Department: Electrical Engineering and Computer Science

A feedback control system regulates an output variable based on information from the output variable itself. It is a type of closed loop control where the control is dependent on the controlled variable. The system which is being controlled is called a plant.

Depending on the specifications, a well-designed feedback system can be one where:

• System output is following commands with very high accuracy.
• Disturbances are rejected.
• Sensitivity to uncertain system parameters is lower.
• Plant’s stability problems are resolved.
• The dynamics of a plant are improved. Those include response time, overshoot, degree of stability, and more.

Feedback system performance can be specified in either the time domain or the frequency domain.

In order to improve system’s performance, various techniques of compensation can be used depending on the designer’s objective. One approach is a series or cascade compensation, where the compensating elements are in series with the plant.

Types of series compensation:

• Proportional control – gain of the loop is varied in order to control the degree of stability.
• Lag compensation – a pole and then a higher frequency zero are placed well below the crossover frequency; this compensation can improve error magnitudes in a system’s responses because it allows for higher gains; however it introduces a long tail transient in the system’s time response.
• Lead compensation – a zero and then a pole are placed around the crossover frequency. This compensation allows us to increase crossover frequency and therefore results in the fastest transient response; however, large bandwidth leads to greater noise sensitivity; low frequency behavior is not improved by this compensation. On the contrary, the steady state error magnitude might increase.
• Lead and lag compensation – we can combine both types of compensation to have improved behavior at all frequencies; lead will improve the bandwidth of the system and ensure reasonable phase margin; lag will provide for higher low frequency gain and therefore low steady state error magnitudes.

Another approach is using minor loop compensation. This type of compensation is used when noise, nonlinearities, and uncertainties can considerably affect characteristics of the plant. The two most frequently used types are single pole compensation and two-pole compensation.

MathWorks, Inc. is currently the leading developer and supplier of system analysis and design software. Matlab, one of their core products, is an interactive program for numerical computation and data visualization; it is used extensively by control engineers for analysis and design. There are many different toolboxes available which extend the basic functionality of Matlab into different application areas. In the area of systems control, the Control System Toolbox contains specialized tools for the design and analysis of automatic control systems. The toolbox provides various control design methods, including root locus and pole placement. A Graphical User Interface allows the user to evaluate control system performance using standard plotting techniques such as Bode, Nichols, Nyquist, pole-zero, and more. Matlab and the Control System Toolbox are supported on Unix, Macintosh, and Windows environments.

In addition to the MathWorks’ software tools, some third-party solutions have been developed. Most of them however build on top of the Matlab computing environment. The most relevant examples are:

• ACD – Automatic controller design and automatic robust controller design by Delzer-Kybernetic in Germany. ACD claims to be able to automatically calculate the parameters for well-known compensator types (P, PI, PD, PID). The control parameters are optimized with respect to a plant model and additional user options.
• RaPID – Robust Advanced PID Control by Intelligent Systems Modeling and Control, Inc. This tool helps in the design and implementation of PID controllers. It claims to integrate data acquisition, automated process modeling, and optimal PID control design with an emphasis on engineering specifications and requirements.
• Software Laboratory for Control Education – hands-on software for control education developed at the McMaster University. The Software Laboratory includes hands-on exercises for the following technologies: single-loop simulation, stability analysis and frequency response, cascade, feed-forward, level control, chemical reactor control, and multivariable control via decentralized single-loop controllers or centralized Dynamic Matrix Control.
• Controls Tutor – graphical user interface for visualizing classical control concepts developed by Terasoft, Inc. The software is meant to help students understand classical control concepts. When Controls Tutor is coupled with The Student Edition of MATLAB by MathWorks, a student can study control characteristics without having to first learn any Matlab syntax.

2.1 Focus

My thesis research will focus on linear feedback systems’ properties and compensation techniques. Non-minimal phase systems and nonlinear systems will not be included unless time permits. The basic functionality of my software tool will be focused on solving for a good series compensator. Later I will begin working on other compensation methods such as minor loop feedback compensation. To simplify analysis, the controller will be positioned in the forward path of the system. After this part is functional, I will try implementing methods to handle compensation in the feedback path.

2.2 Functionality of my system

An enduser provides a system model by one of these three methods:

• specifying the poles, zeros, and gain of the open loop system
• specifying the function of the loop transmission
• using a mouse click on the Bode magnitude plot to specify poles and zeros, as well as a similar way of specifying DC gain

After specifying the system model, the user can:

• Perform systems frequency and time domain analyses (see 1.2.1)
• Provide the desired specifications that should be met and run the automatic compensation tool.

My thesis software toolkit will consist of two major parts:

• The backend responsible for calculations and algorithm solving based on user input specifications and uncompensated system parameters.
• The Graphical User Interface (GUI) responsible for handling user inputs, and presenting the appropriate visuals such as graphs, plots, or numerical values.

3.1 Milestone Specifications:

3.2 Supervision on the project:

My thesis advisor, Professor J. K. Roberge, has agreed to discuss my project weekly on either Tuesdays or Thursdays of each week as necessary and as time permits him.

As a result of my research, I plan on delivering:

1. A software toolkit useful for analyzing feedback systems.

The toolkit will be written in Java since it can be easily moved to many different platforms as well as run on a web browser.

2. Written document.

The thesis document will describe the research and implementation done to complete my thesis. The appropriate background on the topic of feedback compensation and software development in the area will be presented. I will document the methods I used to analyze the system and their advantages. I will present the algorithms used for determining the tradeoff issues. I will include documentation on the use of this toolkit. The thesis will contain appropriate visual aids such as graphs, plots, user interface prints, and other examples. All the code will be included in the appendix.

[1] James K. Roberge, Operational Amplifiers: Theory and Practice, New York, NY: John Wiley & Sons, Inc., 1975.

[2] L. A. Gould, W. R. Markey, J. K. Roberge, D. L. Trumper, Control Systems Theory, Cambridge, MA: Massachusetts Institute of Technology, 1997.