Feedforward Control Law Research Articles

Attitude stabilization of a rigid spacecraft with actuator delay and fault

Time delays and actuator faults are phenomena which are frequently encountered in practical control systems and are found to have significant effects on the performance of operation and control. It is shown that even a very small delay may destabilize the spacecraft system. Therefore, besides considering the effects of modelling uncertainties and external disturbances, time delay and actuator fault effects should be properly handled in the spacecraft to achieve reliable and accurate control. This paper describes a simple and effective method to attitude stabilize a spacecraft. The proposed method works by augmenting a backstepping controller with a modified extended state observer-based feedforward control law. The backstepping control is used to compensate for an unknown delay in the inputs, while the feedforward term attenuates the effects of modelling uncertainties, external disturbances and actuator faults. In particular, actuator faults, modelling uncertainties and external disturbances are viewed as unknown nonlinear functions of the measurable state variables, estimated using a modified extended state observer, and then compensated for. The effectiveness of the proposed control algorithm is analytically authenticated and verified via simulation studies.

Active control of bending waves propagating in an orthotropic rectangular panel

Due to the recent advances in microprocessors, active control of a flexible structure has become a realizable method for suppressing the vibration. Conventional modal-based method encounters difficulties in controlling a distributed parameter structure, since such a structure has an infinite number of vibration modes. To overcome this problem, active wave control has been studied in recent years. This paper presents an active wave control of an orthotropic rectangular panel by expanding the conventional active wave control method for a two-dimensional structural case. First, a transfer matrix method for a rectangular panel is introduced to describe the wave dynamics of the structure. This is followed by the derivation of feedforward control laws for absorbing reflected waves or eliminating transmitted waves. In the proposed method, the control laws are including the modal actuation scheme for uncontrolled direction. Then, from a viewpoint of numerical analyses, basic properties of the proposed method are verified. It is found that the reflected wave absorbing control enables the inactivation of all vibration modes in the controlled direction and the transmitted wave eliminating control enables the generation of an almost vibration-free state.

Fixed-Structure Feedforward Control Law for Minimum- and Nonminimum-Phase LTI SISO Systems

Fundamental limitation of the model-inverse feedforward control results from instability or noncausality of the inverse of nonminimum-phase dynamics which cannot be applied in practice. To overcome this limitation, the approximate-inverse methods have been proposed in the literature. Structures of feedforward controllers proposed so far highly depend on a plant model structure. Therefore, in general, their implementation may be inconvenient or troublesome in industrial applications. In this context, a simple fixed-structure feedforward control law is proposed in this paper in the form of a weighted linear combination of a reference trajectory and its time derivatives. Design rules for selection of the weights are derived and provided in an explicit (analytical) form. The proposed control law can be applied to both nonminimum- and minimum-phase linear time invariant single-input-single-output systems. The new method has been compared with classical feedforward controllers known from the literature, revealing its advantages and limitations. The results of numerical examples and experimental validation tests obtained for an electronic plant have been reported.

Automated generation of feedforward control using feedback linearization of local model networks

An effective but yet simple approach is introduced to automatically attain a dynamic feedforward control law for non-linear dynamic systems represented by discrete-time local model networks (LMN). In this context, feedback linearization is applied to the generic model structure of LMN and the resulting input transformation is used as model inverse. This general and automated approach for model inversion is applicable even when the overall model complexity may be high. Thus, by representing a non-linear dynamic system by an LMN and applying the proposed feedforward control law generation, a dynamic feedforward control for such a non-linear system can be found automatically with the knowledge of measured input–output data only. However, when feedback linearization is considered, the stability of the internal dynamics plays a key role. This paper analyses the occurring internal dynamics for LMN, which directly result from the chosen model structure in identification, and discusses the effects on the transformed system. Finally, the effectiveness of the proposed data-driven feedforward control is demonstrated by a simulation example as well as by an actual application to the pre-distortion of a microelectromechanical systems (MEMS) loudspeaker with electrostatic actuation.

