Osamu Kaneko

Data-Driven Controller Tuning: FRIT approach

Abstract In this tutorial paper, we give a basic concept of FRIT (fictitious reference iterative tuning) as one of the data-driven controller tuning methods. We explain how FRIT can achieve a desired property with only one-shot experiment. In addition, some new results on this tuning method are also presented. We also give comparisons between FRIT and the other data-driven controller tuning methods which yield the desired parameter with only one-shot experiment. Finally, as one of the applications of FRIT, we introduce the data-driven approach to simultaneous attainment of model and controller in the IMC architecture.

Fictitious Reference Iterative Tuning for Internal Model Controller

Abstract Internal model controller (which is abbreviated as IMC in the following ) is widely well-known as one of the easily-understandable controllers from the practical points of view. The reason for this is that IMC has a simple structure which works to decrease the error between the output of the actual plant and the output generated by the internal model included in the controller. In the case in which the internal model c ompletely reflects the dynamics of the actual plant, implementing the model of a plant to IMC yields the desired tracking property. Conversely, in the case in which we do not know a mathematical model of a plant, the achievement of the desired output by some sort of method based on the direct use of the data enables us to identify the plant as the internal model in IMC. Moreover, since the data has a fruitful information of the plant, the direct utilization of the data yields more desirable IMC controller in order to achieve a given specification with reflecting the actual dynamics of the plant. From these ideas, we propose the data-driven approach to IMC with Fictitious Reference Iterative Tuning (which is abbreviated as FRIT) as one of the controller design methods without using a mathematical model of a plant. We show that the minimization of the cost function in FRIT for IMC directly leads to both the optimal controller for achievement of a desired response and a mathematical model reflecting the dynamics of the actual plant, as will become apparent afterwards.

Fictitious reference tuning for the optimal parameter of a feedforward controller in the two-degree-of-freedom control system

In this paper, we propose an effective tuning method to obtain the optimal parameter of a feedforward controller in the two-degree-of-freedom (2DOF) control system for the sake of achieving the desired output without mathematical model of a plant. The first author proposed the effective method for the tuning of parameters of a controller by using only one-shot experimental data instead of using mathematical models of a plant, which is called “fictitious reference iterative tuning” (which is also abbreviated to FRIT). Here, we develop FRIT for the tuning of the feedforward controller in 2DOF control system. We introduce a new cost function consisting of the fictitious reference and the actual data for the purpose of that the required computation can be done by the least squares method (since we do not have to do iterative computation in the least squares method, we call the proposed method here as “fictitious reference tuning”). Since the cost function is quadratically-parameterized, it is possible to analyze how far the obtained parameter is apart from the desired one. For this purpose, we derive the pre-filter to be applied to the actual data. In addition, we also show that our proposed method is applicable for the case in which the initial experiment is performed in the one-degree-of-freedom control system. Finally, we illustrate an example in order to show the utility and the validity of our proposed method.

When Is a Storage Function a State Function in Discrete Time

The purpose of this paper is to investigate when a storage function is a state function in discrete time. As shown by Trentelman and Willems [Systems Control Lett., 32 (1997), pp. 249--259], [SIAM J. Control Optim., 36 (1998), pp. 1703--1749], every storage function is a state function in continuous time. At first glance, the same claim seems to hold also in discrete time. Contrary to this expectation, this is not true in general. In fact, the discrete time counterpart involves not only some different but also some more difficult issues compared with the continuous time case. This paper addresses these issues exactly and shows that every nonnegative storage function is a state function of a supply rate with a linear time-invariant dynamical system in discrete time.

FRIT based PID parameter tuning for linear time delay systems - Simultaneous attainment of models and controllers

Abstract In this paper, we provide a new method of the PID parameter tuning for time-delay systems by utilizing the fictitious reference iterative tuning (FRIT), which is a controller tuning method enabling us to obtain the desired parameter with only one-shot experimental data. Here, by relating the conventional PID controller to the internal model controller (IMC), we show that PID parameters obtained as the result of the FRIT yield not only a desired controller but also a mathematical model of the controlled time delay system. In order to show the validity of the proposed method, we give an illustrative example.

