Piecewise Constant Control Input Research Articles

Event-Triggered Adaptive Control of Coupled Hyperbolic PDEs With Piecewise-Constant Inputs and Identification

In this article, we present an event-triggered boundary control scheme with a, likewise, event-triggered batch least-squares parameter identification for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\times 2$</tex-math></inline-formula> hyperbolic PDE-ODE system, where two coefficients of the in-domain couplings between two transport PDEs, and the system parameter of a scalar ODE, are unknown. The triggering condition is designed based on evaluating both the actuation deviation caused by the difference between the plant states and their sampled values, and the growth of the plant norm. When either condition is met, the piecewise-constant control input and parameter estimates are updated simultaneously. For the closed-loop system, the following results are proved: first, the absence of a Zeno phenomenon; second, finite-time exact identification of the unknown parameters in most situations; third, exponential regulation of the plant states to zero. In the numerical simulation, the design is verified in an application of axial vibration control of a mining cable elevator, where the damping coefficients of the cable and the cage are unknown.

Flatness-Based Discrete-Time Control of a Battery Emulator Driving a Constant Power Load

In this article, a new method for controlling battery emulators in the shape of bidirectional step-down converters driving constant power loads (CPL) is presented. The CPL introduces nonlinear behavior into the system and causes unstable system dynamics. This property and the discontinuity introduced by the switches make it challenging to develop a suitable control strategy. Usually, switching frequencies are assumed to be fast enough for the controller to neglect the fact that the switches are either ON or OFF. As the desired dynamics of the system approaches the switching frequency of the converter, the discontinuity of the switches can no longer be ignored and the controller has to generate a suitable piecewise constant control input. A novel approach for arriving at a piecewise constant control input is presented and compared to state-of-the-art approaches. The advantages of the new control method are demonstrated with simulations as well as measurements from a hardware-in-the-loop testbed.

Robust self-triggered control for time-varying and uncertain constrained systems via reachability analysis

This paper develops a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. The resulting piecewise constant control inputs achieve communication reduction and guarantee constraint satisfactions. In the particular case when there is no uncertainty, we propose a control design with minimum number of samplings over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as computationally tractable mixed integer linear programs. The method is compared with the robust self-triggered model predictive control in a numerical example and applied to a robot motion planning problem with temporal constraints.

모터 제어 입력 제한 조건이 고려된 차륜 이동 로봇을 위한 효율적인 최소 시간 코너링(Cornering) 주행 계획

We propose an efficient minimum-time cornering motion planning algorithms for differential-driven wheeled mobile robots with motor control input constraint, under piecewise constant control input sections. First, we established mobile robot's kinematics and dynamics including motors, divided the cornering trajectory for collision-free into one translational section, followed by one rotational section with angular acceleration, and finally the other rotational section with angular deceleration. We constructed an efficient motion planning algorithm satisfying the bang-bang principle. Various simulations and experiments reveal the performance of the proposed algorithm.

차륜 이동 로봇의 모터 구동 전압 제한 조건을 고려한 코너링(cornering) 모션의 최소 시간 궤적 계획 및 제어

We propose time-optimal cornering motion trajectory planning and control algorithms for differential wheeled mobile robot with motor actuating voltage constraint, under piecewise constant control input condition. For time-optimal cornering trajectory generation, 1) we considered mobile robot's dynamics including actuator motors, 2) divided the cornering trajectory into one liner section, followed by two cornering section with angular acceleration and deceleration, and finally one liner section, and 3) formulated an efficient trajectory generation algorithm satisfying the bang-bang control principle. Also we proposed an efficient trajectory control algorithm and implemented with an X-bot to prove the performance.

Deadbeat control in multivariable non-linear time-varying systems with constraints of control inputs

A new approach to deadbeat control of a class of multivariable non-linear time-varying systems is presented. The approach enables us to find a non-linear control law, minimal positive integer N and a piecewise-constant control input vector subjected to constraints such that the output of closed-loop system coincides with given reference vector r( l) for ≥ NT, where r(<) represents the class of vector functions which can be generated in linear time-invariant systems, T is a given sampling period.

Deadbeat control in multivariable linear systems

A new approach to deadbeat control in multivariable linear time-invariant systems is presented. The approach enables us to find proportional-derivative output feedback gain matrices and a piecewise-constant control input vector such that the output vector of the closed-loop system coincides with a given reference vector r(t) for t≥Td, where r(t) represents the class of vector functions which can be generated in linear time-invariant systems, T is the given sampling period and d is the reachability index of the system.

Deadbeat control in multivariable non-linear time-varying systems

A new approach to deadbeat control of a class of multivariable non-linear time-varying systems is presented. The approach enables us to find a non-linear control law and a piecewise-constant control input vector such that the output vector of the closed-loop system coincides with a given reference vector r(t) for tdT, where r(t) represents the class of vector functions which can be generated in linear time-invariant systems, T is the sampling period and d is a given positive integer. The algorithm is illustrated by simple examples.

Characterization of state controllable time-delay systems with piecewise constant inputs. Part I. Derivation of general conditions†

The possibility of sampled-data feedback control for linear time-invariant multiple delay systems is studied using the constraint of piecewise constant control inputs. A split system representation is utilized to derive both necessary and sufficient conditions for control of the system state to the null function in the state space.