Robust Hybrid Position/Force Control for Robot Manipulators

The composite nonlinear feedback (CNF) control problem with event-triggered strategy for saturated systems with measurement feedback is considered in this paper. Both the full-order measurement and the reduced-order one are investigated to ensure the satisfactory performance of the closed-loop saturated systems under the proposed event-triggered mechanism. Generally speaking, the CNF control is divided into the linear control part and the nonlinear control part, which are designed separately. The purpose of the former is to shorten the rise time, while the latter aims at reducing the overshoot caused by the former. In this paper, a co-design method of linear and nonlinear control parts is proposed such that the control output tracks the reference input asymptotically with a good transient performance. Moreover, the parameter of CNF is applied to the construction of event-triggered mechanism which can efficiently reduce the communication burden. In order to avoid Zeno behavior, the minimum event-triggering time interval is explicitly formulated. Finally, an example of fighter aircraft is given for illustration.

Within the framework of the step‐function method, the stability of a nonlinear fuzzy hybrid control system that incorporates both an impulsive controller and a continuous state feedback controller is investigated. Both the two controllers are assumed to be subject to both actuator saturation and time‐varying delays, which has been given scant attention, if any, in the existing studies. A new assumption is introduced in this article, thereby enabling the use of generalized sector conditions to tackle the double saturation, and the conservatism inherent in stability results is remarkably reduced owing to the improved step‐function approach employed. The stability theorem proposed in this article removes constraints imposed on the time delays of both controllers, which can be also applied to wider scopes of systems, encompassing hybrid control systems with both stabilizing and instabilizing impulses, systems with varying impulsive gain, and systems with Zeno behavior. Numerical simulations of stabilization for different systems by delayed saturated hybrid control have been conducted, which demonstrate the validity of the proposed theorems.

This letter addresses the semi-global output regulation problem for continuous-time linear systems with input saturation and unknown dynamics. First, we employ a low-gain technique to design a state-feedback linear control law such that the control input operates within the linear region of the actuator. Then, taking it as the linear part, we construct a composite nonlinear feedback (CNF) control law, consisting of both linear and nonlinear parts, to improve the transient performance of the closed-loop system. Without requiring prior knowledge of the system dynamics or an initial stabilizing control policy, we propose a novel adaptive dynamic programming (ADP) learning algorithm. This algorithm learns both the linear part and the nonlinear part of the CNF control law using the same set of data. In addition, the algorithm uses single-layer filters, eliminating the need for integral operations during the learning process. Finally, the effectiveness of the proposed algorithm is demonstrated by an illustrative example.

