DECOMPOSITION OF MULTIRATE DYNAMIC SYSTEMS WITH SMALL DISSIPATION

We consider singularly perturbed differential systems which describe the dynamics of manipulator with flexible joints in conditions of small dissipation. The existence of decoupling transformation which converts original multirate system to "block triangular" form with independent slow subsystem. Decoupling transformation is constructed as asymptotic series.

Design Method for Improvement of Transient-State Intersample Output of Multirate Systems Including Integrators

[abstFig src='/00280005/12.jpg' width='300' text='Comparison of output responses' ] This paper discusses a design method for a multirate system including integrators, where the update interval of the control input is shorter than the sampling interval of the plant output. In such a multirate control system, intersample output might oscillate between sampled outputs in the steady state even if the sampled output converges to the reference input. This is because the control input can be updated between the sampled outputs. In a conventional method, a predesigned control law is extended such that the steady-state ripples are eliminated independent of a discrete-time response. However, the conventional method is invalid when integrators are included in a controlled plant. In this study, a difference operation in discrete time is used to address this issue. Moreover, the transient-state intersample response is improved independent of a pre-designed discrete-time response.

Design of an Optimal Preview Controller for Linear Discrete-Time Descriptor Noncausal Multirate Systems

The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.

Fundamentals of Multirate Systems

Digital signal processing (DSP) is an area of science and engineering that has been rapidly developed over the past years. This rapid development is a result of significant advances in digital computers technology and integrated circuits fabrication (Mitra, 2005; Smith, 2002). Classical digital signal processing structures belong to the class of single-rate systems since the sampling rates at all points of the system are the same. The process of converting a signal from a given rate to a different rate is called sampling rate conversion. Systems that employ multiple sampling rates in the processing of digital signals are called multirate digital signal processing systems. Sample rate conversion is one of the main operations in a multirate system (Harris, 2004; Stearns, 2002).

Parametrization of LTI Controllers for Multirate Systems

In this work we consider the problem of parametrizing the set of all stabilizing Linear Time-Invariant (LTI) controllers for multirate systems such that model matching is achieved with a desired transfer function. We consider those systems where the plant output can be measured at a rate (measurement update rate) slower than the control signal updates rate. The solution to the parametrization problem is provided for the two cases: (1) model matching at the control update rate, (2) model matching at the measurement update rate. Unlike model matching at the measurement update rate, model matching at the control update rate allows us to directly improve and characterize the transient response of the continuous-time system. Tools such as up-sampling and down-sampling operators, and modified Z-transforms are utilized to model the closed-loop multirate system and to parametrize the sets of LTI controllers.