Real-time Model Predictive Control of a Pendulum

In this work, a model predictive approach is applied on a mechanical system with a view on a real-time capable implementation. The mechanical system is represented by a pendulum, which consists of a sphere at the end of a long, thin rod. The rod is mounted on gimbals on a cross table, which can be moved by two DC motors. The control objective is trajectory tracking of the sphere, which can be realized by the control of these motors. In this work, linear model predictive control techniques are designed for the pendulum and are simulatively compared with regard to an accurate trajectory tracking and a real-time capable algorithm. A linear time-invariant approach is implemented on the experiment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic modelling and input-energy comparison for the elevator system

The elevator system driven by a permanent magnet synchronous motor (PMSM) is studied in this paper. The mathematical model of the elevator system includes the electrical and mechanical equations, and the dimensionless forms are derived for the purpose of practicable upward and downward movement. In this paper, the trapezoidal, cycloidal, five-degree (5-D) and seven-degree (7-D) polynomial and industry trajectories are designed and compared numerically in various motion and the absolute input energies. From numerical simulations, it is found that the trapezoidal trajectory consumes the minimum energy; the 7-D polynomial trajectory consumes the maximum one. The less end-point constraints are required, the less energy is consumed. Finally, the proposed sliding mode controller (SMC) is employed to demonstrate the robustness and well tracking control performance numerically.     

基于Labview的一级环形倒立摆逆系统轨迹法自动摆起控制

利用求解非线性方程两点边值问题,得到逆系统参考轨迹;通过设计逆系统前馈控制及LQR反馈控制器,对参考轨迹实时跟踪。基于QNET 2.0旋转倒立摆实验平台,采用Labview编程软件,实现了一级环形倒立摆的自动摆起与稳定的实物控制。实验结果证明控制算法的有效性,可以使一级环形倒立摆在一个摆周期内自动摆起,并保持稳定状态。与能量法自动起摆实验比较,逆系统算法具有较好的快速性和稳定性。     

Control of mechanical systems with uncertain parameters by means of small forces

An approach to the construction of a feedback control for non-linear Lagrange mechanical systems with uncertain parameters is developed. A Lagrange mechanical system with uncertain parameters, which is subject to the action of potential forces, control forces and unknown perturbations is considered is considered. It is assumed that the potential forces can be considerably greater than the control forces which, in their turn, are greater than the perturbations. An approach to the construction of a control, is proposed which enables one to bring a system from an arbitrary initial state to a specified final state in a finite time using a bounded control. A procedure, in which the specified nominal trajectory of the motion is tracked, is used. Initially, the trajectory, joining the specified initial and final states of the system, is constructed for a certain dynamical system which is close to the initial system but with completely known parameters. Then, using deviation equations, a control is constructed which brings the initial system onto this nominal trajectory in a finite time and subsequently forces the system to move along this nominal trajectory up to the final state. The control law used in tracking the nominal trajectory is based on a linear feedback, the gains of which depends on the discrepancy between the real trajectory and the nominal trajectory. The gain increase and tend to infinity as the discrepancies tend to zero but the control forces remain bounded and satisfy the conditions imposed on them. The results of numerical modelling of the controlled motions of a plane double pendulum are presented as an illustration.     

Comparing exact inversion and singular perturbation approaches for a serial flexible manipulator

This paper reviews the singular perturbation control theory in the context of flexible multibody systems. The theory is motivated and explained by a simple, but sufficiently complex model. It is explained that based on the singular perturbed model an end-effector trajectory tracking can be achieved by an integral manifold controller. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

卫星姿态跟踪的间接自适应模糊预测控制

对含模型不确定性和未知干扰的卫星姿态系统提出了具有间接自适应模糊补偿的广义预测跟踪控制方法. 首先基于卫星姿态动力学模型设计了非线性广义预测控制律, 再利用自适应模糊系统逼近预测控制律中的模型不确定项, 使得所得到的预测控制算法可实施.证明了当卫星姿态模型中不确定项满足一定条件时, 所设计的控制律可使卫星姿态跟踪误差收敛到原点的小邻域内,并仿真结果验证了所提出方法的有效性.     

