Flatness-based Control Design Research Articles

Discrete-time Flatness-based Controller Design using an Implicit Euler-discretization

In this contribution, we present a constructive method to derive flat sampled-data models for continuous-time flat systems through an implicit Euler-discretization. We show how the sampled-data model can be used subsequently for a flatness-based controller design, and illustrate our results with the well-known planar VTOL aircraft example.

Discrete-time flatness-based control of a gantry crane

This article addresses the design of a discrete-time flatness-based tracking control for a gantry crane and demonstrates the practical applicability of the approach by measurement results. The required sampled-data model is derived by an Euler-discretization with a prior state transformation in such a way that the flatness of the continuous-time system is preserved. Like in the continuous-time case, the flatness-based controller design is performed in two steps. First, the sampled-data system is exactly linearized by a discrete-time quasi-static state feedback. Subsequently, a further feedback enforces a stable linear tracking error dynamics. To underline its practical relevance, the performance of the novel discrete-time tracking control is compared to the classical continuous-time approach by measurement results from a laboratory setup. In particular, it turns out that the discrete-time controller is significantly more robust with respect to large sampling times. Moreover, it is shown how the discrete-time approach facilitates the design of optimal reference trajectories, and further measurement results are presented.

Flatness-based control design for the Saint-Venant equations with experimental results

Control design for a fluid in a pipe with arbitrary cross-sectional area is considered. The position (resp. the velocity) of a piston moving within the tube acts as control input. The system dynamics are described by the so-called Saint-Venant equations defined on a varying spatial domain. The flatness-based approach is utilized in order to parameterize rest-to-rest transitions of the system by means of the water level at the uncontrolled boundary. This way the contribution extends previous results to systems with moving boundary. The proposed control scheme is validated in experimental studies.

A Flatness-Based Nonlinear Control Scheme for Wire Tension Control of Hoisting Systems

A double-rope winding hoisting system (DRWHS) is usually employed to transport weight or workers in mines usually from ultra-deep underground (>1000m). An electro-hydraulic servo system (EHSS), which consists of two hydraulic cylinders, two movable headgear sheaves and lots of indispensable sensors, is employed to actively coordinate two wire tensions. The nonlinear dynamic model of the DRWHS is introduced and it is divided into two subsystems, i.e., the hoisting system and the EHSS with state space representations. However, as a complex machine-electricity-hydraulic system, the accurate dynamic model of the DRWHS is usually hard to obtain. Therefore, a flatness-based controller (FBC), which is insensitive to unmodeled characteristics of the dynamic model and measurement noises of sensors, is proposed to improve the tension coordination of two wire tensions of the DRWHS. The explicit FBC design schemes for the DRWHS and the control law are presented, and the stability of the proposed controller are proved by defining a Lyapunov function. The controller proposed is characterized by no derivatives of state variables and lower controller design complication so that measurement noises of sensors and unmodeled characteristics are not amplified. An experimental bench of the DRWHS is established to verify the performance of the proposed controller. Experimental results show that the proposed controller exhibits a better performance on the tension coordination control of two wire ropes compared with a backstepping controller (BC) and a conventional proportional-integral (PI) controller.

Differential flatness based control design for input and state constrained nonlinear systems via control Lyapunov barrier functions

Differential flatness based control design for input and state constrained nonlinear systems via control Lyapunov barrier functions

PLC-Based Real-Time Realization of Flatness-Based Feedforward Control for Industrial Compression Systems

In this paper, we present a novel programmable logic controller (PLC)-based real-time realization of a flatness-based feedforward control (FFC) scheme. The proposed approach is applied to an industrial fuel-gas compression system which is used to supply fuel gas to the gas turbines in combined cycle power plants. Due to the increasing demand for fast operation point transitions with high performance and accuracy requirements, the currently applied decentralized proportional-integral-derivative controllers appear to be not appropriate any more. Hence, by means of system simulations, a new flatness-based FFC design has been shown to provide improved control performance. In this paper, we bridge the gap between simulation-based control design and practical applicability, in that, we present the real-time realization of the approach on a PLC. Furthermore, the PLC-based controller is tested on a hardware-in-the-loop platform running with a complex compression system model in real time. The results reveal that the flatness-based control design can be implemented on a real compressor system.

