Inverse Linear Quadratic Research Articles

On the Dynamic Positioning Control System of FPSO using Kalman Filtering Techniques

When a FPSO (Floating Production Storage and Offloading) is required to maintain the specified position during oil producing and offloading under the external forces such as ocean current, wind or wave, exact position measurement is firstly taken into consideration. GPS (Global Positioning System) is mainly used to measure ship's position. But the position measurements using GPS contain noise. This noise has large influence on DPS (Dynamic Positioning System), therefore it is necessary to remove the noise.In this paper, Inverse Linear Quadratic (ILQ) optimal servo theory using Kalman filter is applied to design control system of DPS. Generally, Kalman filter is to estimate the low-frequency motions of the vessel so that control can be applied to minimise the position error. But in this paper, Because we already consider motion of FPSO as low-frequency motion, Kalman filter is used to remove the measurement noise.The numerical simulations shows the performance of the combined Kalman filter and ILQ optimal servo system.

Design of a Dynamic Positioning System for Self-Propulsive Barge under External Disturbances

A dynamic positioning system (DPS) is used in order to keep the specified position. By using the inverse linear quadratic (ILQ) optimal servo theory, it will be able to construct a control system of DPS which has no interaction among the controlled variables. In ILQ optimal servo theory, time constant Ti as the design parameters have much influence on the performance of the control system.In this paper, we applied the ILQ optimal servo theory to design the control system of DPS for a self-propulsive barge. We designed the system with Ti defined automatically in response to the dimensions of state variables. We examined the characteristics of the control system using Ti which is defined automatically.

Design of Dynamic Positioning System for Self-propulsive Barge under External Disturbances

When a ship is required to keep the specified position with high accuracy under influence of external disturbances, dynamic positioning system (DPS) is often used in order to keep its position. It will be able to construct a control system which has no interaction among the controlled variables by using the inverse linear quadratic (ILQ) optimal servo theory. It will be also able to express the optimal feedback gain in terms of the system matrices and the design parameters. In ILQ optimal servo theory, time constant Ti as the design parameters have much influence on the performance of the control system, and the suitable values of Ti should be selected as small as possible corresponding to external disturbances. However, it is troublesome to select suitable Ti because we have to carry out numerical simulations repeatedly.In this paper, we applied the ILQ optimal servo theory to design the control system of DPS for a selfpropulsive barge. About time constant Ti, we designed the system with Ti defined automatically in response to the dimensions of controlled variables. Applying this method, it is possible to adjust the suitable values of Ti automatically. From the numerical simulations, it is found that design process taking the system with Ti defined automatically would be more useful and easier than taking usual ILQ optimal servo theory.

An Inverse-LQ Approach to Design of Optimal Servo System with Frequency Weights

This paper presents a design method of optimal servo systems with frequency weights from the view point of the inverse LQ problem. This design method allows us to assign desirable closed-loop transfer functions directly and in addition, to obtain the desired optimal control law in a closed form in terms of design parameters and the system parameters. A numerical example is also shown to illustrate the design method proposed here as well as to show its usefulness.

Tension Control of a Hot Strip Mill Finisher

This paper describes interstand tension control by looper and looper less tension control of a hot strip mill finisher. The looper tension control methods are conventional, non-interactive, LQ (Linear Quadratic), H∞, and ILQ(Inverse Linear Quadratic) control.

Design of Tracking Systems with LQ Optimality and Quadratic Stability

This paper concerns a tracking problem for linear systems with real uncertain parameters. The objective here is to design a state feedback controller such that 1) the closed-loop system is optimal in the LQ sense for the nominal parameter values, 2) quadratically stable and 3) its output tracks the step reference input asymptotically under the parameter uncertainty. One such controller is obtained here by applying our "Inverse LQ design method" of extended type with quadratic stability requirement incorporated. The attractive feature of the proposed design method lies on one hand in the control structure of the designed tracking system with a low-pass filter placed before the control input, and on another hand in the design parameters with clear physical meaning in relation to this structure.

Extension of ILQ Method to Non-Minimum Phase Systems for the Design of Optimal Servo Systems

ILQ (Inverse Linear Quadratic) method is a new design method for control systems which utilizes the result of the inverse problem of optimal regulator. This method is more effective when it is applied to the design of an optimal servo system. It is called “ILQ optimal servo system”. The existing theory has assumed the minimum phase condition for the plant. But this condition can be relaxed to a class of MIMO non- minimum phase systems which includes all SISO systems. This paper describes an extension of this theory to such a class of systems and at the same time it shows this extension is an achievable limit. In the extension, proofs of “analytical description of optimal gains” and “asymptotic property of a closed loop transfer function matrix” which are the basic properties of ILQ optimal servo system, are performed in a way different from the past papers. This paper also contains a numerical example to illustrate the effectiveness of this method for the non-minimum phase plant.

A study on the Automatic Manoeuvring System of a ship based on ILQ Optimal Servo Theory

In the application of the linear quadratic (LQ) optimal regulator theory to control system design, it is difficult to find suitable weighting matrices Q, R in the performance function. That is, the designer must resort to trial and error iteration to find them. And so it is rather difficult to design the optimal control system. The inverse linear quadratic (ILQ) optimal servo theory was recently proposed, this design theory was developed from the practical view point by applying some results on the inverse problem of LQ regulator. In this method there is a close relationship between the characteristic of the transient response of the control system and the design parameters. When the design condition is fulfilled, it is able to construct a control system which has no interaction between the controlled variables, and it is also able to express the optimal feedback gain in terms of the system matrices and the design parameters. In this paper, the authors attempted to apply ILQ optimal servo theory to the design of a control system for the manoeuvring motion of a ship. It is shown that by the ILQ design method the control system for the manoeuvring motion of a ship can be designed very easily compared with the usual LQ design method. Response characteristics can be selected with design parameters. A control system can be constructed no to interact between the control variables, and as the gain is expressed in terms of the system matrices and the design parameters, it is able to construct a control system which is adaptable to the change of the characteristic of the controlled object.

The Design of Robust Servo Systems Based on the Quadratic Stability Theory

The quadratic stability theory is known as a powerful method for robust stabilization of uncertain systems. This paper applies it to the tracking problem from the viewpoint of the inverse regulator problem and proposes a method of designing robust tracking controllers for linear systems with uncertain parameters. First, we solve the inverse problem of a quadratically stabilization problem. We then apply this result to Inverse LQ design theory and then give a criterion of choosing design parameters assuring quadratic stability of the closed system. Finally we show an example to illustrate the validity of the design method.