Derivation Of Control Law Research Articles

Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics

In this paper, the thermodynamic availability function is used as a Lyapunov function for the practical derivation of non linear control laws for the stabilization of a large class of CSTRs far from the equilibrium. The strict convexity of the availability function is guaranteed as long as one of the extensive variables is fixed. In this study, we consider liquid mixture with constant volume, the constraint on the volume being insured by perfect regulation of the outlet flow of the CSTR. Several control laws are then derived which insure global asymptotic stability, exponential stability or simple asymptotic stability. These control laws are discussed regarding the magnitude and the dynamic variations of the control variable. It is shown that the availability function can be split into two parts: one corresponds to the mixing term and depends on mole numbers only and the other depends on both temperature and mole numbers. The two parts are positive and the second one is chosen as a new Lyapunov function. The use of this new Lyapunov function insures smooth variations of the control variable. An exothermal, first order chemical reaction leading to multiple steady-state operating points of the CSTR illustrates the proposed theory.

Nonlinear Optimal Control of Vehicle Active Suspension Considering Actuator Dynamics

Considering the nonlinear characteristic of components in vehicle is very important in designing the controller of automobile active suspension system. To show the importance of this effect, a nonlinear optimal control method is employed in this paper. At first, an optimal law is developed for active suspension by the states prediction of a nonlinear quarter car model. The states of quarter car model are first predicted by Taylor series expansion and then a control law is introduced by minimizing the local differences between the predicted and desired states. In this way, the well defined sky hook linear model is selected as the reference model to be tracked by the nonlinear optimal controller. In order to decrease the vertical accelerations and improve the behavior of the reference model, the sky hook model is controlled beforehand by the LQR method. Derived control law has an analytical form which is easy to apply. The simulations show that under the proposed controller, the car has well passenger comfort and safe maneuverability.

Simplified derivation of control law providing for a vehicle’s motion on a nonlinear path

The paper discusses the problem of a vehicle’s motion control on a preset nonlinear path. The new proof of the velocity addition theorem presented in [4] allowed simplified derivation of control law. The procedures described can be considered the first step in the development of motion control algorithms by back-stepping.

Energy optimal spacecraft attitude control subject to convergence rate constraints

Attitude control of operational satellites is still predominantly performed by standard controllers such as Proportional plus Derivative (PD) control laws, which are still preferred for implementation to the computationally intensive nonlinear optimal control techniques, representing higher implementation complexity. In this paper, an inverse optimal control approach based on phase space geometry is presented, which is easy to implement and free from numerical and computational issues. The optimal control objective is to minimize a norm of the control torque subject to a rapidity constraint on the convergence rate of a Lyapunov function, under the effect of a benchmark controller. The proposed optimization method is shown to significantly enhance the torque-rapidity trade-off compared to the benchmark controller, chosen to be a PD law then a sliding mode controller. The inverse optimal control scheme is implemented on an air bearing table experimental platform.

Model based control of a fed batch process used for catalyst support production

In this paper, a model based control of a fed batch process used for catalyst support synthesis is proposed. The considered model is derived from mass balances and an algebraic equilibrium equation identified using titration experiments. The catalyst quality requires that three variables are controlled during the production process: pH, volume and concentration. A global control structure enabling to simultaneously control the three considered variables is given. The pH controller adjusts a reactive base flow rate while the volume and concentration controllers act on water and reactive acid flow rates, respectively. The process model is used to derive control laws that impose asymptotically stable dynamics. Representative experimental results are presented to prove the relevance of the proposed approach.

A new approach for modelling and control of two-wheel anti-lock brake systems

Anti-lock brake system is designed to actively improve the vehicle safety during hard braking. In this article, optimization-based braking pressure control laws for the front and rear wheels are analytically designed based on a non-linear two-axle vehicle model. The integral feedback technique is also appended to the design method to increase the robustness of the controller in the presence of modelling uncertainties. In order to achieve the maximum braking force for each wheel at any time during braking, a new reference wheel slip model is presented to be tracked by the controller. In this model, the variations of tyre normal load and tyre/road condition are considered in finding the optimum slip of each wheel. The derived control laws are evaluated and their main features are discussed. Finally, the effectiveness of the proposed controller in tracking the new reference model is investigated and the obtained results are compared with the prevalent research results. The simulation studies demonstrate that the designed controller can successfully cope with the strong non-linearity and uncertainty existing in a vehicle dynamics model. Also, the vehicle stopping distance is remarkably reduced by the proposed approach.