Crane Dynamics with Modulated Hoisting

For many types of cranes commonly used in technical applications, the reduction of payload pendulations is an important design issue. Especially for cranes with variable cable length, oscillations are boosted by the hoisting of the payload due to nonlinear effects. Most of the techniques for active damping are based on a control input that displaces the support of the hoisting mechanism perpendicularly to the direction of the pendulum. However, controlled motion of the carrying structure might not be suitable or even impossible for some applications. The possibility to influence and reduce pendulations by means of feedback controlled variations of the cable length is hardly used in crane technology. A control strategy based on the phenomenon of autoparametric resonances in nonlinear dynamical systems is presented that manipulates the desired hoisting velocity by superposition of a suitably modulated motion in order to reduce amplifications of the pendulations, in particular in absence of other effective control inputs. Experimental results for a simple pendulum setup are presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear control of a variable displacement axial piston pump

In this contribution a mathematical model of a variable displacement axial piston pump controlled by a solenoid valve is derived. For the purpose of a controller design the mathematical model is simplified using singular perturbation arguments. The goal of the controller design is to track prescribed trajectories in the load pressure for arbitrary unknown load conditions. The control concept being proposed comprises a feedforward controller and a nonlinear backstepping controller combined with a load estimator for the trajectory error system. The feasibility of this control concept is shown by means of measurements on a test-stand. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

广义双线性系统的输出变结构控制

首次利用广义Lyapunov函数方法针对不确定广义双线性系统的输出变结构控制问题进行研究.首先,选取设计了带有滑动模动态补偿器的切换函数,保证了系统在准切换流形上的渐近稳定性.其次,在不确定参数和扰动范数有界的条件下,设计了变结构控制器,使得在控制下闭环系统在有限时间内实现滑模运动.最后,通过数值算例说明了设计方法的合理性和有效性.     

Model-based control strategies for systems with constraints of the program type

The paper presents a model-based tracking control strategy for constrained mechanical systems. Constraints we consider can be material and non-material ones referred to as program constraints. The program constraint equations represent tasks put upon system motions and they can be differential equations of orders higher than one or two, and be non-integrable. The tracking control strategy relies upon two dynamic models: a reference model, which is a dynamic model of a system with arbitrary order differential constraints and a dynamic control model. The reference model serves as a motion planner, which generates inputs to the dynamic control model. It is based upon a generalized program motion equations (GPME) method. The method enables to combine material and program constraints and merge them both into the motion equations. Lagrange’s equations with multipliers are the peculiar case of the GPME, since they can be applied to systems with constraints of first orders. Our tracking strategy referred to as a model reference program motion tracking control strategy enables tracking of any program motion predefined by the program constraints. It extends the “trajectory tracking” to the “program motion tracking”. We also demonstrate that our tracking strategy can be extended to a hybrid program motion/force tracking.     

Dynamics and chaos control in nonlinear electrostatic transducers

In this paper, we analyze the dynamics of a system consisting of two coupled nonlinearly Duffing oscillators, obtained from a nonlinear electrostatic device which is a prototype of emitters and receivers in communication engineering. Inverse or backward period doubling cascades and sudden transition to chaos are observed. A sliding mode controller is applied to control the electrostatic transducers system. The sliding surface used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. By means of the design of sliding mode dynamics characteristics, the controlled system performance is arbitrarily determined by assigning the switching gain of the sliding mode dynamics. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specification and use less control energy by comparing with the result in the current literature. The results show that the proposed controller can steer electrostatic transducers to the desired reference trajectory without chattering phenomenon and abrupt state change.     

Hybrid design of PID controller for four DoF lower limb exoskeleton

In this paper, a method of tuning a proportional-integral-derivative controller for a four degree-of-freedom lower limb exoskeleton using hybrid of genetic algorithm and particle swarm optimization is presented. Transfer function of each link of the lower limb exoskeleton acquired from a pendulum model, was used in a closed-loop proportional-integral-derivative control system, while each link was assumed as one degree-of-freedom linkage. In the control system, the hybrid algorithm was applied to acquire the parameters of the controller for each joint for minimizing the error. The algorithm started with genetic algorithm and continued via particle swarm optimization. Furthermore, a 3-dimensional model of the lower limb exoskeleton was simulated to validate the proposed controller. The trajectory of the control system with optimized proportional-integral-derivative controller via hybrid precisely follows the input signal of the desired. The result of the hybrid optimized controller was compared with genetic algorithm and particle swarm optimization based on statistics. The average error of the proposed algorithm showed the optimized results in comparison with genetic algorithm and particle swarm optimization. Furthermore, the advantages of the hybrid algorithm have been indicated by numerical analysis.     

