Modeling human visuomotor adaptation with a disturbance observer framework

This monograph examines in mathematical terms an open question in neuroscience on the function of the cerebellum, a major brain region involved in regulation of the motor systems, speech, emotion, and other cognitive functions of the body. Reasoning from the perspective of control theory, we make a hypothesis that the primary function of the cerebellum is disturbance rejection of exogenous reference and disturbance signals. This brings to the fore the internal model principle of control theory: that any good controller must include a model of its environment. The monograph is structured around a pursuit of the validity of this hypothesis. Given the system level architecture and the measurement structure of the cerebellum, is disturbance rejection mathematically feasible? Second, is a disturbance rejection interpretation consistent with experiments? Specifically we investigate the possibility that the cerebellum provides adaptive internal models of signals generated by the environment. After a brief historical overview of computational theories of cerebellar function and of the relevant parts of control theory in the area of regulator theory, we carry out a more or less chronological review of subjects in control theory that impinge on our investigation. We begin with classical regulator theory with its characteristic features of a known plant and known frequency content of disturbance and reference signals. We then pause to examine classical regulator theory from the perspective of modeling the cerebellum, finding that several aspects are not well suited to this endeavor. Foremost is the unrealistic assumption that the plant and exosystem parameters are apriori known. More subtle issues arise from the fact that classical regulator theory developed in a setting where output and error measurements are regarded as persistent, an assumption not valid in the brain. Next, we review adaptive control theory, organized in terms of error models. The main control theoretic tools appear in Section 5, as a synthesis of classical regulator theory and adaptive control, where we present several adaptive internal model designs. To test our hypothesis on cerebellar function, we apply adaptive internal model designs to several motor systems regulated by the cerebellum. These include the slow eye movement systems: the vestibulo-ocular reflex, gaze holding, smooth pursuit, and the optokinetic system. We also study discrete time behaviors regulated by the cerebellum: the saccadic eye movement system and, more generally, visuomotor adaptation. The results from these modeling studies suggest that an interpretation of cerebellar function in terms of disturbance rejection is compelling, with the potential to provide a unifying framework to explain how the cerebellum can contribute to so many different systems in the body. The monograph concludes with suggestions for future research directions.

The special issue on Control Systems in Mechatronics is a significant and timely issue since many robotics and mechatronics engineers now pay attention to the research field of motion control and control theory. In Japan, advanced motion control technology is a key technics to improving the performance of robot systems and/or mechanical automation equipment. The definition of motion control in this issue is the control of mechanical systems driven by electrical actuators such as a do servo motor or an ac servo motor. The means or strategy of motion control has so far been of interest only to electrical engineers and mechanical engineers; it has not been as familiar to robotics engineers. Recently, a control system has been developed with industry applications. Advanced motor control technology in Japan is based on the robust control system, such as the disturbance observer, the H00 control system, the two-degrees-of-freedom control system and so on. The disturbance observer has a simple structure, and it is quite valid for disturbance torque rejection. The robust control system based on the disturbance observer is now widely used in robot and mechanical systems in Japan. The disturbance observer is the original Japanese technology designed by two electrical engineers, Prof. Ohnishi and myself, from the viewpoint of the electrical actuator but control theory. Ho control is linear control technics popular around the world. It can make the desired loop shaping of frequency characteristics for a plant system such as the actuator of a mechanical system. The robust control system based on the mixed sensitivity problem of H00 control theory has good frequency characteristics. Moreover, the availability of large amounts of computational power has enabled us to use complex control theory, and actuators for robotics applications are now mainly electrical ones because of the remarkable progress in power electronics. This change in the control of mechanical systems is a new and attractive one. Motion control is becoming a field of interest to control, electrical, and mechanical engineers who work in robotics. In this issue, the eight papers and the two news reports have been selected to show the current topics concerned with control systems in mechatronics. The first paper is a review paper titled ""robust motion control by the disturbance observer"". Prof. Ohnishi describes the physical meaning of motion control and the purpose of robust control. This review paper also shows the effectiveness of motion control based on the disturbance observer. Four papers in this issue deal with robot motion control systems using the disturbance observer. Mr. Oda explains the decoupling force control method of redundant robot manipulation by workspace disturbance observer which is not a joint space disturbance observer such as an ordinary disturbance observer. Dr. Komada explains the hybrid position/force control method based on second derivatives of position and force, which uses the force-based disturbance observer. Dr. Shimada explains the servo system considering a robot of low stiffness, which is based on the disturbance and velocity observer. This observer is mounted with each joint. Prof. Kuroe explains the decoupling control method of robot manipulation using a variable structure disturbance observer which is not an ordinary linear disturbance observer. The other three papers in this issue deal with robot motion control using the other advanced control system. Prof. Ohishi, myself explains the hybrid position/force control method without a force sensor, which is based on H00 acceleration controller and torque observer. This torque observer is the same observer as the ordinary disturbance observer. Mr. Fujimoto explains the three dimensional digital simulation of legged robots for advanced motion control. Mr. Kang explains the state estimation for mobile robots using a partially observable Markov decision process. This method can estimate the mobile robot state precisely and robustly. The two news reports in this issue deal with control and robot laboratory news from Japanese universities such as news generated by Prof. Hori of the University of Tokyo and Prof. Hori of Mie University. Both Prof. Horis are famous and active researchers in advanced motion control. This issue scans only one aspect of control systems, not the whole. Adaptive control, learning control, and other advanced control methods such as the LMI method are not mentioned. The subject of control systems in mechatronics is now expanding and developing. I greatly appreciate the efforts of the reviewers and authors in producing this issue, and I thank the Chief-Editor, Prof. Toshio Fukuda, for encouraging us to prepare it.

