Parametric Robust Control Research Articles

Parameter Robust Risk-Sensitive Control Synthesis for a Satellite with Structured Parameter Uncertainties

The parameter robust Risk-Sensitive control synthesis is newly developed to deal with the parameter uncertainties of a system. In this synthesis the parameter uncertainties are decomposed into three parts and are reflected in the cost function and the noise models. This new method improves the tolerance of a controller to parameter uncertainties in a system. A nonlinear attitude model of a satellite with thrusters, magnetic torquers and reaction wheels is developed. Then the linearized version of the satellite attitude model is derived for the attitude hold mode. To determine the performance of the parameter robust Risk-Sensitive control method, the steady-state mean square histories of the state and input variables are calculated by finding the covariance matrices. Moreover, the performance and stability robustness of parameter robust Risk-Sensitive control are compared with the classical linear quadratic Guassian control. Finally, as an application of this parameter robust Risk-Sensitive control, we use the Korea Multi-Purpose Satellite model equipped with reaction wheels and thrusters as the attitude control devices. The numerical simulations show that the parameter robust Risk-Sensitive control method has better performance and stability characteristics than the classical linear quadratic Guassian control method, especially when the parameter uncertainties are large.

Quadratic stability analysis of the Takagi-Sugeno fuzzy model

The nonlinear dynamic Takagi-Sugeno fuzzy model with offset terms is analyzed as a perturbed linear system. A sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model. The criterion accepts a convex programming formulation of reduced computational cost compared to the common Lyapunov matrix approach. Parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system. Application examples on fuzzy models of nonlinear plants advocate the efficiency of the method. The examples demonstrate reduced conservatism compared to norm-based criteria.

Reconfigurable Control System Synthesis Using Parameter Estimation and Robust Control

Abstract A new design scheme of a Reconfigurable Control System (RCS) based on a bounding parameter estimation scheme and the parametric robust control method is proposed in this paper. The main advantage of this approach over the existing ones is that it allows the systen designers to integrate the Fault Detection and Isolation (FDI) schemes with the reconfigurable control at the control system design stage. To demonstrate the effectiveness of the proposed scheme, an illustrative example is presented. The simulation results indicate that the proposed scheme has some distinctive features which are potentially useful in the development of a truly Fault Tolerant Control System (FTCS).

High-performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments

This paper studies the high-performance robust motion control of machine tools. The newly proposed adaptive robust control (ARC) is applied to make the resulting closed-loop system robust to model uncertainties, instead of the disturbance observer (DOB) design previously tested by many researchers. Compared to DOB, the proposed ARC has a better tracking performance and transient in the presence of discontinuous disturbances, such as Coulomb friction, and it is of a lower order. As a result, time-consuming and costly rigorous friction identification and compensation is alleviated, and overall tracking performance is improved. The ARC design can also handle large parameter variations and is flexible in introducing extra nonlinear robust control terms and parameter adaptations to further improve the transient response and tracking performance. An anti-integration windup mechanism is inherently built in the ARC and, thus, the problem of control saturation is alleviated. Extensive comparative experimental tests are performed, and the results show the improved performance of the proposed ARC.

Design and Analysis of Robust Control Systems in PARADISE

Most of the methods which are commonly used in parametric oriented robust control design and analysis require extensive symbolic and numerical computations. The Matlab toolbox PARADISE (PArametric Robustness Analysis and Design Interactive Software Environment) offers various methods of parametric robust control for an efficient application in a computer framework. Amongst the currently implemented methods are the parameter space approach, design in an invariance plane, calculation of stability profiles, and computation of stability radii. The application of the toolbox PARADISE is demonstrated by computation of stability radii for a state feedback controlled loading bridge.

Finite element model-based robust controllers for the middeck active control experiment (MACE)

The middeck active control experiment (MACE) is a space shuttle flight experiment intended to demonstrate high authority active structural control in zero gravity (0-g) conditions based on analysis and ground testing. Finite element structural models are very important for the MACE program because they can be used to predict the on-orbit dynamics of the test article. However, finite element models tend to be inaccurate, requiring the use of parametric robust control techniques to achieve good performance. Several such control techniques and an overall design methodology are discussed in this paper. Experimental results from several tests are used to illustrate the feasibility of achieving good H/sub 2/ performance on the test article with robust controllers based on the finite element model. This demonstration improves confidence in the eventual on-orbit performance of this experiment and other future spacecraft.

Force-time curves of a rotary tablet press. Interpretation of the compressibility of a modified starch containing various amounts of moisture.

On a rotary tablet press, the force-time curves are segmented into three phases: the compression phase, the dwell phase during which both stress and strain are variable for plastically deforming materials and the decompression phase. The following seven parameters were investigated: the compression area (A1) and the compression slope (Slc) describing the initial phase, the area ratio (AR) and the peak offset time (t(off)) characterizing the dwell time, the decompression area (A4) and the decompression slope (Sld) describing the terminal phase and the total area under the force-time curve (Atot). AR, t(off), Slc and A1 (the last with limitations) are used for phase-specific allocation of the occurrence of plastic flow, which is found to be a function of compression force and moisture content. Tablet strength, tablet porosity and in-die bulk porosity provide additional information for comprehensive interpretation. The values of A4 for the four starch batches are not significantly different. Sld provides somewhat better information about the elastic compact recovery. In general, however, the short decompression phase seems to be inappropriate for characterization by force-time curve parameters, because it is difficult to separate machine recovery from that of the tablet. Porosity above the porosity limit of the material was found to be a prerequisite for plastic flow within the compact. When the porosity limit is reached, further densification remains elastic and leads to a reduced compact strength during expansion. The area ratio, as a robust in-process control parameter for plastically flowing formulations, is suggested as a means of preventing this effect.

Uncertainty structures in adaptive and robust stabilization

We develop and synthesize results concerning the stabilization of parametrically uncertain linear systems via state feedback. Our main purpose is to bring together the previously disjoint areas of parametric robust control and adaptive control, and to examine and compare the uncertainty structures that can be accommodated by various approaches of adaptive stabilization and robust stabilization. Among adaptive approaches, we consider adaptive design based on the certainty equivalence approach and those based on Lyapunov design, which in turn include the cases of parameter-independent and parameter-dependent Lyapunov functions. Among robust approaches, we consider quadratic as well as non-quadratic stabilization. A hierarchy of uncertainty structures is revealed. As an example of the results established in this paper, we show that the broadest uncertainty structure stabilizable by adaptive control based on a parameter-independent Lyapunov function is the antisymmetric stepwise form, which is strictly larger than the so-called pure feedback form.