Toshiharu Sugie

An iterative learning control law for dynamical systems

Abstract This paper is concerned with an iterative learning control law which enables us to find a control input that generates the desired output exactly over a finite time interval through the repetition of trials. We derive a sufficient condition for nonlinear systems to achieve the desired output by the iterative learning control. Based on this result, we show that the direct transmission term of the plant plays a crucial role in the error convergence of the learning process. Further, we identify the class of plants to which the learning control law is applicable.

Canonical transformation and stabilization of generalized Hamiltonian systems

Abstract This paper introduces generalized canonical transformations for generalized Hamiltonian systems which convert a generalized Hamiltonian system into another one, and preserve the generalized Hamiltonian structure of the original. As in classical mechanics, it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems. Firstly, the class of generalized canonical transformations and some of their properties are indicated. Secondly, it is shown how to stabilize the generalized Hamiltonian systems using canonical transformations. In addition, some examples illustrate how such transformations are utilized for control systems design.

Brief paper: Cooperative control for target-capturing task based on a cyclic pursuit strategy

This paper studies a methodology for group coordination and cooperative control of n agents to achieve a target-capturing task in 3D space. The proposed approach is based on a cyclic pursuit strategy, where agent i simply pursues agent i+1 modulo n. The distinctive features of the proposed method are as follows. First, no communication mechanism between agents is necessary and thus it is inherently a distributed control strategy. Also, it is a simple robust memoryless control scheme which has self-stability property. Finally, it guarantees a global convergence of all agents to the desired formation. Further, it is also guaranteed that no collision occurs. Simulation examples are given to illustrate the efficacy of the proposed method and the achievement of a desired pursuit pattern in 3D space.

Dynamic hybrid position/Force control of robot manipulators--Controller design and experiment

An approach to designing controllers for dynamic hybrid position/force control of robot manipulators is presented, and preliminary experimental results are given. Dynamic hybrid control is an extension of an approach proposed by M.H. Raibert and J.J. Craig (1981) to the case where the full manipulator dynamics is taken into consideration and the end-effector constraint is explicitly given by the constraint hypersurfaces. This design method consists of two steps. The first step is the linearization of the manipulator dynamics by nonlinear state feedback. Formulation of the constraint by the constraint hypersurfaces plays an essential role in establishing the linearizing law. The second step is the design of position and force controllers for the linearized model using the concept of two-degrees-of-freedom servocontroller. The merit of this servocontroller is that it can take account of both the command response and the robustness of the controllers to modeling errors and disturbances. Preliminary experiments using a SCARA robot show the validity of the approach. >

Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations

This paper addresses trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations and passivity-based control. The main strategy adopted in this paper is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. After obtaining the error system, tracking control of the original system can be achieved by stabilizing the error system via passivity-based approach. First, a fundamental framework is provided for constructing the error system via generalized canonical transformations. Then a concrete design procedure is derived for a class of electro-mechanical systems. Furthermore, the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness.

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H ∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H ∞ performance criteria.

Optimal dynamic quantizers for discrete-valued input control

This paper discusses an optimal design problem of dynamic quantizers for a class of discrete-valued input systems, i.e., linear time-invariant systems actuated by discrete-valued input signals. The quantizers considered here are in the form of a linear difference equation, for which we find a quantizer such that the system composed of a given linear plant and the quantizer is an optimal approximation of the given linear plant in the sense of the input-output relation. First, we derive a closed form expression for the performance of a class of dynamic quantizers. Next, based on the performance analysis, an optimal dynamic quantizer and its performance are provided. This result further shows that even for such discrete-valued input systems, a controller can be easily designed by the existing tools for the linear system design such as robust control theory. Finally, the relation among the optimal dynamic quantizer and two other quantizers, i.e., the receding horizon quantizer and the @D@S modulator, is discussed.

Synthesis of Optimal Dynamic Quantizers for Discrete-Valued Input Control

This paper presents an optimal dynamic quantizer synthesis method for controlling linear time-invariant systems with discrete-valued input. The quantizers considered here include dynamic feedback mechanism, for which we find quantizer parameters such that the system composed of a given linear plant and the quantizer is an optimal approximation of the linear plant in terms of the input-output relation. First, the performance of an arbitrarily given dynamic quantizer is analyzed, where we derive a closed form expression of the performance. Based on this result, it is shown that the quantizer design is reduced to a nonconvex optimization problem for which it is hard to obtain a solution in a direct way. We obtain a globally optimal solution, however, by taking advantage of a special structure of the problem which allows us to relax the original nonconvex problem. The resulting problem is easy to solve, so we provide a design method based on linear programming and derive an optimal structure of the dynamic quantizers. Finally, the validity of the proposed method is demonstrated by numerical examples.

Brief paper: Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.

Iterative feedback tuning of controllers for a two-mass-spring system with friction

In this paper, we present a two-degree-of-freedom controller tuning for two-mass-spring systems with friction based on the iterative feedback tuning (IFT) approach. While two-mass-spring systems are widely used as fundamental components of the mechanical servo systems, they have sometimes severe friction. In order to cope with such cases, we adopt two strategies. One is the separate tuning of feedback and feedforward controllers. In particular, the feedback controller is tuned to achieve low sensitivity rather than tracking. The other is to introduce a quasi-Newton method into a parameter renewal law. The effectiveness of the proposed method is demonstrated through numerical simulations. Furthermore, we evaluate its effectiveness by experiments.