Simultaneous attainment of model and controller for linear time delay systems with the data driven Smith compensator

Abstract In this paper, we propose a data-driven approach to the Smith compensator for the simultaneous attainment of a controller and a mathematical model of linear time-delay SISO systems. Under the situation in which we do not know a mathematical model of a plant, the proposed method here enables us to obtain the optimal Smith compensator for the desired tracking property based on the direct utilization of a one-shot closed loop experimental data. In addition, by introducing the special structure to the feedback controller used in the Smith compensator, it is possible to obtain not only the desired controller but also the mathematical model of a plant with a time-delay. Finally, we also give an experimental result in order to show the validity of the proposed method.

Fictitious reference iterative tuning for a system with a time-delay and/or unstable zeros in the internal model control architecture

As one of the interesting and meaningful applications of a controller parameter tuning, this paper proposes a simultaneous attainment of both of a desired controller and a mathematical model of a plant in the internal model control (IMC) architecture. Particularly, we focus on systems with a time-delay and/or unstable zeros which cannot be neglected in many applications. For the purpose of the simultaneous attainment of a controller and a model of the plant, we introduce a specific structure of the feedback controller with a tunable parameter in IMC. And then, we utilize the fictitious reference iterative tuning (FRIT), which is a useful controller parameter tuning with only one-shot experimental data, for the tuning of the parametrized feedback controller and the parameterized internal model. In addition, we explain how the utilization of FRIT and the proposed structure on the feedback controller are effective for obtaining not only the desired control parameter but also an appropriate mathematical model of the plant. Finally, in order to show the validity of the proposed method, we give an illustrative example.

Fictitious reference iterative tuning of internal model controllers for a class of nonlinear systems

This paper presents a direct data-driven design or tuning of the internal model control architecture for a class of non-linear systems to achieve the desired output. We assume that the structure of a nonlinear system addressed here is known and the parameters are unknown. In addition, a nonlinear system addressed here is assumed to be with the property that the input time series and the output time series has one to one relation. For this type of nonlinear system, the internal model controller that is represented by the parameters of a model is introduced. Then, fictitious reference iterative tuning, which is one of the data-driven controller tuning methods based on the direct use of one-shot experimental data, is extended for tuning the parameterized internal model controllers. It is also shown that the cost function to be minimized in fictitious reference iterative tuning is related to both of the achievement of the desired tracking and the attainment of a model. That is, the proposed method in this paper enables us to simultaneously obtain a model and a controller by applying only one-shot experimental data to the parameterized internal model controller. A numerical example is also illustrated to show the validity of the result.

The canonical controller approach to data-driven update of state feedback gain

In this paper, a data-driven update or design method of desirable state feedback gains is presented. By utilizing the “canonical controller” developed in the behavioral framework, we derive a fundamental kernel representation of the canonical controller which yields a desirable state feedback gain and is also compatible with the trajectory of the system. We also show that such a kernel representation for the canonical controller can be obtained by minimizing a cost function which is linearly represented with respect to only one-shot experimental data. Finally, an illustrative example is given to show the validity of our proposed method.

Fictitious Reference Iterative Tuning of Disturbance Observers for Attenuation of the Effect of Periodic Unknown Exogenous Signals

Abstract In this paper, we develop a data-driven controller tuning for the disturbance observers. Particularly, we focus on the disturbance attenuation problem for a periodic unknown disturbance. However, in the case where it is difficult to construct inverse mathematical model of a plant which is implemented in the disturbance observer, we have to tale much time and costs for identification. In order to overcome such a difficulty, we utilize fictitious reference iterative tuning (FRIT), which is data-driven controller tuning with only one-shot experimental data, for tuning of parameters of controllers to eliminate the effect of the disturbance.