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## Über dieses Buch

This book provides readers with alternative robust approaches to control design for an important class of systems characteristically associated with ocean-going vessels and structures. These systems, which include crane vessels, on-board cranes, radar gimbals and a conductivity temperature and depth winch, are modelled as manipulators with oscillating bases. One design approach is based on the H-infinity control framework exploiting an effective combination of PD control, an extended matrix polytope and a robust stability analysis method with a state-dependent coefficient form. The other is based on sliding-mode control using some novel nonlinear sliding surfaces. The model demonstrates how successful motion control can be achieved by suppressing base oscillations and in the presence of uncertainties. This is important not only for ocean engineering systems in which the problems addressed here originate but more generally as a benchmark platform for robust motion control with disturbance rejection.

Researchers interested in the robust control of mechanical systems operating on unstable bases will find this monograph valuable. MATLAB® and Simulink® programs are available for download to make the methods described in the text easier to understand and to allow readers to experience practical procedures at first hand.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
This introductory chapter first defines the key terminology “oscillatory-base manipulator,” which represents a model system associated with mechanical systems installed on the oscillatory base. This category consists of two groups depending on the presence or the absence of external oscillatory disturbance. Typical examples with external oscillatory disturbance can be found in marine mechanical systems, such as offshore cranes, drill ships. The other group, i.e., with no external oscillatory disturbance, mainly contains space robots mounted on the flexible base. This monograph will focus on the former group of marine mechanical systems. We introduce related works and our own research history where the $$\mathcal {H}_\infty$$ control framework and the sliding-mode control one have played important roles, and present the organization of the monograph.
Masayoshi Toda

### Chapter 2. Problem Definition, Dynamical Model Formulation

Abstract
This chapter presents the problem definition and dynamical model formulation of an oscillatory-base manipulator considering an illustrative example, which we will work on throughout the monograph. We will consider three types of control problems, specifically attitude control in local coordinates (base-fixed coordinates) which is associated with on-board operations such as cargo handling, attitude control in global coordinates (earth-fixed coordinates), e.g., radar gimbal systems, and position control in global coordinates, e.g., heave-motion-compensated cranes. Further, as patterns of base oscillation, we consider three patterns, single-frequency sinusoidal oscillation, double-frequency sinusoidal one, and ocean-wave imitated oscillation based on the Bretschneider spectrum. Using combinations of those cases, we will demonstrate control system design and analysis, control simulations and experiments.
Masayoshi Toda

### Chapter 3. Experimental Apparatus and Analysis on Parameter Variation Due to Payload

Abstract
We developed an experimental apparatus in order to evaluate control systems for oscillatory-base manipulators (OBMs) by hardware experiments. We call the apparatus the “experimental OBM,” which was designed to be in accordance with the problem definition described in Chap. 2, and moreover to accommodate robust control demonstrations by exchanging the attached payloads of different weights. In this chapter, we first introduce the experimental OBM. Then, considering the illustrative model given in Chap. 2, and the experimental OBM, we analyze how the parameters in the dynamical model vary according to the payload variations, the results of which will be utilized in robustness analyses and robust control simulations for the control systems in the sequel.
Masayoshi Toda

### Chapter 4. Motion Control Using an $$\mathcal {H}_\infty$$ H ∞ -Control-Based Approach

Abstract
This chapter presents the key contents of the monograph, that is, the $$\mathcal {H}_\infty$$-control-based approach for the OBM robust control problems. This control methodology consists of several schemes, specifically nonlinear state-feedback control to reduce the nonlinearity, parametric model uncertainty representation, $$\mathcal {H}_\infty$$ control with weighting functions, and additional linear state-feedback control to compensate for the $$\mathcal {H}_\infty$$ control scheme. In particular, in order to less conservatively and effectively represent parametric model uncertainties due to the payload variations, we have developed a machinery the “extended matrix polytope,” which is an extension of the conventional matrix polytope, in the aim of representation of a non-convex parameter space. In this chapter, we begin with brief review of the basic notion of $$\mathcal {H}_\infty$$ control, and introduce the extended matrix polytope. Then, we present the control design method with some design examples considering four types of $$\mathcal {H}_\infty$$ controllers, and perform analyses on the designed control systems in terms of properties such as system poles and zeros, frequency response, and robustness by utilizing two different approaches, one of which is based on $$\mu$$-analysis with the extended matrix polytope, and the other one is a Lyapunov-theory-based one with a state-dependent coefficient (SDC) form. From the results of analyses, the designed control system reveals favorable properties in terms of disturbance rejection, tracking control, and robustness. Hence, their practical control performances can be also expected, which will be shown in the next chapter.
Masayoshi Toda

### Chapter 5. Simulations and Experiments for the $$\mathcal {H}_\infty$$ H ∞ -Control-Based Approach

Abstract
This chapter presents control performance evaluations of the $$\mathcal {H}_\infty$$-control-based approach by simulations and hardware experiments separately from Chap. 4. We have performed demonstrations of control performance considering the three types of control problems and three patterns of base oscillations mentioned in Chap. 4, and the four types of $$\mathcal {H}_\infty$$-controllers presented in Chap. 4. For those demonstration cases, we investigate the respective control performance, with respect to nominal-case performance, robust control performance against the payload variations, influence of sensor error, and moreover comparison with the conventional PID control. Those results show that the $$\mathcal {H}_\infty$$-control-based approach and the extended matrix polytope are practically useful and effective from the viewpoint of control performance.
Masayoshi Toda

### Chapter 6. Motion Control Using a Sliding-Mode-Control-Based Approach

Abstract
In this chapter, we present the other highlight of the monograph, the sliding-mode control (SMC)-based approach for the OBM robust control problems. In our attempt to apply the SMC framework to such problems, we have developed a novel nonlinear sliding surface, which is called the “rotating sliding surface with variable-gain integral control (RSSI).” The advantageous feature of this method is the control system can achieve successful tracking control and disturbance rejection in not only steady state but also transient state with less control inputs. We present the control design method, stability analyses on the RSSI and control performance demonstrations by simulations in comparison with those of the $$\mathcal {H}_\infty$$-control-based approach. The results show that, in the ideal situation in terms of sensor resolution, sampling period, control input limitation, the SMC-RSSI system is considerably superior to the $$\mathcal {H}_\infty$$ controllers, however once such ideal conditions have been violated, its performance are dramatically deteriorated. Therefore, the SMC-based approach is promising, but needs to be improved in the sense of practical implementation.
Masayoshi Toda

### Chapter 7. Base Oscillation Estimation via Multiple $$\mathcal {H}_\infty$$ H ∞ Filters

Abstract
This chapter presents a complementary technique to support the aforementioned control methodologies which have assumed that accurate measurements of the base oscillation can be available for the control system. Here we present an estimation algorithm of the base oscillation assuming a low-cost rate gyro sensor. The heart of this algorithm is a method of selectively combining multiple $$\mathcal {H}_\infty$$ filters according to an innovation-based criterion. We introduce this algorithm and demonstrate its estimation performance by simulations using the Bretschneider oscillation in Chap. 2. The results show that among the multiple filters appropriate ones can be selected with the innovation-based criterion, and thus the estimation algorithm is effective.
Masayoshi Toda

### Backmatter

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