FRTN15 Projects

Project Topics in FRTN15 Predictive Control 2011

Important Dates

You should have chosen a project and formed a project team before October 10, 2011.

Requirements

Your project will be accepted if it passes the following requirements:

A short, 5–10 pages, project report should be written. The report should be written with a word processing system.
A few projects will be selected for oral presentation. The exact presentation time will be given by the instructor, but it will typically be 5-10 minutes.

For projects that are done jointly with the course FRTN01 Real-time Systems the following is also required. These projects are market with a * after the number.

Project participants should organize the work so that real-time project and predictive control project proceed in parallel. To that purpose, software from the real-time workshops may be re-used.
A program that fulfills the specifications should have been demonstrated for your project supervisor. Each team member should be able to answer questions about the program structure and about why a certain solution has been chosen.
The project should be demonstrated during the second hour of the project presentation lecture.

Standard Projects

These projects are well related to your take home problems. They will give you a good insight into predictive and adaptive controllers and their behavior. The outcome is also quite predictable. The projects can be done entirely with pencil and paper and simulations.

Project 1 - Control of an Inverted Pendulum

A simple linearized model of an inverted pendulum is G(s)=k/(s² -b) where the input is acceleration of the pivot, the output is the angle, and k and b are unknown constants. It is difficult to make an adaptive controller for the pendulum because it may fall down during the initial transient. An alternative is to make an adaptive controller for the pendulum in the downward position. The model is then G(s)=k/(s² +b)

Let the adaptive controller tune with the pendulum in the downward position until a good performance is obtained. Use this controller to compute a controller for the upward position. Show that your proposed scheme work by simulating the system obtained. You could design the controller based on the specifications that the closedloop response should be given by

G_m(s)=a²/(s² +2ςas + a²)

Base the controller of estimation of the parameters of the model

H(z) = (b₁z+b₂)/(z² +a₁z + a₂)

which has four parameters. The problem is closely related to the problems you have already done. Use the previous results and the model parameters you used in the homework problems. Simulate your system using the real nonlinar model.

Project 2 - Control of an Inverted Pendulum

Same as project 1 but base the estimation on a continuous time system with only two parameters k and b of the model H1I. The continuous time model should be sampled and a discrete time design should be used. Simulate your system using the real nonlinar model.

Project 3 - Control of an Inverted Pendulum

Compare the approaches used in projects 1 and 2. You can use material from previous projects for this.

Control of Laboratory Processes

The idea is to try a specific control design method on a laboratory process. This is more complicated than to simulate but it gives a much better appreciation of real engineering issues in implementation of adaptive controllers. There are toolboxes and program libraries for control design and estimation which you can use. Those projects marked with a * may be done as joint projects with the course FRTN01 Real-time Systems.

Project 4* - Mass-Spring-Damper System

A mass-spring-damper system arranged for linear acceleration is available in our laboratory. Apply adaptive control for improved damping of oscillation modes.

Project 5* - Control of an Inverted Pendulum

Same as Project 1 but implement the system in a real-time environment and try it out on the real pendulum.

Project 6* - Control of an Inverted Pendulum

Same as Project 2 but implement the system in a real-time environment and try it out on the real pendulum. Approximate the continuous time controller by sampling fast and run the parameter estimator at a slower sampling rate.

Project 7* - Adaptive Control of the See-saw Process

Try indirect adaptive control of the see-saw process.

Project 8* - Control of the Helicopter Model with Gain Scheduling

Try gain scheduling control on the helicopter process.

Project 9* - Adaptive Friction Compensation

Consider a controller that stabilizes an inverted pendulum. A simple model of friction leads to a piece-wise linear systems for which the standard adaptive techniques apply. Implement an adaptive friction compensator and explore its properties. This project can be expanded to a Masters thesis.

Project 10 - Model Predictive Control of a DC servo motor

Implement a model predictive controller for the DC servo process using appropriate MPC software (MPCtools or Matlab MPC toolbox). Since the process dynamics are relatively fast there will be limits on the size of the optimization problem that can be solved. Investigate the effects of prediction horizon on stability and performance. Experiment with the use of constraints on the control signal and the output.

Project 11* - Autotuning of Robust PID Controllers

The goal of the project is to implement automatic tuning on a process with time delay. The project involves use of a new Matlab program for derivation of optimal robust PID controllers, that have been developed at the department. The incorporated PID design method has several advantages to existing methods in industrial autotuners. The program has, however, so far only been used in simulations on models and the project is therefore interesting from a research point of view.