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

The paper deals with design and simulation of nonlinear adaptive control of a shell and tube heat exchanger. The method is based on factorization of the controller on a nonlinear static part and an adaptive linear dynamic part. The nonlinear static part is derived using inversion and subsequent exponential approximation of simulated or measured steady-state characteristics of the exchanger. The linear dynamic part is then obtained from an external linear model of nonlinear elements of the closed-loop. The parameters of the external linear model are recursively estimated via a corresponding delta model. The control law in the 1DOF and 2DOF control system structures is derived using the polynomial approach. INTRODUCTION Heat exchangers are an essential part of many technologies in energy and chemical industry, polymer manufacturing, petroleum refineries, and many others. By construction, heat exchangers can be classified into exchangers with direct contact, various types of plate exchangers, and, shell and tube heat exchangers (STHEs), see, e.g. (Smith 2005; Hewitt et al. 1994; Incropera et al. 2011). As known, STHEs are most common types of heat exchangers. From the system theory, they belong to a class of nonlinear distributed parameter systems with mathematical models in the form of nonlinear partial differential equations. Modelling and simulation of such processes are described in many publications, e.g. in (Luyben 1989; Corriou 2004; Babu 2004; Ogunnaike and Rao 1994). As known, these processes can be hardly controllable by conventional methods that can lead to control of a poor quality. In this case, some advanced control methods should be used such as adaptive, predictive, optimal or nonlinear control, and some others. Obviously, control design always requires a preliminary steady-state and dynamic analysis of the process by simulation tools. Some methods of numerical mathematics used to build simulation models can be found e.g. in (Nevriva et al. 2009; Cook 2002). The aim of the paper is an application of nonlinear control and subsequent control simulation of a simple type of the shell and tube heat exchanger. The control strategy is based on the idea of factorization of the controller on a nonlinear static part (NSP) and an adaptive linear dynamic part (LDP). Similar approaches can be found e.g. in (Chen et al. 2006; Dostal et al. 2011b). The nonlinear static part is obtained from simulated or measured steady-state characteristic of the STHE, its inversion, exponential approximation, and, subsequently, its differentiation. On behalf of development of the linear part, the NSP including the nonlinear model of the STHE is approximated by a continuous-time external linear model (CT ELM). For the CT ELM parameter estimation, an external delta model with the same structure as the CT model is used. The basics of delta models have been described e.g. in (Mukhopadhyay et al. 1992; Garnier and Wang 2008). Although delta models belong into discrete models, they do not have such disadvantageous properties connected with shortening of a sampling period as discrete zmodels. In addition, parameters of delta models can directly be estimated from sampled signals. Moreover, it can be easily proved that these parameters converge to parameters of CT models for a sufficiently small sampling period (compared to the dynamics of the controlled process), as shown in (Stericker and Sinha 1993; Dostal et al. 2004). The 1DOF and the 2DOF control system structures are considered. In the first case, the control system includes only a feedback controller, in the second case, the controller consist of a feedback and a feedforward part. Such structures were described and applied e.g. in (Dostal et al. 2011a; Grimble 1993). Then, resulting CT controllers are derived using the polynomial approach and the pole placement method (Kucera 1993; Mikles and Fikar 2004). The simulations are performed on a nonlinear model of the STHE. MODEL OF THE STHE Consider an ideal plug-flow shell and tube heat exchanger in the fluid phase and with the counterflow cooling. The fluid flowing in tubes is cooled by a fluid flowing in the shell as shown in Fig. 1. Heat losses and heat conduction along the metal walls of tubes are Proceedings 28th European Conference on Modelling and Simulation ©ECMS Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani (Editors) ISBN: 978-0-9564944-8-1 / ISBN: 978-0-9564944-9-8 (CD) assumed to be negligible, but dynamics of the metal walls of tubes are significant. All densities, heat capacities, and heat transfer coefficients are assumed to be constant. Under above assumptions, the STHE model can be described by three partial differential equations (PDEs) in the form

The best exoskeleton control strategy depends on the task, motivating the development and analysis of an exoskeleton capable of position, force, and impedance control. In this paper, we implement and compare the three controller types via sliding mode control on a custom-built pneumatic cylinder ankle exoskeleton. To evaluate each controller's performance, the exoskeleton was tested on the benchtop and with human subject experiments. With the position controller, the exoskeleton achieved an root-mean-square error (RMSE) of under 5 deg for both the benchtop and human tests. It had a bandwidth of approximately 12 rad/s. The force controller tracked sinusoidal trajectories acceptably well at low frequencies (15% of force range at 6 rad/s), with a bandwidth of approximately 24 rad/s. The error was significantly higher (RMSE of 24% of force range) for the more biologically relevant trajectory. The impedance controller demonstrated the desired spring-like behavior, with position RMSE generally under 5 deg compared to expected position. All three controllers worked equally well for benchtop and human tests. Thus, a pneumatically powered ankle exoskeleton with sliding mode control is capable of accurate position and impedance control and is capable of marginally acceptable force control.

This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller.

This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.

