Kiheon Park

A general theory for the Wiener-Hopf design of multivariable control systems

Multivariable control system design in a quadratic cost setting is treated for a completely general configuration. The class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite. This controller class is parameterized in terms of an arbitrary real rational strictly-proper matrix Z(s), which is analytic in the closed right-hand side of the s-plane. The choice Z identical to 0 gives the controller which minimizes the quadratic cost functional. >

Wiener-Hopf design of servo-regulator-type multivariable control systems including feedforward compensation

Frequency-domain design in a quadratic cost setting is treated for a multivariable control system which includes disturbance feedforward, output feedback, and reference-input compensation (i.e. a three-degrees-of-freedom control system). The cost function is taken to account for tracking accuracy, plant saturation and plant sensitivity. The class of all controllers is determined for which the given system is internally asymptotically stable and the quadratic cost function is finite. This controller class is parametrized in terms of arbitrary real rational matrices Zz Zu and Zw which are strictly proper and analytic in Re s ≥ 0. The optimal solution is obtained by setting the Z matrices to zero.

H 2 design of one-degree-of-freedom decoupling controllers for square plants

Decoupling design of one-degree-of-freedom controllers is treated for the generalised plant model within the H 2 framework. The class of all realisable closed loop transfer matrices is parametrised under a mild assumption on non-unity feedback sensors. A set of compact assumptions is presented to guarantee the existence of the optimal H 2 controller. Together with the optimal one, the class of all H 2 controllers that yield finite H 2 cost is obtained. The optimal closed transfer matrix and its associated controller are shown to be strictly proper under the reasonable order assumptions on the generalised plant.

Numerical calculation of the optimal three-degree-of-freedom Wiener-Hopf controller

State space algorithms are developed for the optimal three-degree-of-freedom Wiener-Hopf controller without placing any restriction on the plant. The algorithms are obtained not only for the regulator problem but for the servo problem as well and with or without feedforward control.

Brief Wiener-Hopf design of the optimal decoupling control system with state-space formulas

The optimal decoupling controller minimizing a given quadratic cost function is derived for the generalized plant model with two-degree-of-freedom controller configuration. A minimal set of assumptions for the existence of the optimal controller is presented in both the frequency and the state-space domains. The optimal controller formula is described in the frequency domain and the corresponding state-space formula is derived for computational efficiency.

Decoupling Controller Design for H ∞ Performance Condition

The decoupling design for the one-degree-of-freedom controller system is treated within the framework. In the present study, we demonstrate that the performance problem in the decoupling design is reduced into interpolation problems on scalar functions. To guarantee the properness of decoupling controllers and the overall transfer matrix, the relative degree conditions on the interpolating scalar functions are derived. To find the interpolating functions with relative degree constraints, Nevanlinna-Pick algorithm with starting function constraint is utilized in the present study. An illustrative example is given to provide details regarding the solution.

On performance enhancement of a following tracker using stereo vision

A stereo vision system has a distinctive advantage capable of obtaining exact and wide range of the distance information. The use of stereo vision system has been increased due to the advances in hardware technology. This paper deals with design of the active vision system which acquires the distance and the direction information of the target using the stereo vision system. This paper also implements the tracker that follows the main tracker, which we call a following tracker, without identifying the target. In addition, the CAMShift algorithm which tracks the target based on the color information is used to acquire the center point of the object. A following tracker algorithm generates the control input that makes the following tracker aim the same target based on the sensing results from the active vision system. A following tracker needs the exact distance information between the system and the target to track the object accurately. We first build the mathematical model of object tracking system and following tracker, design the system controllers, and then compare the tracking accuracy under the two conditions: the presence and the absence of the distant information.

H 2 design of decoupling controllers based on directional interpolations

Decoupling design for the generalized plant model is treated within the H2 framework. The class of all decoupled closed loop transfer matrices is parameterized using the directional interpolation approaches under the assumption of simple transmission zeros. A set of compact assumptions is presented to guarantee the existence of the optimal H2 decoupling controller.

Persistent inputs and the standard H 2 multivariable control problem

The H 2 control problem is formulated with exogenous inputs having unstable shape-deterministic components. Such inputs are called persistent. Some issues in connection with past solutions of the H 2 control problem in this case are carefully described and addressed. In particular, it is established that two- and three-degree-of freedom (2DOF and 3DOF) systems with persistent inputs cannot be treated within the framework of the standard configuration. In addition, past treatments of persistent inputs within the framework of the generalised 2DOF configuration focused on solutions which yielded stable error transforms without explicitly requiring the same for controller outputs. In this article, a more general configuration is treated and physical considerations are invoked to justify imposition of the requirement that both the regulated variable z(s) and the controller output u(s) be stable. A persistent input model for which there exists a stabilising controller that makes both z(s) and u(s) stable is called acceptable and the necessary and sufficient condition for such acceptability is determined. Also considered is a persistent input model for which there exists a stabilising controller that makes the controller output, the measured output and the regulated variable stable. Such a model is called strictly acceptable and the necessary and sufficient condition for strict acceptability is given. The subset of all stabilising controllers associated with an acceptable persistent input model is parameterised and this parameterisation is used to formulate an H 2 optimisation problem with persistent inputs which can then be solved using standard procedures.

Existence conditions of decoupling controllers in the generalized plant model

Necessary and sufficient conditions for the existence of diagonal, block-diagonal and triangular decoupling controllers in linear multivariable systems are presented for the most general setting. The plant model in this paper is general enough to accommodate non-square plant and non-unity feedback cases with 1DOF (one-degree-of-freedom) or 2DOF controller configuration. It is shown that the existence condition is finally described in terms of rank conditions on coefficient matrices in partial fraction expansion.