Simulation of Adaptive Controllers

There are several simulation tools that can be used to simulated adaptive controllers. Simulink is a traditional simulator connected to Matlab. Modelica has a strong represenation in Lund.

Project 12 - Indirect Adaptive Control in Modelica

Write a toolbox for simulation of a direct self-tuning controller. Think about a suitable structure which is pedagogic and easy to use. Verify the program by applying it to Examples 3.4 and 3.5 in the book and Homework 1. This project can be expanded to a Masters thesis.

Project 13 - Simulation of Effects of Initial Conditions

Use the Simulink toolbox for indirect adaptive control and develop an educational sequence that illustrates the choice of initial conditions in the parameter estimator. You can experiment with different intial values as well as different excitation. You may have to extend the model library. Use the standard cases in the book as illustrations. This project can be expanded to a Masters thesis.

Project 14 - Simulation of Effects of Forgetting

Expand the Simulink toolbox for indirect adaptive control so that it can deal with different schemes for forgetting. Develop some experiments that illustrates the properties of the different forgetting schemes. This project can be expanded to a Master thesis.

Project 15 – Control of Dissolved Oxygen Level

This project treats control of dissolved oxygen in a bioreactor where the oxygen supply is manipulated using the stirrer speed. In batch and fed-batch cultivations the operating conditions change significantly which may cause tuning problems if a fixed controller is used. Investigate how a control strategy based on PID control and gain scheduling can be used to account for the process variations. An approximate process model is available. A possible alternative is to develop a simple adaptive controller for the process. This project can be extended to a Master thesis.

Project 16 – Extremum Control

For some processes it is difficult to find the best operating point or a suitable reference value. A classical example is control of air-fuel ratio in combustion motors where the optimum depends on temperature, fuel quality, etc. One would then like to have a way to find and track the optimum operating point. This kind of problem is often referred to as extremum control. The topic of this project is to study extremum control of two simple processes. One where the nonlinearity is of on-off-character, as in a lambda sensor, and one where the non-linearity is of saturation type.

Theoretically Oriented Projects

The following projects have a theoretic flavor. The first project is of interest for those who are studying nonlinear dynamics.

Project 17 - Chaotic Behavior of Adaptive Systems

Adaptive systems may have chaotic behavior. Verify this by investigating the simple adaptive system discussed in Section 6.2 in the textbook. Investigate the properties of the system in the boundary of the stability region in Fig. 6.1. In particular explore what happend at the corners of the stability region. Look for period doubling and explore the nature of the attractors. This project can be expanded to a Masters thesis.

Project 18 -Nonlinear Dynamics and Adaptive Control

Consider the system described by the differential equation

d²x/dt² +(a-x)dx/dt +x(x²-3x+2)=u

Mathematics Part

Let the control signal be zero. Let the parameter a have the nominal value 3. Explore the differential equation obtained. Determine equilibrium points and their character. Investigate if there are periodic solution. Determine the phase plane. Explore how the nature of the equilibria changes with the parameter a.

Control Part

Determine an indirect self-tuning adaptive controller that gives a closed loop system characterized by

d²x/dt² + dx/dt +x =u_c

Investigate how the system behaves when the command signal is

u_c(t) = vt+b sin(t)

Investigate the behavior for different values of v. Explain what happens analytically?

Project 19 - Literature Study

Pick some section of the book that you find interesting and study the proofs in full detail complemented by literature studies.

Project 20 - Literature Study

Read a paper on adaptive control in IEEE Transaction on Automatic Control or Automatica. Try to understand the article and verify it by simulation. We will
help you to select a good paper.

Project 21 - Nonlinear Adaptive Control

There are recent results on adaptive control of nonlinear systems. See e.g. Section 5.10. Study some of this methods and apply them to a simple case.

Project 22 - The Phenomenon of Peaking

There is a phenomenon called "peaking" which means that an adaptive controller may have a large initial transient. It is claimed that some of the new nonlinear methods give less peaking. Study this and try to understand what happens. This project can be expanded to a Masters thesis.

Project 23 - PI Adjustments

Investigate the MRAS with PI adjustment of parameters. Show that this is very similar to one of the nonlinear control schemes.

Project 24 - Your Own Ideas

If you have your own idea about a project please feel free to come and discuss it, but please remember that the project should be no longer than a week.

//1996 K. J. Åström/ Revised 1998, 1999, 2000, 2004, 2007, 2008, 2009, 2010, 2011 R. Johansson