Flat Controller Research Articles

Point-to-point virtual model control of a flexible joint robotic manipulator using trajectories of motion

This paper considers the use of trajectories of motion as a means of addressing the problem of unwanted oscillations and improving steady-state accuracy in the point-to-point motion of a flexible joint robotic manipulator using a novel third-order Poynting–Thomson virtual model control. A differentially flat model of the manipulator was exploited for classical controller design. The trajectories of motion were generated through a Newton interpolation procedure. The conditions for motion from rest to rest were derived and used to generate the trajectories required to steer the manipulator from one static point to another. Simulation and laboratory experiments confirmed that with the use of the trajectories of motion, rest-to-rest displacement is achieved without the unwanted swings about the final position. A marginal improvement in trajectory tracking performance was also verified by comparing it with the classical controller and state feedback controller. Moreover, the new controller showed better external disturbance rejection than the classical flat controller.

Differentially Flat Learning-Based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter

Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for faster computation, or nonlinear optimization methods, which typically perform better but can limit real-time applicability. In this work, we present a novel nonlinear controller that exploits differential flatness to achieve similar performance to state-of-the-art learning-based controllers but with significantly less computational effort. Differential flatness is a property of dynamical systems whereby nonlinear systems can be exactly linearized through a nonlinear input mapping. Here, the nonlinear transformation is learned as a Gaussian process and is used in a safety filter that guarantees, with high probability, stability as well as input and flat state constraint satisfaction. This safety filter is then used to refine inputs from a flat model predictive controller to perform constrained nonlinear learning-based optimal control through two successive convex optimizations. We compare our method to state-of-the-art learning-based control strategies and achieve similar performance, but with significantly better computational efficiency, while also respecting flat state and input constraints, and guaranteeing stability.

Control of single input Hamiltonian systems based on the flatness of their tangent linearization

We explore the incremental flatness based control of single input under-actuated nonlinear Hamiltonian systems exhibiting a controllable tangent linearization model around a given equilibrium point. General properties of controllable linearized Hamiltonian systems are presented, which significantly ease the stabilizing, or output reference trajectory tracking, feedback controller design for the nonlinear system. Controllability of the tangent linear system is equivalent to its flatness. A flat filter controller and a set of nested controllers are presented which are based on incremental position measurements alone. There will be no need for explicit estimations of the conjugate momenta through observers. The proposed controller is constituted by a set of nested, second order linear Flat Filter compensation networks acting on the second order pure integration models, naturally present in the input-to-flat output system structure. For pure integration perturbed systems, Flat Filters have been shown to be equivalent, in general, to reduced order extended state observer based Active Disturbance Rejection controllers. A challenging stabilization problem for an unstable, nonlinear, two spring–mass system carrying an inverted pendulum is considered. Computer simulations illustrate the effectiveness of the proposed controller design in the presence of flat output measurement noise.

Differentially flat trajectory generation and controller design for a quadrotor UAV

A control strategy of differentially flat trajectory generation and a backstepping controller for tracking the desired trajectory are developed for a quadrotor unmanned aerial vehicle (UAV). A glob...

Differentially flat trajectory generation and controller design for a quadrotor UAV

Differentially flat trajectory generation and controller design for a quadrotor UAV

Robust Flat Filtering Control of a Nonlinear Manipulator-Direct Current Motor System

This paper presents a linear robust output reference trajectory tracking controller, addressed here as a flat filtering controller (FFC), for nonlinear differentially flat systems. Here, we illustrate the controller's performance, via digital computer simulations and, also, via laboratory experiments, carried out on a single link-direct current (DC) motor driven robot manipulator undergoing a reference trajectory tracking task. The proposed linear FFC only requires the output to be regulated of the composite system and none of the internal states of the resulting third-order nonlinear system. The controller is designed on the basis of a drastic simplification of the combined single link-DC motor dynamics to a, perturbed, third-order pure integration system. This demonstrates the robustness of the proposed scheme with respect to ignored nonlinear state-dependent, endogenous, disturbances and, also, to independent unstructured exogenous disturbances inevitable in an experimental setup. Simulation and experimental results, as well as comparisons with other controllers, are presented.

