On sliding mode observers via equivalent control approach

In this paper, a decentralized controller is designed for cross coupled MIMO Twin rotor aerodynamic system (TRAS). The decentralized controller design is done by decoupling the MIMO system into two decoupled, a pitch and a yaw system. Then 2-DOF controller is designed using control technique in continuous and discrete time. The performance of these controllers are tested through extensive simulations in MatLAB and results are compared between discrete and continuous time systems.

Sliding Mode Control in Discrete Time Linear Systems

This paper presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations that is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. Using mixed-monotone decompositions, the proposed observer is correct and positive by construction without the need for additional constraints/assumptions. This, in turn, allows us to directly leverage techniques for positive systems to design an ISS and L1-robust interval observer via mixed-integer (linear) programs instead of semi-definite programs with linear matrix inequalities. Further, our observer design offers additional degrees of freedom that may serve as a surrogate for coordinate transformations. Finally, we demonstrate the effectiveness of our proposed observer on some CT and DT systems.

American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison

In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.

It is shown how genetic algorithms can be applied for system identification of both continuous and discrete time systems. It is shown that they are effective in both domains and are able to directly identify physical parameters or poles and zeros. This can be useful because changing one physical parameter might affect every parameter of a system transfer function. The estimates of poles and zeros are then used to design a discrete time pole placement adaptive controller. Simulations for minimum and nonminimum phase systems and a system with unmodeled dynamics are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

To reduce simulation times, continuous time (CT) sigma-delta modulators can be modeled as equivalent discrete time (DT) systems so that DT simulators can be used. This method reviews two popular methods of converting from CT to DT and applies them to a second order CT complex ADC. The ADC being designed is for use with a low IF receiver and achieves 80dB SNDR in simulation.

SummaryLinear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.

We present a survey of results on models of consensus in asynchronous multiagent systems with discrete and continuous time. We consider mathematical methods developed over recent years, which are used in the analysis of stability, stabilization, and consensus problems for linear multiagent systems with discrete time. These methods are based on the idea of using the notion of joint/generalized spectral radius of a set of matrices to analyze the rate of convergence of matrix products with factors drawn from certain sets of matrices with special properties.

The model-following servo controller is useful for the nonlinear robot arm. We analyzed unit step response of this controller and cleared transient characteristics in both cases of continuous and discrete time systems. We used linear quadratic optimal control law with integral action and a criterion function considering the square of control error and weighted controlling input. The overshoot is always 8.1% regardless of continuous time, discrete time and the weight for controlling input. A function of the weight and the sampling time determines the speed of responses.

On the Consistency of the Lucas Pricing Formula

In this paper, we consider nonlinear discrete time systems modeled with polytopic uncertain linear systems. We develop the CPWL (Canonical Piecewise Linear) approach proposed by Labit [1] to the case of discrete time systems associated with the new discrete time stability condition proposed by de Oliviera [2] then improved by Daafouz [3]. The obtained linear matrix inequalities condition leads to necessary and sufficient, and less conservative control design condition. This method (Discrete time -CPWL approach and poly-quadratic stability) takes also advantages of the systematic design of robust controllers in one shot and the insuring scheduling for the nonlinear discrete time system control.

A simple control structure in servo system is occasionally needed for simple industrial application which precise and high control performance is not exessively important so that the cost production can be reduced efficiently. Simplified vector control, which has simple control structure, is utilized as the permanent magnet synchronous motor control algorithm and genetic algorithm is used to tune three PI controllers used in simplified vector control. The control performance is obtained from simulation and investigated to verify the feasibility of the algorithm to be applied in the real application. Simulation results show that the speed and torque responses of the system in both continuous time and discrete time can achieve good performances. Furthermore, simplified vector control combined with genetic algorithm has a similar performance with conventional field oriented control algorithm and possible to be realized into the real simple application in the future.

Optimal Hedging in Discrete and Continuous Time

Continuous approximation of collective system behaviour: A tutorial