In this paper, we analyze robust invariant set for peak-constrained disturbances. In the case of the periodically time-varying system, its performance is more difficult to analyze the robust invariant set accurately than that of the linear time-invariant system. We propose a method to improve the accuracy of estimating robust invariant set by using a combination of sequential state updates and invariant ellipses in a previous study. In this paper, we apply the method to a periodically time-varying system and verify its effectiveness.
Control barrier functions (CBFs) have been successfully implemented in various control strategies; one of those is a human assist control for moving obstacle avoidance by using time-varying CBFs. However, the human assist control contains the complete information on the motion of environments; in general, a derivative of moving obstacle states needs estimating. In this paper, we apply an exact differentiator to estimate derivatives of obstacle state signals in real time. Then, we propose a human assist control by using both a time-varying CBF and an exact differentiator. Moreover, the effectiveness of the proposed method is confirmed by computer simulation and experiments of an electric wheelchair.
This paper develops for a ball and beam system a design method of control system transferring the ball to a target position considering restricted beam angle. First, we compensate the beam drive system as a second-order delay system to reduce the beam angle constraint to an input one. Using modal decomposition methods, we decompose the plant into the stable and unstable subsystems, and derive a nested saturating control law globally asymptotically stabilizing the unstable one. The control system using this control law has the property that when the ball is transferred, its speed is mostly limited less than a specified value. To reduce the steady-state error of the ball position as well as to alleviate the reset windup, a new type of IMC controller is introduced where a saturated output error between the actual plant stabilized by the saturating control law and the model is fed back. The effectiveness of the control law is demonstrated numerically and experimentally.
On-/off-drive-type tracked vehicles are machines used for agricultural and snow vehicles. The kinematics model of this vehicle is a nonlinear system (called a driftless system), for that reason which general linear control theory cannot be used. One method to solve this problem is to use conversion to a time-state control form, which considers one of the state variables as a time axis. This conversion allows us to make the model a linear system. In addition, a converting input law in which the continuous-valued inputs obtained by state feedback are converted into discrete-valued inputs, is used for discrete-valued input systems control. However, when the above-mentioned conversion input law is applied to a system with a time-state control form, the theoretical conditions cannot be satisfied and errors may occur. This problem not only leads to theoretical discrepancies but also causes large response degradation due to excessive storage of errors in a servo system that includes an integrator. Therefore, in this study, we propose a method to reduce the theoretical discrepancies and prevent response degradation by adjusting the input time for on-/off-drive-type tracked vehicle control, using a time-state control form. We applied the proposed method to a linear tracking control using a servo system and confirmed its effectiveness through numerical simulations and experiments.