Optimal Output Consensus Control for Systems of Agents with Continuous Linear Dynamics

AbstractIn this paper we study the output consensus problem for systems of agents with linear continuous, time invariant dynamics. We derive control laws with minimal energy that solves the problem, while using only relative information. Instead of considering a fixed communication topology for the agents, and derive the optimal control for that topology, we derive the optimal control law for any communication topology between the agents. We show that the optimal control uses only relative information but requires the connectivity graph to be complete and in general requires measurements of the state errors. We identify the cases where the optimal control is only based on output errors, and show that in the infinite time horizon case, the optimal controller can always be expressed as a dynamic controller that is only based on the output errors. Regarding the theoretic contributions of this paper, the control laws are derived using methods from linear vector space optimization and are given in closed form. To the authors knowledge these methods have not been used within this context before.

Tuning and noise attenuation of a second order system using Proportional Retarded control

AbstractThis paper presents a tuning strategy for Proportional Retarded (PR) control laws in closed loop with second order systems and experimental results on the noise attenuation performance of a DC servomotor. The PR controller is compared with other commonly employed strategies for avoiding the time-derivative measurement in Proportional Derivative control laws. The experiments show that the PR controller combines good noise attenuation and tracking performance with a simple implementation.

Position control of magnetic beads by means of electromagnetic fields with respect to apodal locomotion systems

Motivated by the technical progress, electromagnetic action principles are more and more used in micro systems. It is well known that the discrete positioning of magnetic beads like ferrofluid droplets can be realised using an array of electromagnets whereat the position of the beads depends on the arrangement of the electromagnets. This paper refers to the analogous positioning of magnetic beads independent from the arrangement of the electromagnets. Therefore a control strategy was designed to position magnetic beads like ferrofluid droplets, ferrogels or ferroelastomers. The derived control law allows the definition of dynamic properties like time and damping constant. To achieve these properties, the controller is adjusted based on a model of the plant. This model regards the dynamical movement of the mentioned materials in electromagnetic fields and is characterised by simplified, nonlinear, ordinary differential equations. The theoretical results are verified by means of a basic assembly allowing the positioning of spherical ferroelastomers on macro scale. The measurements illustrate that the theoretically derived position controller meets the requirements of a predefined time and damping constant.

New feedback laws for stabilization of unstable periodic orbits

In this note a gain tuning scheme for prediction-based chaos control of discrete-time systems is proposed, extending previous work by T. Ushio and S. Yamamoto. The derived control laws are proved to be stabilizing. Three different time-invariant or time-varying laws are proposed, leading to different convergence rates and sizes for the basins of attraction. The results are illustrated by numerical simulations. A parallel between finding unstable periodic orbits and chaos control is done.

Active control and simulation test study on torsional vibration of large turbo-generator rotor shaft

Reduction of shaft vibration is very important for safe and efficient functioning of a large turbo-generator. This paper presents a theoretical study and proposes an active vibration control scheme for controlling torsional vibration of a rotor shaft due to electromagnetic disturbances or unsteady flow in large steam turbine generator sets. A form of the conventional linear quadratic regulator (LQR) control algorithm has been proposed in this paper. The optimal LQR control problem is solved for each time interval with the weighting matrices, through the Ricatti equation, leading to time-varying gain matrices. The test is conducted using modified direct current electromotor as torsional vibration exciter and actuator, mounting on the rotor shaft. The actuator applies suitable force to control torsional vibration. Suitable force of actuation is achieved by varying the control current in the actuator depending upon a proportional and derivative control law. Preliminary theoretical study and test simulation show good reduction in torsional vibration response.

A novel method for non-linear control of wheel slip in anti-lock braking systems

Anti-lock braking system (ABS) provides active safety for vehicles during braking by regulation of the wheel slip at its optimum value. Due to the non-linear characteristics and model uncertainties in vehicle dynamics, a non-linear controller with increased robustness should be designed for ABS. In this paper, to achieve this aim, an optimization-based braking torque control law is developed for ABS using the prediction of the wheel slip response from a continuous non-linear vehicle dynamics model. To increase the robustness of the controller, the integral feedback technique is appended to the design method. The derived control law and its special cases are evaluated and discussed. At the end, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of braking on dry and slippery roads. The simulation results indicate that, the wheel slip tracking error is remarkably decreased by the proposed controller. Moreover, the achieved control input is entirely smooth and suitable for implementation.