Flat control of industrial robotic manipulators

A new approach to tracking control of industrial robot manipulators is presented in this paper. The highly coupled nonlinear dynamics of a six degrees of freedom (6-DOF) serial robot is decoupled by expressing its variables as a function of a flat output and a finite number of its derivatives. Hence the derivation of the flat output for the 6-DOF robot is presented. With the flat output, trajectories for each of the generalized coordinates are easily designed and open loop control is made possible. Using MATLAB/Simulink S-functions combined with the differential flatness property of the robot, trajectory tracking is carried out in closed loop by using a linear flat controller. The merit of this approach reduces the computational complexity of the robot dynamics by allowing online computation of a high order system at a lower computational cost. Using the same processor, the run time for tracking arbitrary trajectories is reduced significantly to about 10 s as compared to 30 min in the original study (Hoifodt, 2011). The design is taken further by including a Jacobian transformation for tracking of trajectories in cartesian space. Simulations using the ABB IRB140 industrial robot with full dynamics are used to validate the study.

Robust flat filtering DSP based control of the boost converter

The article deals with the design and implementation of a flat filter tracking digital controller for a boost DC-DC power converter. A highly perturbed switched boost converter circuit is shown to be efficiently controlled, in a trajectory tracking task for its non-minimum phase output, by means of a suitable linear filter, here addressed as a flat filter. Flat filtering is a natural robust version of generalized proportional integral control (GPIC) by which the effects of arbitrary time varying exogenous disturbances, unknown endogenous nonlinearities and un-modeled dynamics can be jointly attenuated in a conceptually similar fashion to observer-based active disturbance rejection control (ADRC) and algebraic identification based model free control (MFC) but: a) without using extended state observers and b) respecting the original system order in a time-varying simplified model while avoiding algebraic estimation techniques. The proposed control technique based on the TMS320F28335 digital signal processor chip is tested by means of realistic simulations and experimental setup.

Hierarchical Distributed Control for Interconnected Systems

Most approaches concerning distributed control for physically interconnected systems assume a flat controller structure, i.e. the subsystems exchange state information directly and in each timestep. In this paper, ideas from distributed control, network topology optimization and optimal control are combined in order to construct a distributed two-layer state feedback control structure. A decomposition algorithm is proposed which groups the subsystems into distinct clusters. Within each cluster, information is exchanged between the subsystems in every timestep. On the upper layer of the hierarchy, informaton is exchanged between the clusters with a lower frequency. The underlying communication topology is optimized to obtain a compromise between control performance and communication cost. This leads to reduced communication between the subsystems compared to existing hierarchical approaches.

Flat controller design for hardware-cost reduction in polar-axis photovoltaic systems

Abstract Initial costs of solar-photovoltaics have remained a significant factor contending against the wide-spread utilization of solar energy. The paper demonstrates that the concept of differential flatness could be used to design controllers for a polar-axis solar tracker that would enable reduction in hardware costs. Key results show that, the implementation of trajectories of motion in the controller can reduce the drive power requirement and associated photovoltaic (PV) cost by about 31%, and enable the use of smaller drive motors with a possible 25% reduction in drive motor costs; and that the implementation of sensorless control in the polar-axis tracking system is able to further lead to sensor cost elimination.

A novel OLED controller with fractal scan scheme

Based on the mathematical model of the optimal scan architecture of gray-scale imaging, this paper presents the design and logic implementation of a novel organic light-emitting display (OLED) gray-scale controller with the fractal scan scheme to efficiently increase the scan utilization and imaging quality. Through the exploration of the sub-space code sequences and bit code sequences for different gray levels, the authors first complete the design and implementation of the parameterized fractal scanning IP core for various gray levels, which can be used in every flat panel display controller. And then a novel OLED gray-scale controller embedded in a fractal scanning IP core is designed. It can efficiently increase the imaging gray levels and speed up frame frequency of display systems. Serial applications and tests indicate that the novel controller can obtain 100% scan utilization and a significant decrease in the system clock frequency (a multiple of 29 for 256 gray levels), compared with the traditional scan methods. With the proposed method there is no need of using high-speed IC circuits to realize the high articulation and resolution display of video images. Thus, the paper provides a new approach and an engineering way to solve one of the pressing problems of high-resolution flat panel display technology.

Theoretical fundamentals of the method for thermal diffusivity measurements from auto-oscillation parameters in a system with a thermal feedback

Theoretical fundamentals of the method to determine thermal diffusivity from auto-oscillation parameters in a control system, CS, with thermal feedback through the test specimen, are developed. The equation of a CS with a flat specimen and proportional controller (nonlinear boundary value problem of nonstationary heat conduction) is considered. Periodic solutions of the boundary value problem, which is linearized in the vicinity of the stationary solution, are analyzed. It is proved that, with a certain value of CS gain factor, excitation of auto-oscillations occurs. Their frequency ωc is related to the thermal diffusivity α as α = Cωc, where C is constant. By nonlinear analysis, it is revealed that the auto-oscillation excitation mode is soft and the frequency depends on the gain factor to a very weak degree. Formulas for calculation of the thermal diffusivity and the specimen temperature field are obtained.