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Luis Rodrigues Associate Professor Department of Electrical & Computer Engineering Concordia University |
| 1515 St. Catherine W., EV12.111 Montréal, Québec, Canada H3G 2W1 | |
| Tel.: (514) 8482424 Ext.3135 Fax.: (514) 8482802 Email: luisrod at encs.concordia.ca | |
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Research Interests
All of these research interests fit into my three primary focus areas within the theory and practice of automatic control systems: (1) the development and validation of mathematical models of complex dynamic systems; (2) the computer-aided analysis of the stability and performance properties of these systems and (3) the computer-aided synthesis and the validation of automatic controllers that can improve stability and performance of these systems. My main research interest, besides increasing knowledge and understanding, is the development of technology leading to novel automatic controllers that can be used in industry to enhance performance of engineering systems. To synthesize such novel controllers, it is essential to understand the physical principles behind the particular engineering system to be controlled to be able to develop an accurate mathematical model that can then be used for controller design.  >
My research group is working on novel switching controller design methods that can be cast as optimization problems that can then be solved numerically. The focus is on a particular class of switched controllers with a special switching structure, called piecewise-affine controllers. The final objective is the development of modeling and synthesis algorithms that can be easily programmed into available computer-aided design software such as, for example, Matlab/Simulink (a trademark of The Mathworks Inc.) and then interfaced with a real-time operating system for implementation in engineering systems. The advantages of considering switched controllers in engineering applications is twofold: (1) switched controllers add flexibility and can therefore increase performance as compared to fixed controllers (2) certain systems have a physical structure that prevents them from being stabilized by a fixed controller that is smooth and time-invariant. An example of situation (1) is the fact that most engineering systems have trade-offs, for example between transient time performance and steady state performance, and are therefore more naturally controlled by a switched controller with different properties in transient and steady state than by a fixed controller. For example, engine valves have stringent performance requirements of very fast transient response and small contact velocity. An example of situation (2) is the control of mechanical systems with nonholonomic constraints such as, for example, automatic parking of an automobile. Another important area of research in my group is the development of a systematic methodology for extension of local linear controllers to global or semi-global piecewise-affine controllers that can provide the same performance of the linear controller close to a desired operating point, but that are however guaranteed to stabilize the system even when operating far from the desired point. This methodology holds a strong potential to be implemented in those engineering applications in industry that currently use only local linear controllers that cannot guarantee stability under large perturbations. top of page
My research group has been working on switched (piecewise-affine) controller synthesis for applications to flight simulation of new autopilots, control of spacecraft isolated or in formation (in collaboration with the Canadian Space Agency – CSA), uninhabited air vehicles (UAVs) and micro air vehicles (MAVs): aircraft (in collaboration with Dr. Dolatabadi and Dr. Rabbath) and helicopters (in collaboration with Dr. Gordon). One of the main difficulties in controlling these vehicles is the fact that their dynamics are highly nonlinear and, as one scales down these vehicles to the micro scale (considered to be around 15 cm wingspan or even less), aerodynamics at small Reynolds numbers must be considered instead of the more conventional large Reynolds number condition. On top of this, the communication between vehicles in formation and the associated delays and possible package losses of the wireless network add complexity to the task of controller design. The computer-aided design methodology we are developing, approximates the nonlinear terms by piecewise-affine terms and then designs a piecewise-affine controller for this approximate model that is guaranteed to stabilize the original system for small enough modeling errors. The research of our group has focused so far on the following aerospace applications: (1) modeling, simulation and piecewise-affine controller design for a UAV (built by Capstone students supervised by me at Concordia University in the academic year of 2003-2004), (2) modeling and piecewise-affine control of an aerobatic helicopter (in collaboration with Dr. Gordon) (3) satellite integrated sensor fusion and piecewise-affine control (in collaboration with CSA) (4) navigation and control of MAVs. Concordia has had several groups working on the design and manufacturing of MAVs. The first MAVs were manufactured in April 2006. One of these MAVs won the Canadian Society for Mechanical Engineering (CSME) prize for best student design in 2006. This is work in collaboration with Dr. Dolatabadi. Future work in collaboration with Dr. Rabbath will include vehicle coordination and control. 
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Switched controller synthesis is also being investigated in my research group for automotive applications, mostly in active suspension systems, ABS and engine valves. In suspension systems, magneto-rheological actuators exhibit a characteristic behavior that can be described accurately by a piecewise-affine function. The dynamic models are thus naturally in the framework of piecewise-affine systems for which the computer-aided design methodology being developed in my group is the appropriate tool to be used. In ABS systems, the variation of the coefficient of adhesion to the road versus slip coefficient can be accurately approximated by a piecewise-affine characteristic with only three sectors. The methodology being developed in my research group can then be applied to design controllers that guarantee a working point close to the maximum coefficient of adhesion to the road. Finally, the unthrottled control of engine valves has the potential to be made possible using voice coil actuators controlled by a Pulse Width Modulation (PWM) controller that switches between two voltage levels: one for good performance in the transient period and another for good performance in steady state. The analysis and synthesis of such controller falls under the framework of switched control and the tools developed in our group are also applicable (collaboration with Dr. Hong). 
top of page Speech signals are nonstationary signals. However, for speech frames of very small periods of time (typically on the order of miliseconds), the speech signal can be assumed to be stationary. For articulatory models (models of the mechanical articulators, such as lips, tong and teeth) of speech frames of this duration,a linear model turns out to be accurate. Therefore, switched linear systems are adequate articulatory speech models for speech frames having minutes to hours of speech. The research in this area, in collaboration with Dr. Kroeker from Eliza Corporation has focused on the modeling of speech production systems and the study of properties such as controllability and state transfer, as well as the energy of speech. In the future, controller synthesis for speech production and speech recognition will be targeted. 
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The model of inventory in production systems leads naturally to a constrained switched system. The switching variable is the stock level. When the stock level is positive, the produced parts are being stored. When the stock level is negative it leads to backorders, which means that orders for production of parts are coming in and there are no stocked parts to immediately meet the demand. These two situations correspond to different models that are switched based on the sign of the stock level. A state feedback controller that forces the stock level to be kept close to zero (sometimes called a just-in-time policy), even when there are fluctuations in the demand, can be designed using piecewise-linear H-infinity control theory. The synthesis of the state feedback controller that quadratically stabilizes the production dynamics and at the same time rejects the external demand fluctuation (treated as a disturbance) can be cast as a set of linear matrix inequalities (LMIs) and solved numerically in a efficient way, given that the resulting optimization problem is convex. Future work will concentrate on the study of interconnected production systems in supply chains (collaboration with Dr. E.-K. Boukas from Ecole Polytechnique). top of page If you are a student with a background on either electrical or mechanical and aerospace engineering, and you are interested in one of these topics, here is what I am looking for in the background of students:
I am the founder of the HYbrid CONtrol Systems (HYCONS) Lab at Concordia University. Control Theory
Aerospace Control
Automotive Suspension Control
From left to right: Behzad Samadi, KyungJae Baik, Scott Casselman, Luis Rodrigues, Shaun DiSalvo, Xiaoxi Huang, Giancarlo Luglio Collaborations with Postdoctoral Fellows:
The following students have worked in my lab and have already graduated:
Graduate Degrees: Undergraduate Degrees: |