Human Motor Control and the Internal Model Principle

The main problem in control theory is controlling the output of a system to achieve the asymptotic tracking of desired signals and/or asymptotic rejection of disturbances. Among the existing approaches to asymptotic tracking and rejection, tracking via an internal model, which can handle the exogenous signal (The term “exogenous signal” is used to refer to both the desired signal and the disturbance when there is no need to distinguish them.) from a fixed family of functions of time, is one of the important approaches [1]. The basic concept of tracking via the internal model originated from the internal model principle (IMP) [2, 3]. The IMP states that if any exogenous signal can be regarded as the output of an autonomous system, then the inclusion of this signal model, i.e., the internal model, in a stable closed-loop system can ensure asymptotic tracking and asymptotic rejection of the signal. Given that the exogenous signals under consideration are often nonvanishing, the characteristic roots of these autonomous systems that generate these exogenous signals are neutrally stable. To produce asymptotic tracking and asymptotic rejection, if a given signal has a certain number of harmonics, then a corresponding number of neutrally stable internal models (one for each harmonic) should be incorporated into the closed-loop based on the IMP. Repetitive control (RC, or repetitive controller, also abbreviated as RC) is a specialized tracking method via an internal model for the asymptotic tracking and rejection of general T-periodic signals [4].

In complex industrial situations, modern permanent magnet synchronous motor (PMSM) servo drive system always face different kinds of disturbances, especially constant or slowly-varying disturbances (load disturbances) and periodic disturbances (torque ripples). Conventional disturbance rejection techniques, e.g., the extended state observer based control (ES-OBC) and the disturbance observer based control (DOBC), can only reject asymptotically single kind of disturbances (constant or slowly-varying disturbances). To this end, it is essential to extend the conventional disturbance rejection approach for multiple disturbances. Inspired by the internal model principle (IMP), appropriately embedding the model of disturbances into the design of disturbance observer, a composite disturbance observer based control is proposed for PMSM with multiple disturbances. The proposed disturbance observer (named as IMESO), consisting of the internal model principle (IMP) and the extended state observer (ESO), can reject multiple disturbances asymptotically. Thus, a composite control law consisting of proportional feedback and disturbance feedforward compensation is developed to control the speed loop. The proposed method is effective to reject the intricate multiple external disturbances and unmodeled dynamics. Simulations and experiments both verify the effectiveness of the proposed method.

In the practical application, Brushless DC motor (BLDCM) faces various disturbances including parametric uncertainties, load disturbance and unmodeled dynamics. These disturbances can be divided into two types of periodic disturbances (sinusoidal/cosinoidal) and aperiodic (slowly-varying or constant) disturbances. Velocity ripples can be seen as the result of a plurality of periodic interference signals of different frequencies acting on the system. In the paper we propose a composite control scheme combining integral sliding mode control (ISMC) based on disturbance observer (DO) embedded with the internal model principle to improve the speed performance of BLDCM. Conventional disturbance observer, such as extended state observer (ESO) can only asymptotically estimate slowly-varying or constant disturbances and is not good at estimating periodic disturbance. So we combine internal model of disturbance into disturbance observe for high precision. Then, the estimates are introduced in the feedforward compensation, and a composite speed controller is obtained. At last, experimental comparisons with conventional proportional-integral (PI) and ISMC+ESO, are given to validate the effectiveness of the proposed method.

This study presents an effective control algorithm to improve the robustness of fast steering mirror (FSM)-based laser-beam steering systems against dynamic disturbances, such as repetitive disturbances resulting from operating conditions. A stable control system must be able to maintain the required high-precision control, even when dynamic disturbances affect the FSM system. In this study, an improved control method is proposed using an internal model principle (IMP)-based nonlinear controller with a disturbance observer (DOB) for the FSM system. This IMP-based controller with DOB can attenuate the residual control-error signal under dynamic disturbance conditions.

Classical control theory will be used to explain what happens in the presence of observation noise and modeling errors. In addition, the relationship between real systems equipped with DC motors and robust control theory is explained. An example of how the reaction force observer realizes force sensorless control is shown. Specifically, the concept of disturbances and the basic design methods are introduced, and disturbance rejection control and acceleration control methods are explained. An observer for estimating the reaction force is introduced, and then the internal model principle and two-degrees-of-freedom control system are addressed. The chapter considers implementing a control system using a disturbance observer in a real system. The term “robust control” means control that is not easily affected by external disturbances or modeling errors due to parameter variations. Later, since the 1980s, research on robust control theory has been emphasized, and control theory using coprime factorization has been developed.