This paper presents a stability analysis of nonlinear bang-bang impact control for a one degree of freedom robotic manipulator based on an analysis in L/sub 2/ space. The physical implications of sufficient stability conditions are explained in terms of sampling time, accuracy of inertia estimation, control gains, and rate of change in the Coriolis, centrifugal, and disturbance forces. The stability conditions are not stringent and are verified by simulations.

In this paper, model-based precision force and position control of an ionic polymer metal composite (IPMC) is presented. A 23.8 mm × 3.4 mm × 0.16 mm IPMC strip was used as an actuator in a cantilever configuration. Open-loop force and position responses of an IPMC are not repeatable, and hence closed-loop precision control is of critical importance to ensure proper functioning, repeat-ability and reliability. After feedback controllers were designed and implemented with empirically obtained fourth-order plant transfer functions, the overshoot decreased from 460 to 2.8 per cent and the settling time was reduced from 37.5 to 3.22 s in force control. In position control the overshoot decreased from 333 to 20.3 per cent and the settling time was reduced from 21.5 to 2.56 s. Microscale precision force and position control capabilities of the IPMC actuator were also demonstrated experimentally. An 8 μN force resolution was achieved with a force noise of 0.5μN r.m.s., and the position resolution was 6 μm with a position noise of 2.5 μm r.m.s. The maximum force and tip displacement achieved with the IPMC actuator under closed-loop control were 2 mN and 5 mm respectively. The IPMC actuator could follow various commanded force and position trajectories such as sinusoidal and trapezoidal position profiles, and a velocity profile with a 3 mm/s maximum velocity. A novel hybrid force and position control strategy demonstrated its utility in practical micromanipulalion applications where the actuator force must be limited to prevent damaging micro-objects. High-precision control of the IPMC at low force level proved its potential for micromanufacturing and micromanipulation applications such as robotic and biomedical microgrippers.

In this paper, position control of BLDC motor as actuator locomotive simulator platform is studied. The nominal plant is a combined part that consists of BLDC motor as a linear part and load torque disturbance as a nonlinear part. The linear part is obtained from position of BLDC motor when the cabin of the simulator is not attached. Meanwhile, the nonlinear part is an estimated load torque from a static behaviour when the cabin rotates on pitch motion. Linear Quadratic Error (LQE) and Integral Sliding Model Control (ISMC) are adopted to improve position tracking performance with nonlinear load torque problem so that the BLDC motor for driving the cabin according to reality. The simulation results show that LQE and ISMC have successfully improved the tracking performance than using a standard preinstalled PI controller and also inferred that ISMC has the best performance.

To address the demands for precision and load-bearing capacity in the installation of building panels, a hybrid force-position driven robot with redundant actuation has been developed. The mechanical performance of this robot is primarily governed by its central parallel mechanism, which is equipped with redundant actuators matching the degrees of freedom. Non-redundant and redundant actuators are respectively responsible for position and force control. The inclusion of redundant force-driven joints has increased the internal coupling within the mechanism. To enhance the coordination between position and force control, a hybrid synchronized control method based on cross-coupling has been proposed. Initially, kinematic and dynamic models of the parallel structure were established. Under predefined trajectories, the theoretical inputs for each actuator were calculated using inverse kinematics and dynamics. Subsequently, employing the principle of cross-coupling, the torque output from the position actuators was used as feedback. This feedback was processed by a synchronized coordination controller to adjust the output force of the redundant force-driven joints. By adjusting the output force of the redundant actuators, the torque burden on the position actuators was effectively reduced, thereby enhancing the precision of position control. Additionally, under the same load conditions, smaller power actuators could be utilized for position control, reducing the overall weight of the robot and improving its load-to-weight ratio. To validate the effectiveness of the proposed control strategy, a robotic simulation environment was established. The simulation results demonstrated significant reductions in the average torque required by the position actuators across three different trajectories, with reductions of 91.43%, 54.56%, and 80.6% respectively. Finally, the load-bearing capacity and the load-to-weight ratio of the prototype were assessed. Experimental results confirmed that the prototype achieved a load-to-weight ratio of 15.83%, validating the effectiveness of the hybrid synchronized control method based on cross-coupling.

