Abstract: A vibration isolation technology for precise position
control of a rotary system powered by two permanent magnet DC
(PMDC) motors is proposed, where this system is mounted on an
oscillatory frame. To achieve vibration isolation for this system,
active damping and disturbance rejection (ADDR) technology
is presented which introduces a cooperation of a main and
an auxiliary PMDC, controlled by discrete-time sliding mode
control (DTSMC) based schemes. The controller of the main
actuator tracks a desired position and the auxiliary actuator
simultaneously isolates the induced vibration, as its controller
follows a torque trend. To determine this torque trend, a
combination of two algorithms is introduced by the ADDR
technology. The first torque-trend producing algorithm rejects
the disturbance by counteracting the perturbation, estimated
using a model-based observer. The second torque trend applies
active variable damping to minimize the oscillation of the output
shaft. In this practice, the presented technology is implemented
on a rotary system with a pendulum attached, mounted on a
linear actuator simulating an oscillation-transmitting structure.
In addition, the obtained results illustrate the functionality of the
proposed technology.
Abstract: The random dither quantization method enables us
to achieve much better performance than the simple uniform
quantization method for the design of quantized control systems.
Motivated by this fact, the stochastic model predictive control
method in which a performance index is minimized subject to
probabilistic constraints imposed on the state variables of systems
has been proposed for linear feedback control systems with random
dither quantization. In other words, a method for solving optimal
control problems subject to probabilistic state constraints for linear
discrete-time control systems with random dither quantization has
been already established. To our best knowledge, however, the
feasibility of such a kind of optimal control problems has not
yet been studied. Our objective in this paper is to investigate the
feasibility of stochastic model predictive control problems for linear
discrete-time control systems with random dither quantization. To
this end, we provide the results of numerical simulations that verify
the feasibility of stochastic model predictive control problems for
linear discrete-time control systems with random dither quantization.
Abstract: In this paper, we consider the parametrization of the
discrete-time systems without the unit-delay element within the
framework of the factorization approach. In the parametrization,
we investigate the number of required parameters. We consider
single-input single-output systems in this paper. By the investigation,
we find, on the discrete-time systems without the unit-delay element,
three cases that are (1) there exist plants which require only one
parameter and (2) two parameters, and (3) the number of parameters
is at most three.
Abstract: In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l2-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.
Abstract: Recently, feedback control systems using random dither
quantizers have been proposed for linear discrete-time systems.
However, the constraints imposed on state and control variables
have not yet been taken into account for the design of feedback
control systems with random dither quantization. Model predictive
control is a kind of optimal feedback control in which control
performance over a finite future is optimized with a performance
index that has a moving initial and terminal time. An important
advantage of model predictive control is its ability to handle
constraints imposed on state and control variables. Based on the
model predictive control approach, the objective of this paper is to
present a control method that satisfies probabilistic state constraints
for linear discrete-time feedback control systems with random dither
quantization. In other words, this paper provides a method for
solving the optimal control problems subject to probabilistic state
constraints for linear discrete-time feedback control systems with
random dither quantization.
Abstract: Recently, optimal control problems subject to probabilistic
constraints have attracted much attention in many research field. Although
probabilistic constraints are generally intractable in optimization problems,
several methods haven been proposed to deal with probabilistic constraints.
In most methods, probabilistic constraints are transformed to deterministic
constraints that are tractable in optimization problems. This paper examines
a method for transforming probabilistic constraints into deterministic
constraints for a class of probabilistic constrained optimal control problems.
Abstract: In this paper, we consider the two-stage compensator
designs of SISO plants. As an investigation of the characteristics of
the two-stage compensator designs, which is not well investigated
yet, of SISO plants, we implement three dimensional visualization
systems of output signals and optimization system for SISO plants by
the parametrization of stabilizing controllers based on the two-stage
compensator design. The system runs on Mathematica by using
“Three Dimensional Surface Plots,” so that the visualization can
be interactively manipulated by users. In this paper, we use the
discrete-time LTI system model. Even so, our approach is the
factorization approach, so that the result can be applied to many
linear models.
Abstract: In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.
