Normalized Coprime Factor Plant Research Articles

Design of Disturbance Observer via the Robust Stabilization and H∞ Loop Shaping Methods

The Disturbance observer (DOB) method is known to be effective in enhancing the performance of dynamic systems in the presence of disturbances. DOBs of various structures have been proposed to improve systems’ sensitivity functions for better disturbance rejection performance and robustness. However, the improvement to the sensitivity function may deteriorate robustness and transient responses. In this paper, we propose a new systematic method of designing the DOB. This method is based on the robust stabilization of the normalized coprime factor plant description and H∞ loop shaping method. In our method, good system robustness can be achieved by Nehari stability margin, and the design parameters of the Q-filter for system robustness and performance can be determined systematically using a target loop transfer function. We applied this method to a MEMS stage. Simulation results show that the disturbance effect of the stage is reduced, and a robust system is achieved in the presence of parameter uncertainties.

Coprime factorisation approach in designing multi-input stabiliser for damping electromechanical oscillations in power systems

The application of loop shaping in H∞ control design through a dual-input power system stabiliser (PSS) in a benchmark power system model is demonstrated. The PSS stabilises two key system poles contributing to critical electromechanical oscillations involving turbine generators and electrical network. The IEEE First Benchmark Model has been considered in this study to demonstrate the effectiveness of the control. A linearised model of the system is pre- and post-compensated using loop-shaping approach. The problem of robust stabilisation of a normalised coprime factor plant description is formulated into a generalised H∞ problem and the solution is obtained analytically. The performance of the controller shows robustness to electromechanical modes, which were otherwise very poorly damped or undamped depending on operating conditions. The robustness is further validated in Simulink, including nonlinearities and device saturation limits.

LMI approach to normalised [Hamiltonian (script capital H)]∞ loop-shaping design of power system damping controllers

Application of the normalised ℋ∞ loop-shaping technique for design and simplification of damping controllers in the LMI framework is illustrated. A linearised model of the power system is pre- and post-compensated using the loop-shaping approach. The problem of robust stabilisation of a normalised coprime factor plant description is translated to a generalised ℋ∞ problem. The solution is sought numerically using LMIs with additional pole-placement constraints. This ensures that the time-domain specifications are met besides robust stabilisation.

Intelligent Material and Fluid Systems. Large Scale Active Microvibration Control System Using Piezoelectric Actuators Applied to Semiconductor Manufacturing Equipment.

This paper verifies the performance of the active microvibration control system using piezoelectric actuators with a table length of 3 m, a width of 1.8 m and a weight of 4000kg applied to large-scale semiconductor manufacturing equipment whose microlithographic accuracy was actually degraded due to the constant vibration. The mounted equipment was the integral-design semiconductor manufacturing equipment weighting 2600 kg. The controller was designed by a method dependent on the normalized coprime factor plant model in the preceding study used to prevent the elastic vibration of the equipment and table from causing the spillover phenomena of the control system. For the frequency-forming algorithm, the model matching method and the H∞ method were employed. As a result of this system's application, the microlithographic accuracy of the manufacturing equipment could be improved from about 2μm (before application) to an intrinsic value of nearly 0.1 μm.

Coprime factorization approach to robust stabilization of control structures interaction evolutionary model

Stabilization in the presence of uncertainties is a fundamental requirement in the design of feedback compensators for flexible structures. The search for the largest neighborhood around a given design plant for which a single feedback controller produces closed-loop stability can be formulated as an H^ control problem. It has been shown that the use of normalized coprime factor plant descriptions, where the plant perturbations are defined as additive modifications to the coprime factors, leads to a closed-form expression for the maximal-neighborhood boundary allowing optimal and suboptimal HOC compensators to be computed directly without the usual 7iteration. This paper describes an application of normalized coprime factor stabilization theory to the computation of robustly stable compensators for the NASA Control Structures Interaction Evolutionary Model. Results indicate that the suboptimal version of the theory has the potential of providing low authority compensators that are robustly stable for significant regions of variations in design model parameters and additive unmodeled dynamics.

Simultaneous robust stabilisation of two normalised coprime factor plant balls

The problem treated concerns the design of a single controller which simultaneously stabilises two nonconcentric balls of single-input/single-output plants. This is done by using the normalised left coprime factor plant description with H∞-bounded uncertainty to characterise each plant ball. Necessary conditions for being able to solve this problem are developed and used to provide a computational approach for determining a controller. Several examples are given to demonstrate the validity of the necessary conditions and the controller synthesis procedure.

Loop-shaping basedH∞ robust control of a horizontal shaft magnetic bearing

This paper considers H∞ control design of a magnetic bearing from the viewpoint of loop shaping. Feedback control is indispensable for a magnetic bearing, since it is essentially an unstable system. For feedback control, a mathematical model is required. However, it does not always express the exact behavior of the system, hence the model has various uncertainties such as the errors of parameters, neglected nonlinearities, or unmodeled dynamics. The controller is needed to guarantee robustness for both stability and performance against these uncertainties on the model. First, based on some assumptions, a linear state space model of a magnetic bearing is shown. Second, the experimental machine and the surroundings of its controller are introduced. The experimental machine is a 4-axis controlled horizontal shaft magnetic bearing. The controller consists of a digital signal processor with fast A/D converters and D/A converters. Third, the control system is designed using normalized coprime factor plant descriptions. Selecting shaping functions in this procedure called “The Loop-Shaping Design Procedure (LSDP),” shape the open-loop transfer function and the transfer functions of the closed-loop system can be shaped. Finally, several experiments are carried out according to the aforementioned designed controller.

Pole-zero cancellations and closed-loop properties of an H∞ mixed sensitivity design problem

Abstract We examine an H ∞ mixed sensitivity design problem in order to gain an understanding of the pole-zero cancellation phenomenon that is known to occur with such designs. It is shown how the pole-zero cancellation phenomenon is dependent upon the choice of weighting functions used in the problem formulation, and a particular construction of weighting function is given that gives the designer freedom to exploit or prevent the phenomenon. Furthermore, this weighting function is then a mechanism for (partial) pole placement. As a consequence of the construction of this weighting function, it is shown that for a certain class of plant, the Normalized Coprime Factor design procedure of Glover and McFarlane (1989, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions . Springer-Verlag, Berlin) gives rise to (possibly undesirable) pole-zero cancellations. The results are presented for multivariable systems, and are illustrated with a simple design example.

Robust Control of a Flexible Arm by H.INF. Control Theory.

In this paper we apply the robust stabilization problem using normalized coprime factor plant descriptions, which is proposed by Glover et al., to the robust control design for a flexible arm. First we design the feedback controller for this robust stabilization problem, which stabilizes the nominal plant including a rigid body mode and the first two flexible modes. The feedback system with this controller satisfies some design objectives, e. g. the bandwidth requirement. We show that by this controller we can reject the spillover effect of the remaining higher flexibility modes. Furthermore we consider robust stability analysis for the structured uncertainty. We investigate the dependence of the maximum robustness margin on the damping coefficient. Then we calculate a range of the damping coefficient in which stability is guaranteed by the controller which achieves the maximum robustness margin.

Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty

The problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by H/sub infinity / bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system. This problem can be reduced to a Nehari extension problem directly and gives an optimal stability margin. All controllers satisfying a suboptimal stability margin are characterized, and explicit state-space formulas are given. >