It is known that some rotational machines such as compressors, pumps and so on often generate noises and vibrations due to periodic disturbances synchronised with the rotational speed. Vibration suppressing systems such as repetitive control are known to be effective to suppress the periodic disturbances. However, the control input of the repetitive controller may become larger and larger when the control input is saturated. This paper designs a generalised disturbance observer using the internal model principle that is effective to suppress periodic disturbances, and proposes a method that can make control performance deterioration minimal even if the control inputs are saturated. First, the proposed system estimates disturbances using the disturbance observer. Next, the estimated disturbances are passed into a filter of which the gain is one and phase lag is zero at the disturbance's frequencies, and are added into the control input in order to cancel the periodic disturbance. This filter is designed using the internal model principle, and the reason is explained why the filter should not be set to one. Some motor system simulations show that the phase lag of the estimated disturbances correspond to that of the periodic disturbances so that the method can make control performance deterioration minimal. The method is appropriate to rotational machine systems such as compressors and pumps in which the vibrations and noises should be avoided.

This paper proposes a sliding-mode control (SMC) scheme based on the internal model principle (IMP) for robust reference tracking and disturbance rejection. The linear IMP controller is known for the capability of perfect tracking and disturbance rejection with an internal model of exogenous signals, while the SMC controller is robust to system perturbations and exogenous signals with unknown dynamics. An SMC design based on IMP is proposed to combine the best feature of these two fundamentally different but effective methods. Furthermore, with the help of the SMC, an initial state of the internal model is determined independently of system perturbations in order that transient performance is greatly improved as compared with that of the linear IMP controller. In addition, by properly assigning the initial state of the internal model, a sliding control law is derived to ensure the existence of a sliding mode during an entire response. This global sliding motion yields excellent robustness of the entire system at the beginning of system response and afterwards. Simulation results show the feasibility of the proposed scheme.

This paper describes a control method for the self-sustained operation of a photovoltaic (PV) generation system to compensate the output voltage distortion compensation. In order to improve the output voltage distortion, the control circuit consists of sinusoidal tracking control based on the internal model principle. Moreover, the control system is configured by combining the sinusoidal tracking control and a notch type disturbance observer. Thus, this configuration of the control system produces lower output voltage distortion. In addition, the zero location of sensitivity function is relocated by appropriately modifying the feedback element of the disturbance observer. The simulation and experimental results confirm that the proposed disturbance observer effectively reduces the output voltage distortion and improves the disturbance suppression characteristics. The THD of the output voltage is improved by 3.15 % using the proposed zero re-allocated disturbance observer in the case of the resistance and rectifier.

This paper presents the design of digitally controlled speed electrical drive, with the asymptotic compensation of external disturbances, implemented by using the IFOC (Indirect Field Oriented Control) torque controlled induction motor. The asymptotic disturbance compensation is achieved by using the DOB (Disturbance Observer) with the IMP (Internal Model Principle). When compared to the existing IMP-based DOB solutions, in this paper the robust stability and disturbance compensation are improved by implementing the minimal order DOB filter. Also, the IMP-based DOB design is improved by employing the asymptotic compensation of all elemental or more complex external disturbances. The dynamic model of the IFOC torque electrical drive is, also, included in the speed-controller and DOB section design. The simulation and experimental measurements presented in the paper illustrate the effectiveness and robustness of the proposed control scheme.

The internal model principle (IMP) was first proposed by Francis and Wonham [2, 3]. It states that if any exogenous signal can be regarded as the output of an autonomous system, then the inclusion of this signal model, namely, internal model, in a stable closed-loop system can assure asymptotic tracking or asymptotic rejection of the signal. Until now, to the best of the authors’ knowledge, there exist at least two viewpoints on IMP. In the early years, for linear time-invariant (LTI) systems, IMP implies that the internal model is to supply closed-loop transmission zeros which cancel the unstable poles of the disturbances and reference signals. This is called cancelation viewpoint here and only works for problems able to be formulated in terms of transfer functions. In the mid-1970s, Francis and Wonham proposed the geometric approach [4] to design an internal model controller [2, 3]. The purpose of internal models is to construct an invariant subspace for the closed-loop system and make the regulated output zero at each point of the invariant subspace. This is called geometrical viewpoint here.

According to the internal model principle from control engineering, error feedback together with a controller containing an internal model that generates an expected disturbance signal can achieve perfect delay-tolerant disturbance rejection using only modest loop gains. While internal models of plant dynamics have been central to the study of human motor control, internal models of reference or disturbance signal generators have received very little attention. In this paper we show how the internal model principle suggests a certain control strategy for achieving steady oscillatory motion in a virtual spring-mass. The strategy relies on haptic feedback in its dual roles of carrying power and information and this dual reliance may be used to derive numerous testable hypotheses. We present results from an initial study involving N=5 human subjects in which high time-correlation between surface electromyography and commanded torque signals suggests the adoption of a control strategy based on the internal model principle.

The internal model principle of control theory