Abstract: In recent decades, probabilistic constrained optimal
control problems have attracted much attention in many research
fields. Although probabilistic constraints are generally intractable
in an optimization problem, several tractable methods haven been
proposed to handle probabilistic constraints. In most methods,
probabilistic constraints are reduced to deterministic constraints
that are tractable in an optimization problem. However, there is a
gap between the transformed deterministic constraints in case of
known and unknown probability distribution. This paper examines
the conservativeness of probabilistic constrained optimization method
for unknown probability distribution. The objective of this paper is
to provide a quantitative assessment of the conservatism for tractable
constraints in probabilistic constrained optimization with unknown
probability distribution.
Abstract: Batch production plants provide a wide range of
scheduling problems. In pharmaceutical industries a batch process
is usually described by a recipe, consisting of an ordering of tasks
to produce the desired product. In this research work we focused
on pharmaceutical production processes requiring the culture of
a microorganism population (i.e. bacteria, yeasts or antibiotics).
Several sources of uncertainty may influence the yield of the culture
processes, including (i) low performance and quality of the cultured
microorganism population or (ii) microbial contamination. For
these reasons, robustness is a valuable property for the considered
application context. In particular, a robust schedule will not collapse
immediately when a cell of microorganisms has to be thrown away
due to a microbial contamination. Indeed, a robust schedule should
change locally in small proportions and the overall performance
measure (i.e. makespan, lateness) should change a little if at all.
In this research work we formulated a constraint programming
optimization (COP) model for the robust planning of antibiotics
production. We developed a discrete-time model with a multi-criteria
objective, ordering the different criteria and performing a
lexicographic optimization. A feasible solution of the proposed
COP model is a schedule of a given set of tasks onto available
resources. The schedule has to satisfy tasks precedence constraints,
resource capacity constraints and time constraints. In particular
time constraints model tasks duedates and resource availability
time windows constraints. To improve the schedule robustness, we
modeled the concept of (a, b) super-solutions, where (a, b) are input
parameters of the COP model. An (a, b) super-solution is one in
which if a variables (i.e. the completion times of a culture tasks)
lose their values (i.e. cultures are contaminated), the solution can be
repaired by assigning these variables values with a new values (i.e.
the completion times of a backup culture tasks) and at most b other
variables (i.e. delaying the completion of at most b other tasks).
The efficiency and applicability of the proposed model is
demonstrated by solving instances taken from a real-life
pharmaceutical company. Computational results showed that
the determined super-solutions are near-optimal.
Abstract: Model predictive control is a kind of optimal feedback
control in which control performance over a finite future is optimized
with a performance index that has a moving initial time and a moving
terminal time. This paper examines the stability of model predictive
control for linear discrete-time systems with additive stochastic
disturbances. A sufficient condition for the stability of the closed-loop
system with model predictive control is derived by means of a linear
matrix inequality. The objective of this paper is to show the results
of computational simulations in order to verify the effectiveness of
the obtained stability condition.
Abstract: In this paper we propose a discrete tracking control of
nonholonomic mobile robots with two degrees of freedom. The
electromechanical model of a mobile robot moving on a horizontal
surface without slipping, with two rear wheels controlled by two
independent DC electric, and one front roal wheel is considered. We
present backstepping design based on the Euler approximate discretetime
model of a continuous-time plant. Theoretical considerations are
verified by numerical simulation.
Abstract: In the paper, the predictive control method is proposed to control the synchronization of two perturbed satellites attitude motion. Based on delayed feedback control of continuous-time systems combines with the prediction-based method of discrete-time systems, this approach only needs a single controller to realize synchronization, which has considerable significance in reducing the cost and complexity for controller implementation.
Abstract: In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.
Abstract: A direct adaptive controller for a class of unknown nonlinear discrete-time systems is presented in this article. The proposed controller is constructed by fuzzy rules emulated network (FREN). With its simple structure, the human knowledge about the plant is transferred to be if-then rules for setting the network. These adjustable parameters inside FREN are tuned by the learning mechanism with time varying step size or learning rate. The variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the boundary of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The validation of the theoretical findings is represented by some illustrated examples.
Abstract: This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer-s observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.
Abstract: This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.
Abstract: This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system length as well as some performance measures at random epochs by using the supplementary variable method. Thirdly, still based on the supplementary variable method we give the probability generating function (PGF) of the number of customers at the beginning of a busy period and give a stochastic decomposition formulae for the PGF of the stationary system length at the departure epochs. Additionally, we investigate the relation between our discretetime system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.
Abstract: In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.
Abstract: A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.