Flatness-Based Torque Control of Saturated Surface-Mounted Permanent Magnet Synchronous Machines

Modern permanent magnet synchronous machines (PMSMs) may also be operated in regimes where significant magnetic saturation occurs. Classical fundamental wave models do not incorporate magnetic saturation in a systematic way. Mostly, only heuristic extensions can be found in the literature. Control schemes based on such $dq0$ -models are thus often unable to achieve the given control demands. This paper proposes a flatness-based torque control strategy for a saturated surface-mounted PMSM. Different to existing works, magnetic saturation is considered in a thorough and physically consistent way. Based on a calibrated magnetic equivalent circuit model of the PMSM, a simplified model suitable for the flatness-based controller design is derived. The proposed 2-DOF control scheme inherently accounts for the mutual coupling of the phase windings. Furthermore, the time-varying controller gains are obtained by pole placement technique. In contrast to the majority of controllers used for PMSM control, the proposed control scheme is formulated in the stator-fixed reference frame, and hence, no coordinate transformation is necessary. The flatness-based torque controller is implemented on an experimental test bench. An accelerated run-up of the PMSM with about four times the rated torque is performed to highlight the feasibility of the proposed approach. Finally, the flatness-based torque controller is compared with a common vector control implementation based on a $dq0$ -model of the motor.

Dynamical Modeling and Flatness Based Control of a Belt Drive System

AbstractBelt driven systems are part of many industrial applications, like computerized numerical control (CNC) machines in particular cutting machines and 3D‐printers. In this paper the dynamical modeling and a flatness based controller design for belt driven systems are proposed. Due to the special kinematics, the stiffness of the belt is nonlinear, leading to nonlinear equations of motion. By neglecting some minor dynamical effects, the resulting system simplifies to a differentially flat one. This allows to calculate nominal feed‐forward control torques by using the flat output of the system. To stabilize the error dynamics, an additional PD control law is introduced. The proposed method is compared with a controller, where elastic deflections for the feed forward part are neglected and elastic deformations are compensated by modifying the desired trajectories in a model‐based manner. The tracking performance of both methods is evaluated in certain simulations and experiments. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

1214 多入力多出力系に対するフラットネスを利用した非線形制御系設計(GS-10・15・16 制御技術)

1214 多入力多出力系に対するフラットネスを利用した非線形制御系設計(GS-10・15・16 制御技術)

Flatness based control design for a nonlinear heavy chain model

Flatness based trajectory generation and control design for the spatially distributed nonlinear model of a planar heavy chain with freely movable suspension point is presented. By means of the method of characteristics it is shown, that the solution of the governing equations can be parametrized by the trajectory of the uncontrolled end of the chain using time-delays and advances.

Control Design of a Continuous Furnace with Separated Heating Zones

In this contribution a new flatness-based control design for a continuous furnace with separated heating zones is developed. This system is described by a hyperbolic first order partial differential equation (PDE). The two degrees of freedom structure is used to solve the trajectory tracking problem. Therefore, a new control approach regarding the saturation of the actuators is introduced, in order to realize the underlying controller. Using the method of characteristics in combination with sensors attached to the good, the control design based on the characteristic differential equations can be done. The approach is applied to an experimental setup.

FLATNESS BASED CONTROL OF LINEAR TIME VARYING BOND GRAPHS

A general flatness based control design and parametrization procedure for single input time varying systems modelled by bond graphs is presented. The methodology is introduced in an algebraic framework provided by differential rings and modules theory. The method is applied to a flatness based control design of separately excited DC motor.

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.