Block-oriented feedforward control with demonstration to nonlinear parameterized Wiener modeling

Block-oriented modeling (BOM) is a multiple-input, multiple-output modeling approach for nonlinear dynamic processes. Current implementation of BOM into feedforward control (FFC) results in linearization of the model and decomposition into separate components for each input. This work presents a multiple-input BOM FFC approach that does not linearize and decompose the BOM into separate components for each input. This implementation uses a new FFC law that uses the complete BOM in the time domain. The approach is demonstrated with a Wiener model for a simulated continuous stirred tank reactor (CSTR) with four (4) measured inputs. The Wiener model is nonlinear in the physically-based dynamic parameters of the transfer functions and linear in the static parameters of the static gain function. The static gain function has a second order linear regression form with interaction and quadratic terms. The Wiener model is built under open-loop conditions using a Box–Behnken statistical experimental design consisting of 27 sequential step tests. Under a sequence of multiple input changes, the addition of this feedforward controller to the feedback controller reduced the standard deviation of the controlled variable from its set point by 70% in comparison to the response with only feedback control.

Fourth-Arm Common-Mode Voltage Mitigation

The adverse effect of common-mode voltage (CMV) in pulse-width modulation inverters is widely acknowledged. Various approaches for mitigating CMV effect in PWM inverters have been proposed in the literature but they either show limited effect or impair the utilization of the drive. This paper proposes an active method for eliminating CMV in multilevel inverters which is independent on the inverter topology or its modulation scheme. In particular, the proposed method does not restrict the modulation index range of the drive. A detailed analysis of the active filter circuitry and a closed-form feed-forward control law are provided. Finally, selected simulation and experimental results are presented to validate the theoretical part.

Nonlinear Flatness-Based Control of Driveline Oscillations for a Powertrain with Backlash Traversing

Load changes in automotive powertrains may cause uncomfortable vibrations during vehicle acceleration. These driveline oscillations occur due to flexible and underdamped shafts. Furthermore, backlashes in the drive train represent hard nonlinearities and lead to challenges in control. Reducing vibration only by feedback control may destabilize the closed loop due to time delays in the powertrain system. This paper proposes a flatness-based feedforward control law based on a two-mass powertrain model with backlash to compensate oscillations. In addition, a proportional feedback controller is used to damp remaining oscillations arising from model mismatches and disturbances after the set-point transition. Simulation results show improved tracking performance in comparison to a feedforward approach without considering backlash explicitly.

Automated generation of a dynamic feedforward control law using local model networks with disturbance inputs

AbstractAn effective approach is presented, which automatically generates a dynamic feedforward control law for nonlinear dynamic systems represented by a discrete‐time local model network (LMN) as one class of data‐driven models. In this context, feedback linearization is applied to the generic model structure of LMN and the resulting input transformation is used as model inverse. Thus, by representing a nonlinear dynamic system by an LMN and applying the proposed feedforward control law generation, a dynamic feedforward control for such a nonlinear system can be found automatically with the knowledge of measured input/output data only. In addition, several disturbance inputs are considered in the feedforward control law without restrictions on their relative degree. However, only multiple input LMN where no internal dynamics are involved, i.e. the LMN has full relative degree with respect to the control signal input, are considered in this manuscript. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Improved direct inverse tracking control of a piezoelectric tube scanner for high-speed AFM imaging

For a piezoelectric tube scanner (PTS), this paper proposes an improved direct inverse tracking control algorithm and apply it to an atomic force microscope (AFM) to accomplish high-speed scanning tasks. That is, to enhance the high-speed tracking control performance of a PTS, an improved direct inverse rate-dependent Prandtl–Ishlinskii (P–I) model is firstly constructed, which includes a polynomial module to eliminate the structure nonlinearity. Based on the model, a practical feedforward control law is then designed to implement high-speed tracking control for a high-frequency trajectory with strong robustness, which presents the advantages of high-speed response, simple structure and convenient implementation. Subsequently, the designed feedforward law is combined with a feedback component, and the combined control strategy is employed in an AFM to accomplish fast imaging tasks. Numerous experimental results are then collected, which convincingly demonstrate the superior performance of the proposed practical model/control scheme.

An Extended Static and Dynamic Feedback–Feedforward Control Algorithm for Insulin Delivery in the Control of Blood Glucose Level

The potential for successful automatic control of blood glucose concentration (BGC) has entered a new era because of recent technological advancements in insulin pumps and blood glucose sensors. However, a critical advancement necessary for full automation and long-term use is a control algorithm that can effectively maintain tight control of BGC under extreme variation of important disturbances such as activity, stress, and food consumption. Because feedforward control (FFC) models disturbances directly, it has the potential to eliminate the effects of disturbances completely. A Wiener-type feedforward control law is limited to the inclusion of only input (i.e., modeled disturbances and the manipulated variable) dynamics. Using a semicoupled modeling network that includes pseudo-blood insulin concentration, this work presents a more phenomenological FFC law that includes input dynamics, blood insulin and blood glucose dynamics, and blood glucose levels. Modeling results on 15 adults with type 1 diabetes ...