Dynamic soft variable structure control of singular systems

The dynamic soft variable structure control (VSC) of singular systems is discussed in this paper. The definition of soft VSC and the design of its controller modes are given. The stability of singular systems with the dynamic soft VSC is proposed. The dynamic soft variable structure controller is designed, and the concrete algorithm on the dynamic soft VSC is given. The dynamic soft VSC of singular systems which was developed for the purpose of intentionally precluding chattering, achieving high regulation rates and shortening settling times enhanced the dynamic quality of the systems. It is illustrated the feasibility and validity of the proposed strategy by a simulation example, and an outlook on its auspicious further development is presented.     

Trajectory Planning and Feedforward Control Design for the Temperature Distribution in a Cuboid

The design of a feedforward tracking controller is considered for the temperature distribution in a cuboid, where the temperature on a single lateral surface can be arbitrarily prescribed by a control input. It is shown that there exists a so–called flat or basic output, which allows to explicitly derive the inverse infinite–dimensional system representation suitable for trajectory planning and for the determination of the respective control input necessary to track the desired trajectory in open–loop. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaos control of chaotic dynamical systems using backstepping design

This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lü systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results.     

Hybrid control for tracking of invariant manifolds

This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ free dynamics. The approach uses a stable manifold tracking objective in a computationally efficient, optimization-based switching control design. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Our method is validated for the cart–pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. The resulting feedback map for the cart–pendulum has a switching structure similar to existing energy based swing-up strategies. We use the Lyapunov function from these prior works to numerically verify local stability for our feedback map. However, unlike the energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.     

Adaptive-Repetitive Visual-Servo Control of Low-Flying Aerial Robots via Uncalibrated High-Flying Cameras

This paper presents the design and implementation of an adaptive-repetitive visual-servo control system for a moving high-flying vehicle (HFV) with an uncalibrated camera to monitor, track, and precisely control the movements of a low-flying vehicle (LFV) or mobile ground robot. Applications of this control strategy include the use of high-flying unmanned aerial vehicles (UAVs) with computer vision for monitoring, controlling, and coordinating the movements of lower altitude agents in areas, for example, where GPS signals may be unreliable or nonexistent. When deployed, a remote operator of the HFV defines the desired trajectory for the LFV in the HFV’s camera frame. Due to the circular motion of the HFV, the resulting motion trajectory of the LFV in the image frame can be periodic in time, thus an adaptive-repetitive control system is exploited for regulation and/or trajectory tracking. The adaptive control law is able to handle uncertainties in the camera’s intrinsic and extrinsic parameters. The design and stability analysis of the closed-loop control system is presented, where Lyapunov stability is shown. Simulation and experimental results are presented to demonstrate the effectiveness of the method for controlling the movement of a low-flying quadcopter, demonstrating the capabilities of the visual-servo control system for localization (i.e.,, motion capturing) and trajectory tracking control. In fact, results show that the LFV can be commanded to hover in place as well as track a user-defined flower-shaped closed trajectory, while the HFV and camera system circulates above with constant angular velocity. On average, the proposed adaptive-repetitive visual-servo control system reduces the average RMS tracking error by over 77% in the image plane and over 71% in the world frame compared to using just the adaptive visual-servo control law.     

Switched safe tracking control design for unmanned autonomous helicopter with disturbances

In this paper, the switched safe tracking control scheme is investigated for the attitude and altitude system of a medium-scale unmanned autonomous helicopter with output constraints and unknown external disturbances. To keep the attitude angles and altitude within the desired constrained range, an output boundary protection approach is adopted to generate an output constrained trajectory which is piecewise differentiable. The disturbance observer-based control method is employed to handle the unknown external disturbances of the system. Because of the piecewise differentiability of the output constrained trajectory, the closed-loop error system with the safe tracking controller can be seen as a switched system with jump dynamics. The multiple Lyapunov function method is adopted to guarantee the tracking performance with designed average dwell time. Simulation results of an example are provided to illustrate the effectiveness of the proposed control scheme for the unmanned autonomous helicopter system.     

Adaptive cooperative control of networked uncalibrated robotic systems with time‐varying communicating delays

This paper investigates the trajectory tracking control of the networked multimanipulator with the existence of time‐varying delays and uncertainties in both kinematics and dynamics. To address time‐varying delays in the communication links, a novel control scheme is established by the design of delay–rate‐dependent networking mutual coupling strengths. Besides, to handle the kinematic and dynamic uncertainties, an adaptive controller is designed. The proposed control scheme guarantees that the networked robotic system can track a commonly desired trajectory cooperatively with the strongly connected communication graph, uncertainties, and time‐varying communicating delays. A Lyapunov–Krasovskii functional is employed to rigorously prove the asymptotic convergence of both tracking errors and synchronization errors. The simulation results are provided to verify the effectiveness of the control method proposed by this paper.