. In Chapter 14, right-half-plane transmission zeros indicate dynamic performance limitations; the singular value decomposition provides insight about possible steady-state performance limitations. The topic of plantwide control is the focus of Chapter 15, followed by model predictive control in Chapter 16. Specific topics are presented in the pages that follow.

Given a process, be able to do the following:

• Identify the control objective and the state, output, manipulated, and disturbance variables

• Develop the fundamental nonlinear model

• Solve for the steady state

• Linearize the nonlinear model about the steady state to find the state-space model

• Find the transfer functions relating each input to each output

• Convert to different sets of units

Given experimental step responses, the reader should be able to estimate parameters for low-order transfer function models that match the measured process output.

Given steady-state information, the reader should be able to do the following:

• Convert deviation variable results to physical variable results

• Convert physical variable results to deviation variables

Given a process transfer function, be able to

• Relate the gain-time constant form and the pole-zero form

• Relate poles and time constants

• Relate the location of a pole in the complex plane to the speed of response

• Consider a first-order + dead time transfer function (Why does the first-order Padé approximation for dead time provide a good approximation for the response to a step input? Hint: Think of RHP zeros.)

• Use the final- and initial-value theorems of Laplace transforms

Given a physical process with feedback control (a process instrumentation and control diagram), the reader should be able to do the following:

• Draw the block diagram for any type of feedback control (all variables should be clearly identified on the block diagram

For a given block diagram, the reader should be able to do the following:

• Derive the closed-loop transfer functions (for example, relate the setpoint to the output for a feedback control scheme)

• Relate the disturbance to the output for a feedback control scheme

For a given process transfer function, the reader should be able to do the following:

• Determine the offset due to proportional feedback control

• Perform a closed-loop Ziegler-Nichols (continuous oscillation) test

• Compare the performance of Ziegler-Nichols and Tyreus-Luyben suggested tuning parameter values

• Use the Routh stability criterion to determine if a closed-loop system is stable (the denominator of your closed-loop transfer function will usually be a polynomial with an order of 2–4

• Determine the range of tuning parameter values that will yield a stable feedback system if the controller tuning parameters are not given

• Use the direct synthesis method to find a control algorithm that yields a desired closed-loop response. Find the corresponding PID parameters if the controller has PID form (sometimes in series with lead-lag)

• Calculate the poles and discuss the response characteristics for a closed-loop transfer function that results in a first or second-order polynomial

• Discuss the response characteristics if you are given the closed-loop poles for a higher order closed-loop polynomial

Given a Bode diagram of g_c(w)g_p(w), be able to do the following:

• Determine the gain and phase margins

• Use that information to calculate the amount of additional deadtime allowable before instability occurs

Given a Nyquist diagram of g_c(w)g_p(w), be able to do the following:

• Determine if the closed loop system will be stable

• Understand the relationship between Bode and Nyquist plots (How is the information from a Bode plot translated to the Nyquist diagram? How is information of the Nyquist diagram translated to a Bode plot?)

Understand that the closed-loop Ziegler-Nichols method is equivalent to finding the proportional controller gain where the phase angle is –180^o when the open-loop (g_c*g_p) amplitude ratio is one.

For a given transfer function the reader should be able to:

• Determine the magnitude of the output from the transfer function at low input frequencies and at high input frequencies

• Understand what is meant by the term "nonminimum phase"

• Be able to determine if a transfer function is proper, semi-proper, or improper

Be able to handle the complete IMC design procedure for a given process transfer function:

• Factor g_p(s) into minimum-phase and nonminimum-phase elements {good [g_p-(s)] vs. bad [g_p+(s)] stuff}

• Invert the minimum phase elements to form the ideal IMC controller

• Cascade the ideal IMC controller with a filter that is high enough order to form a physically realizable IMC controller

• Determine what the closed-loop response will look like for an IMC scheme with a perfect model

• Understand the effect of l, the IMC filter time constant, on the closed-loop response (How does l impact the robustness? A good first guess for tuning l is to use roughly one third to one half the dominant time constant, depending on the amount of time-delay and model uncertainty; note that l has units of time)

• Know that the IMC-based PID procedure will give the same closed-loop results as the IMC strategy when there are no time delays (the behavior will be different when there are time delays because the IMC-based PID procedure uses a Padé approximation for the time delay)

Design a physically realizable feed-forward controller

Derive equivalent transfer functions to analyze a cascade-control strategy as a standard feedback control strategy

Use ARW techniques (controllers with integral action can exhibit "reset windup" when the manipulated input becomes constrained)

For multivariable systems, the reader should be able to do the following:

• Use the RGA for input-output pairing for MVSISO systems

• Renumber the inputs and outputs such that the favorable RGA pairings appear on the diagonal of the new gain matrix

• Realize that you should never pair on a negative or zero relative gain

• Find the structure of the control matrix that corresponds to the RGA pairing that has been selected

• Find the closed-loop transfer functions for any multivariable block diagram

• Realize that the order of multiplication for matrices is critical

• Implement steady-state decoupling

• Calculate multivariable transmission zeros

• Use a singular value decomposition to understand directional effects

• Implement MV IMC, using a diagonal factorization

For a system with more than two inputs and two outputs, the reader should know the following:

• To check the RGAs of all reduced-order structures (this is to make certain that when a control loop is out of service, the reduced order system is not failure sensitive)

Place control loops on a process flow sheet (one heuristic is that one stream in a recycle loop should be under flow control)

Understand the basic idea behind MPC. For the step response-based technique of DMC, understand

• How the model length (N) is determined

• Are longer prediction horizons (P) more robust than shorter ones?

• Are shorter control horizons (M) more robust than longer ones?

Modules

The modules in the final section of the text provide detailed application examples to illustrate the techniques presented in the Chapters. Module 1 reviews MATLAB, while Module 2 covers SIMULINK. Numerical integration of ordinary differential equations using MATLAB is presented in Module 3, while Module 4 presents useful functions available in the Control System Toolbox. An isothermal CSTR with a series/parallel reaction structure (the van de Vusse reaction) is studied in Module 5. Frequency response techniques are used to analyze the classic first-order + dead time model in Module 6. Biochemical reactors and the classic exothermic CSTR are convered in Modules 7 and 8, respectively. Steam and surge drum level control problems differ significantly, as presented in Modules 9 and 10. Batch reactors are studied in Module 11, followed by biomedical systems in Module 12. Linear and nonlinear effects in distillation are discussed in Module 13. A set of case studies is summarized in Module 14; these are particularly useful for open-ended final projects in a typical process control course. Flow and digital control, Module 15 and Module 16, complete the text.