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This paper is concerned with finite frequency negative imaginary (FFNI) systems. The paper introduces the concept of FFNI transfer function matrices, and the relationship between the FFNI property and the finite frequency positive real (FFPR) property of transfer function matrices is established. The paper also establishes an FFNI lemma which gives a necessary and sufficient condition on the matrices...
This paper addresses the problem of controller order reduction for linear discrete-time systems. The proposed approach considers the minimization of an upper bound on the ℓ∞-gain of the error between the system with the full controller and the system with the reduced controller. This upper bound is defined using the so-called star norm performance. The method considers explicitly time-domain performance...
We demonstrate the design of a pre- + post- + feedforward compensator that places the transmission zeros of a stabilizable and detectable multi-input multi-output linear-time-invariant plant at arbitrary locations.
It is well-known that the two situations: gain margin being infinite and phase margin being infinite are individually special cases of dissipativities with respect to suitable supply rates; the small gain theorem and passivity result being the respective theorems. However, in practice, the two margins being finite also allows concluding closed loop stability using the Nyquist stability criteria. We...
This paper considers both synthesis and analysis problems for continuous-time stochastic systems in the presence of limited information. First, a novel linear matrix inequality (LMI) optimization problem is formulated to obtain a linear quadratic controller over an additive white-noise channel subject to a power constraint. We next consider a more general setting and, using tools from information...
The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probability distributions, the intuition is to quantify the uncertainty in the response using Polynomial Chaos expansion and discard all the information provided about the randomness of the output and extract only the...
Minimum variance control is an established method in control of systems corrupted by noise. In these cases, as it is not possible to directly control the actual value of the system variables, one aims to reduce the variations instead. However, when the system noises are non-Gaussian, this approach fails because non-Gaussian noise cannot be characterised by simple measures such as variance. In these...
This paper discusses the infinite horizon static output feedback Nash games for stochastic weakly-coupled large-scale systems with state-dependent noise. It is shown that the conditions for the existence of Nash equilibria depend on the solutions of a new set of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing the asymptotic structure along with the positive semidefiniteness...
For a class of high-order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control variables without the strict triangular conditions, this paper studies the problem of state-feedback stabilization for the first time. The main contribution of this paper is the development of a systematic design approach for stochastic nonlinear systems in the absence...
This note considers the long-run aver- age cost control problem for a class of discrete-time stochastic systems. The stochastic system is assumed to be linear with respect to the state but the controls possess a general structure, possibly a nonlinear one. The main contribution of this paper is to show that the existence of a minimal second moment system state implies the existence of an optimal stationary...
In this paper we show that the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear-quadratic optimal controller) can be solved using elementary mathematics as a static optimization problem. The derivations require only a basic (undergraduate) usage of linear...
This paper describes a recent and very advantageous upgrade of the undergraduate controls laboratory in the Mechanical and Nuclear Engineering Department at Kansas State University. The current lab has been in use for about a decade. Details regarding the original hardware fundamental to the laboratory activities, including the embedded digital signal processor (DSP) and the brushless DC motor stand...
Dynamic Systems & Control is one of the most difficult courses to teach in the mechanical engineering curriculum. The subject is very mathematical and the mathematical framework is unfamiliar to novice students. Recently we began using a video game to demonstrate and teach content of the course. The game provides a natural way to align instruction with constructivist theories on how people learn...
A wooden game board named Shoot-the-Moon has interesting dynamics properties despite its simple structure of one steel ball rolling on two cylindrical rods. In this paper, we derive the equations of motion for Shoot-the-moon using an Eular-Lagrangian approach and explore its underactuated, nonlinear, nonholonomic dynamics. Two positon controllers are designed, one for a local linearization and another...
The straight beam in the ball and beam control experiment was replaced by a curved beam mounted away from its center of rotation. The resulting system is much harder to understand, model and control than the ball and straight beam. Nonetheless, the apparatus was constructed, a model was derived using Lagrangian mechanics, and a controller was designed using a linearized model and the LQR. This controller...
This paper shows how: i) (strongly) positive real; ii) (asymptotically stable) dissipative (strictly-input) passive; and iii) (Lm2-stable strictly) positive; continuous time system definitions are equivalent for linear time invariant (LTI) systems. In parallel this paper shows how: i) (strictly) positive real; ii) (asymptotically stable) dissipative (strictly-input) passive; and iii) (lm2-stable strictly)...
Combining solid oxide fuel cell and gas turbine (SOFC/GT) system is a promising concept for future clean and efficient power generation. An SOFC/GT system exploits the complementary features of the two power plants, where the GT recuperates the energy in the SOFC exhaust stream and thereby boosting the overall system efficiency. Through model based transient analysis, however, it is shown that the...
Solid Oxide Fuel Cell (SOFC) power systems are under active development for a range of applications. Tight thermo-chemical operating constraints together with strong thermal coupling in SOFC systems present significant challenges for system and control design. To facilitate model-based system design addressing steady state and transient performance requirements, first principles based component and...
Product quality and uncertainty, e.g. of demand, quality etc., are two important issues in the long-term planning of natural gas production systems. This paper presents a stochastic pooling problem formulation to address these two issues, where the qualities of the flows in the system are described with a pooling model and the uncertainty in the system is handled via a multi-scenario, two-stage stochastic...
We demonstrate an alternative approach for the hedging of flexible energy conversion networks appropriate for use in campus scale and municipal scale utilities with complex energy requirements, fuel sources, and operational flexibility. This new approach utilizes empirical modeling of price models for alternative commodity fuels coupled with a previously reported class of bilinear models for estimating...
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