Date of Award
Fall 11-24-2023
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Electrical and Computer Engineering
First Advisor
Susan Schneider
Second Advisor
Edwin Yaz
Third Advisor
Chung Seop Jeong
Abstract
Proportional Integral Derivative control is the most dominant control technique used in industrial applications. Multivariable systems typically have multiple inputs and outputs which means the number of individual PID controllers and gains to be increased. The tuning of these systems to meet specific performance criteria would be impractical in these situations. The transient performance of a system can be modeled through the locations of its poles and zeros and through pole placement, we can mold the response to meet certain criteria. Linear Matrix Inequalities is an efficient way to solve this pole placement problem through the use of Regional Eigenvalue Assignment (REA). REA allows through the solving of an LMI, to assign the eigenvalues of a system within a prescribed region. This thesis derives a state feedback PID controller for a continuous linear time invariant multivariable systems that assigns the poles of a system through Regional Eigenvalue Assignment through solving Linear Matrix Inequalities. A double mass spring damper system is used as a case study to show the effectiveness of the method. First, performance criteria determined by the designer are used to define regions in the complex plane. Next an LMI is solved in order to find the control gains necessary to place the eigenvalues within the region. Then a reduced order observer is constructed in order to estimate unknown states for feedback control. An additional performance criterion, H2 control, is also used to add energy related optimal performance to the result. It is shown that the method presented in this thesis allows one to find PID controller gains that reduce the effort of tuning multivariable systems for certain time domain criteria. It is also shown that through the combination of H2 control and REA, the eigenvalues of a system can be placed in an optimal way with regards to a performance output while still remaining within the prescribed LMI region.