Isao Takami

Robust LQ control with adaptive law for MIMO descriptor system

This paper presents a robust LQ control system with Model Reference Adaptive Control(MRAC) law for MIMO system which is described as descriptor form. Generally, the performance degradation is expected to happen in case that uncertainty excess the upper and lower bound which are considered in the robust control synthesis process. For this problems, adaptive control algorithms have potential to improve performance and reliability in control system. In this study, we focus on this characteristics of adaptive control algorithms and add adaptive law into usual robust control system. The proposed system is synthesized by two-step approach. First of all robust LQ controller is synthesized through solving some LMI conditions. This robust LQ controller can be handle with limited uncertainty parameters. Second, adaptive law is designed and consolidated closed loop stability of adaptive loop and the robust LQ control loop is analyzed though solving quadratic stability conditions. The feature of this study are as follows: 1. Quadratic stability is analyzed in case of MIMO system described as descriptor form with adaptive law. 2. Convergence speed is considered at the design process of adaptive law with σ-modification. 3. The effectiveness of the proposed method is verified by some experiments using a test-scale 2 Degree-of-Freedom (2DOF) helicopter.

Robust LQ control of ABS based on polytopic representation using descriptor representation and linear fractional transformation

In this paper, a method is proposed to guarantee the robust stability for anti-lock braking system (ABS). The objective of ABS is to maintain the slip rate at the optimal value in any road condition. The dynamics of ABS depends rationally on the uncertain parameters, which are car velocity and the coefficient of friction between tire and road. The robust stability is required to design ABS with respect to these uncertain parameters. Descriptor representation and linear fractional transformation (LFT) are adopted to obtain an equivalent polytopic representation of dynamics, which is multi-affine to the uncertain parameters. The problem can be formulated as solving a finite set of linear matrix inequalities (LMIs) by using polytopic representation. The effectiveness of the proposed method is verified by simulations and experiments.

An online generation of time-optimal trajectories via simple feedforward filter and its implementation with two-degree-of-freedom system

Step response is usually used as the performance index of controlled systems. Thus, the ideal system would be one that has an output which approaches to the step signal quickly without error or over-shoot. However, if the output of an actual plant converges to the reference signal in a very short period, it can be dangerous to the surrounding environment as well as the operators. In such situations, some limitations on the acceleration and/or velocity of the plant would be necessary. In addition, any actual system has some limitations on their state variables and/or inputs usually caused by input saturation. For these actual systems, step function is not an achievable trajectory and in the worst cases, it makes the system unstable. Therefore, a moderated reference whose velocity and acceleration are constrained in certain values is important. In this paper, a non-linear feedforward filter for the step signal is proposed. The proposed filter, which has simple structure and requires less computational burden, produces time-optimal trajectories whose acceleration and velocity guarantee the limitations that are given a priori. Furthermore, a synthesis method of the two-degree-of-freedom system with the proposed filter is discussed and the effectiveness is substantiated with experimental results.

Robust control of active suspension — Improvement of ride comfort and driving stability using half car model

This paper presents a method of robust control for an active suspension to improve both ride comfort and driving stability. The ride comfort is related to the vertical and pitch vibration of car body. To improve ride comfort more effectively, the loop shaping is used for vertical and pitch motions based on ISO2631-1. On the other hand, the driving stability is evaluated by the fluctuation of vertical force of wheels which is affected by the pitch motion. To consider both of them more realistically, a half car model including vertical and pitch motions are analyzed. For practical application, to consider uncertain parameters is important. This paper focuses on the car body mass. The controller is designed to guarantee the robust stability for the uncertain parameter with polytopic representation. LQ controller, which can consider both performance and input energy, is used. The problem is formulated to solving finite LMIs. The effectiveness of proposed method is evaluated by the experiments.

Gain scheduled control for active magnetic bearing system considering gyroscopic effect

This paper proposes gain scheduled (GS) control for an active magnetic bearing (AMB) system. The system levitates and supports a rotor without contact. The AMB is unstable and strongly nonlinear due to characteristics of the magnetic levitation. Furthermore, gyroscopic effect occurs corresponding to the rotational speed and the moment of inertia of the rotor. Thus, the AMB system tends to be unstable by the gyroscopic effect. The rotational speed is not fixed but variable in actual operation. It is treated as a time-varying parameter. The moment of inertia does not changed in operation but different by situations. It is treated as an uncertain time-invariant parameter. The robust stability for the uncertain parameters in the rotational speed and the moment of inertia is guaranteed by using polytopic representation. Linear fractional transformation (LFT) is applied to design the GS controller via parameter dependent Lyapunov function. The problem of designing the GS controller can be formulated as solving a finite set of linear matrix inequality (LMI) conditions. The effectiveness of the proposed method is illustrated by simulations.