Optimal Disturbance Rejection Control of Underactuated Autonomous Underwater in Vertical Plane

To realize the optimal control of underactuated autonomous underwater vehicle (AUV) in vehicle plane with external disturbances, a optimal disturbance rejection controller is proposed with respect to the quadratic performance indexes. Firstly, the depth control model of underactuated AUV system and the wave model is proposed; Then based on the theory of the quadratic optimal control and stability degree constraint, a feedforward and feedback optimal disturbance rejection control law with a higher mean-square convergence rate is derived from the Riccati equation and the Sylvester equation, which can reject the disturbance influence to AUV. Finally, the controller is applied to the dive plane control of AUV with wave force disturbances, and the results demonstrate the effectiveness and robustness of the controller. DOI: http://dx.doi.org/10.11591/telkomnika.v13i1.6889

Motion planning for a piezo‐actuated structure modeling a wingsail

AbstractThis contribution presents the modeling and the motion planning of a flexible interconnected beam structure representing a wingsail. The structure is equipped with spatially distributed embedded actuators. The solution of the motion planning provides a feedforward control law to realize a desired spatial‐temporal out‐of‐plane deflection trajectory. For this, a systematic flatness‐based methodology is proposed, that allows for an efficient numerical solution exploiting, e.g., finite element approximations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Automatic Generation of Feedforward Controllers using Dynamic Local Model Networks

A new approach for the automatic generation of a dynamic feedforward control law for nonlinear dynamic systems represented by discrete-time local model networks (LMN) is proposed. The generic model structure of LMNs offers the opportunity to apply such a general and automated approach for model inversion, even when the overall model complexity may be high. LMNs can represent nonlinear dynamic systems of almost arbitrary complexity. Their generic structure allows the generation of a feedback linearizing input transformation in a highly automated way. This paper proposes and discusses such an approach for the important class of LMNs with minimum-phase property. As a subclass of the class of minimum-phase LMNs, only those without numerator dynamics are considered in this manuscript. By using the input transformation, which results from feedback linearization, the feedforward control law is obtained. It can then be applied online for any reference trajectory without pre-planning. Thus, by representing a nonlinear dynamic system by the generic structure of an LMN and applying the proposed feedforward control law generation, a dynamic feedforward control for such a nonlinear system can be found automatically. Finally, the effectiveness of the method is shown on results for a Wiener model.

Optimal Vibration Control for Vehicle Active Suspension Discrete‐Time Systems with Actuator Time Delay

This study researches the vibration control approach for vehicle active suspension discrete‐time systems with actuator time delay under road disturbances. First, the discrete‐time models for the quarter vehicle active suspension system with actuator time delay are presented, and road disturbances are considered as the output of an exosystem. By introducing a discrete variable transformation, the discrete‐time system with actuator time delay and the quadratic performance index are transformed into equivalent ones without the explicit appearance of time delays. Then, the problem of original vibration control with actuator time delay is transformed into the optimal vibration control for a non‐delayed system with respect to the transformed performance index. Based on the maximum principle, the feedforward and feedback optimal vibration control law is obtained from Riccati and Stein equations. The existence and uniqueness of the optimal control law is proved. A reduced‐order observer is constructed to solve the physically realizable problem of the feedforward compensator. Finally, the feasibility and effectiveness of the proposed approaches are validated by a numerical example.

A mixed approach for the control of a testing equipment employed for earthquake isolation systems

This paper presents an activity concerning the modelling and control of a system adopted to perform shear tests on seismic isolators. The test rig consists of a hydraulic actuation system that drives a sliding table mounted on linear bearings. The system is characterized by non-linearities such as hydraulic proportional valve dead zone and frictions. A non-linear model is derived and then employed for parameter identification procedure. The test rig needs a suitable controller able to guarantee the desired table displacement in presence of unknown reaction force of the device under test. The proposed approach consists of a feedforward control integrated with a feedback one. The feedforward control law takes the form of a non-linear inverse model of the system. In this way, it is possible to obtain the desired target without affecting the stability of the test rig. The feedback control has the function to compensate for tracking error due to the model uncertainties and the unknown isolator reaction force. Therefore, the feedback control is not required to compensate for the large non-linearities: in this manner, it is possible to obtain good tracking results without the increasing of the feedback control gain that would change the stability properties of the plant. Numerical simulations have been performed in order to evaluate the goodness of the designed control with and without the specimen under test. Experimental tests show that the controlled system simulations are able to predict the controller performance. The experimental results also confirm that the performance of the proposed controller fully satisfy the standards concerning the testing procedure of seismic isolators.