ABSTRACTHeart rate can be used to define exercise intensity; feedback control systems for treadmills which automatically adjust speed to track arbitrary heart rate target profiles are therefore of interest. The aim of this study was to compare linear (L) and nonlinear (NL) controllers using quantitative performance measures. Sixteen healthy male subjects participated in the experimental L vs. NL comparison. The linear controller was calculated using a direct analytical design that employed an existing approximate plant model. The nonlinear controller had the same linear component, but it was augmented using static plant-nonlinearity compensation. At moderate-to-vigorous intensities, no significant differences were found between the linear and nonlinear controllers in mean RMS tracking error (2.34 vs. 2.25 bpm [L vs. NL], p=0.26) and average control signal power (51.7 vs. m2/s2, p=0.16), but dispersion of the latter was substantially higher for NL (range 45.2 to 56.8 vs. 30.7 to m2/s2, L vs. NL). At low speed, RMS tracking errors were similar, but average control signal power was substantially and significantly higher for NL (28.1 vs. m2/s2 [L vs. NL], p<0.001). The performance outcomes for linear and nonlinear control were not significantly different for moderate-to-vigorous intensities, but NL control was overly sensitive at low running speed. Accurate, stable and robust overall performance was achieved for all 16 subjects with the linear controller. This points to disturbance rejection of very-low-frequency heart rate variability as the overriding challenge for design of heart rate controllers.

In hybrid control of robot manipulators separate controllers are designed for force and position errors control. Controllers are designed either in task or joint space and their outputs combine to provide input torque to the manipulator. Position and force controllers performance in a constrained robotic task is affected by their interaction to a degree dependent on the controller's ability to reject disturbances. Ideally, decoupling of the two control loops is desired to achieve the best performance in position and force directions. In this article, analysis of control loop interactions is performed for contact and noncontact phases, and controller design requirements are developed to achieve maximum decoupling. Design requirements involve output subspace of each controller leading to control discontinuities for contact and noncontact phases. In the noncontact phase, satisfaction of design requirements leads to a fully linearized and decoupled system. When in contact with the constraining surface, design requirements eliminate disturbances in the force loop, but minimize disturbances in the position loop to an extent dependent on force loop performance. Known hybrid control schemes analysis is performed to reveal existence of control loop interactions in these schemes. Confirmation of theoretical analysis is done through simulation of a three revolute planar manipulator. © 1998 John Wiley & Sons, Inc.

This paper presents the design of an adaptive hybrid controller for linear switched reluctance motor (LSRM) to be used in pick and place industrial applications. The hybrid controller consists of two main controllers, the proportional-derivative controller (PDC) and the fuzzy logic controller (FLC). In this paper, the proposed Adaptive hybrid PD-fuzzy logic controller (AHPDFLC) uses, at the beginning, the adaptive PDC (APDC) for coarse position error while for fine position error the position control process is achieved using conventional FLC. This hybrid controller exploits the advantages of both controllers, APDC which can vary its gains online to avoid the overshoot problems and FLC which can decrease the steady-state error to roughly zero value to get an acceptable position tracking response of the underlying LSRM. The adaptivity of the hybrid controller refers to the variation of PDC's proportional and derivative gains to adapt a wide range of loading conditions i.e. a specific reference position signal, load force, mover mass, friction constant, applied dc voltage and phase resistance. PDC gain scheduling is achieved online based on fuzzy rules and reasoning. The results of AHPDFLC are compared with the results of non-adaptive position controllers. This comparison between different position controllers' response verifies the simplicity and the effectiveness of the proposed adaptive hybrid position controller for a wide range of variable loading conditions. Finite Element Method Magnetics (FEMM) and MATLAB/Simulink simulation programs are used throughout the paper to model the different modules of LSRM to prove the validity of this position controller approach on simulation environment.