Robust control design for ball screw system focusing on the friction model

This paper proposes a method to solve practical problems of positioning control using a ball screw system. The practical problems contain two difficulties. First difficulty is that friction reduces the positioning performance. In this paper, the friction is divided into three components, which are a linear term including viscous friction, the Stribeck effect and a nonlinear term including static friction and Coulomb friction. The linear term friction can be considered in the framework of linear control synthesis. The nonlinear friction and the Stribeck effect are considered as disturbances. These are compensated by adding one integrator inside the controlled loop and loop shaping. The second difficulty is that the change in the mass of the load affects the system response. Moreover, it is shown that the viscous friction coefficient varies by some experiments. The controller is designed to guarantee the robust stability for uncertain parameters, which are the mass of the load and the viscous friction coefficient. The effectiveness of the proposed method is verified by simulations and experiments.

Robust H 2 control of active suspension — Improvement of ride comfort and driving stability

This paper suggests a method of robust control for an active suspension to improve both of the ride comfort and the driving stability using half car model. The ride comfort is evaluated by the vertical acceleration and the pitch acceleration of the human body. The driving stability is evaluated by the vertical force of front and rear wheels. The purpose of this paper is to improve the ride comfort and the driving stability by using state feedback. On the other hand, the robust stability is also important factor to evaluate the performance of the car. In this study, the front and rear weights of car body are considered as uncertain parameters depending on the passengers and the loads. Their weights influence on the pitch motion of the car body. The robust H2 controller is designed to guarantee the robust stability for the system with uncertain parameters with polytopic representation. These problems are solved by a finite set of Linear Matrix Inequality (LMI). The effectiveness of the proposed method is illustrated by simulations and experiments.

Nonlinear control for first-order nonholonomic system with hardware restriction and disturbance

In this paper, the tracking controller for a firstorder nonholonomic system affected by friction is synthesized. A linear approximated system of this system does not ensure the controllability. The system cannot be stabilized by using linear time-invariant state feedback. Control Moment Gyroscope (CMG) is a first-order nonholonomic system. Furthermore CMG has hardware restriction of a motion range. In this research, the state equation of CMG is converted into a chained system which is a canonical form of nonholonomic systems. The tracking controller is synthesized based on a backstepping approach. The integrator is applied in the controller to eliminate a steady-state error caused by coulomb friction. The stability of the system with the integrator is guaranteed theoretically by a Lyapunov function. The effectiveness of the proposed method is illustrated by simulations.

Robust control design for ball screw system via descriptor representation and loop shaping

This paper proposes a method to solve practical problems of positioning control using a ball screw system. The practical problems contain two difficulties. First difficulty is that friction affects the performance of it. In this paper, the friction is divided into three components, nonlinear term including static friction and coulomb friction, Stribeck effect and linear term including viscous friction. Nonlinear friction and Stribeck effect are considered as disturbance. These are compensated by designing controller including integrator and loop shaping. In contrast, linear term friction can be considered in framework of linear control synthesis. Second difficulty is that the change in mass of load affects the system response. Moreover, the experiment shows viscous friction coefficient varies. The controller is designed to guarantee the robust stability for uncertain parameters, which are the mass of load and the viscous friction coefficient. It is designed by using descriptor representation, polytopic representation and linear matrix inequality. The effectiveness of the proposed method is verified by simulations and experiments.

Gain scheduling control for magnetic levitation device using redundant descriptor representation

This paper proposes Gain Scheduling (GS) control for magnetic levitation device using redundant descriptor representation. The purpose of this study is to stably float a steel ball and let the distance between a coil and a steel ball follow the reference without error. GS control has a potential not only to deal with large variation range but also to improve the control performance. In this study, designed controllers are able to let a steel ball float stably in not a one equilibrium point but some variation range by scheduling an equilibrium point. However, designing a GS controller is difficult in the framework of state space representation. The redundancy of descriptor representation is applied to this difficulty. It is shown that a GS controller can be easily designed by introducing redundant descriptor variables. The robust stability for the system with uncertain parameters is guaranteed theoretically by using matrix polytope representation. Then, the problem is formulated as solving a finite set of Linear Matrix Inequalities (LMI) based on previous research. Finally, the effectiveness of the proposed method is verified by comparing a GS controller and a robust LQ controller in some simulations and experiments.