A Feedforward Controller to Regulate the Chemical Composition of Molten Steel in a Continuous Casting Tundish

A feedforward controller for the automatic regulation of chemical composition of molten steel in the tundish of a continuous casting machine is proposed in this work. The flow of molten steel inside the tundish is modeled as a distributed parameter system, and the resulting partial differential equation is transformed into a set of ordinary differential equations by means of the finite differences technique. From the above set and using a proper boundary condition, a feedforward control law is synthesized. No experimental tests are reported, however, the dynamic performance of the controller is illustrated by means of numerical simulations.

Improving transient performance for output regulation problem of linear systems with input saturation

SUMMARYThis paper addresses the transient performance of output regulation problem for general linear system with input saturation. To improve the transient performance, the composite nonlinear feedback (CNF) control technique is introduced to solve the output regulation problem. On the basis of the linear feedback control law that solves the output regulation problem, a state feedback CNF control law and an output feedback with feedforward CNF control law are constructed, respectively. The CNF control law consists of a linear feedback part and a nonlinear feedback part. Introducing the nonlinear feedback part does not change the solvability condition of the output regulation problem, but the transient performance can be improved significantly by appropriately choosing the linear feedback gain and the nonlinear feedback gain in the CNF control law. The effectiveness of the CNF control is illustrated by a disturbance rejection problem.Copyright © 2012 John Wiley & Sons, Ltd.

Constrained Temperature Control of a Solar Furnace

A new constrained control strategy for a solar furnace is proposed in this paper with the goal of attaining a minimum-time transition between two values of the temperature subject to constraints on both the saturation and slew rate level of the process input. In the case of set-point step-shape signals, the strategy basically consists in implementing a (model-based) feedforward control law with maximum positive and negative velocity phases in order to obtain a minimum-time transition with no overshoot. In the case of ramp-shape set-point signals (addressing the output slew-rate constraint), the suitable feedforward control law is obtained by also inverting the dynamics of the system. Implementation issues are discussed. Simulation and real experimental results demonstrate the effectiveness of the methodology.

Study on the Congestion Controller for Timedelay Networked Control Systems with External Disturbances

Abstract A successive approximation approach (SAA) is developed to obtain a new congestion controller for the singularly perturbed time-delay networked control systems affected by external disturbances. Based on the slow-fast decomposition theory of singular perturbations, the system is first decomposed into a fast non-delay subsystem and a slow time-delay subsystem with disturbances. Then, the perturbation approach is proposed to solve the slow-time scale time-delay optimal control problem, and the feedforward compensation technique is used to reject the external disturbances. We obtain the conditions of existence and uniqueness of the feedforward and feedback composite control (FFCC) law. The FFCC law consists of linear analytic functions and a time-delay compensation term which is a series sum of adjoint vectors. The linear analytic functions can be found by solving a Riccati matrix equation and a Sylvester equation respectively. The compensation term can be approximately obtained by an iterative formula of adjoint vector equations. A reduced-order disturbance observer is constructed to make the FFCC law physically realizable. Numerical examples are presented to illustrate the effectiveness and robustness of the proposed design approach.

Minimum-time rest-to-rest feedforward action for PID feedback MIMO systems

In this paper we present a methodology for the design of a feedforward control law to be applied to a closed-loop PID-based control system for a multi-input multi-output process in order to achieve a minimum-time rest-to-rest transition of the system from an equilibrium point to another subject to constraints on both the control and process variables. In particular, the proposed approach uses decentralized PID controllers which can be designed by any of the conventional methods, such as, for example, those aiming at rejection of load disturbances. Then, the closed-loop generalized bang-bang command input vector is determined by applying a linear programming approach in order to minimize the rest-to-rest output transitions. Conditions for the constraints for which the problem admits a solution are given. Simulations for a two-inputs two-outputs plant highlight the effectiveness of the approach.