Modeling and Control of the MARES Autonomous Underwater Vehicle

AbstractIn this work, we address the modeling and control problems in the domain of underwater vehicles. We focus on a prototype of an autonomous underwater vehicle. Although the work presented here is applied to a particular vehicle with four controllable degrees of freedom, the method may be easily extended to several submerged bodies. In the engineering area, modeling of systems is done frequently, as it yields a mathematical translation of their behavior. Since models can become an important tool to solve problems related to its motion or even to the design of controllers, we obtain a model with six degrees of freedom for such a vehicle.Robust control of underwater vehicles is an area in which many efforts were applied over the last two decades. However, due to nonlinear dynamics, it may be hard to design robust controllers that yield the expected behavior, and there is no general procedure to develop them. Here, we propose an approach that combines nonlinear controllers based on the deduced model and on the Lyapunov theory to control the velocities of the vehicle with linear controllers that control the vehicle’s position. We derive control laws to perform several maneuvers, both in the vertical and the horizontal planes, in a decoupled way, which is made possible through the configuration of thrusters. Finally, we present realistic simulations and experimental results that validate the proposed approach in the definition of the control laws.

Robust stabilization of a wheeled vehicle: Hybrid feedback control design and experimental validation

In this paper, the problem of robust stabilization of a wheeled vehicle is addressed. The configuration (position and orientation) set of the vehicle is divided into two parts: global and local configuration sets. The novelty of this paper is the design of a hybrid feedback controller that assigns different objectives in the vehicle’s global and local behaviors. Two Lyapunov functions for individual objectives are introduced that allow a hybrid feedback control law to pursue different objectives. In the global sense, it is important to reach the target point as quickly as possible, but once the vehicle reaches is near the goal, a precise maneuvering by rejecting disturbances including tire slippage and measurement noise becomes important. The asymptotical stability and robustness of the closed loop system are assured. The derived control law is validated by simulations and experiments using an autonomous forklift.

Stabilizing Controllers for Delay Systems subject to Positivity Constraints

Abstract For time-varying forward-complete nonlinear systems with delay in the input, a new reduction model approach is proposed. It presents three advantages. First, the derived control laws have no distributed terms. Second, it yields closed-loop systems with positive solutions that can be easily found. Third, the stabilized systems possess some robustness properties that can be estimated.

Optimal Deployment Control of Spinning Space Webs and Membranes

Future solar sail and solar power satellite missions will consider using centrifugal forces for deployment and stabilization. Some of the main advantages with spin deployment are that the significant forces are in the plane of rotation, and a relatively simple control can be used and the tension in the membrane or web can be adjusted by the spin rate. Existing control strategies seem to either consume excessive energy or cause oscillations. In this study, control laws are derived from the solution to relevant optimal control problems and existing controls. The derived control laws are used in deployment simulations with both simple analytical three-degree-of-freedom models and a fully-three-dimensional finite element model. The results indicate that the derived control laws can be used to minimize the energy consumption and oscillations as for an optimal control, yet retain the simplicity of previous control laws.

A new strategy for minimum usage of external yaw moment in vehicle dynamic control system

Due to the loss of vehicle directional stability in emergency maneuvers, a new complete desired model for vehicle handling based on the linear two-degrees-of-freedom (2DOF) model and tire/road conditions is presented to be tracked by the direct yaw moment control (DYC) system. In order to maintain the vehicle actual motions, yaw rate and side-slip angle, close to the proposed desired responses without excessively large external yaw moment, a complete linear quadratic (LQ) optimal problem is formulated and its analytical solution is obtained. Here, the derived control law is evaluated and its different versions are discussed. It is shown that the side-slip tracking by DYC is more effective than the yaw rate control to stabilize vehicle motions in nonlinear regimes. Also, optimal property of the control law provides the possibility of reducing the external yaw moment as low as possible, at the cost of some admissible tracking errors. Simulation studies of vehicle handling, with and without control, have been conducted using a full nonlinear vehicle dynamic model. The results, obtained during various maneuvers, indicate that when the proposed optimal controller is engaged with the model, improvements in the handling performance through a reduced external yaw moment can be acquired.

Indirect adaptive output feedback control of a biorobotic AUV using pectoral-like mechanical fins

This paper treats the question of servoregulation of autonomous underwater vehicles (AUVs) in the yaw plane using pectoral-like mechanical fins. The fins attached to the vehicle have oscillatory swaying and yawing motion. The bias angle of the angular motion of the fin is used for the purpose of control. Of course, the design approach considered here is applicable to AUVs for other choices of oscillation patterns of the fins, which produce periodic forces and moments. It is assumed that the vehicle parameters, hydrodynamic coefficients, as well the fin forces and moments are unknown. For the trajectory control of the yaw angle, a sampled-data indirect adaptive control system using output (yaw angle) feedback is derived. The control system has a modular structure, which includes a parameter identifier and a stabilizer. For the control law derivation, an internal model of the exosignals (reference signal (constant or ramp) and constant disturbance) is included. Unlike the direct adaptive control scheme, the derived control law is applicable to minimum as well as nonminimum phase biorobotic AUVs (BAUVs). This is important, because for most of the fin locations on the vehicle, the model is a nonminimum phase. In the closed-loop system, the yaw angle trajectory tracking error converges to zero and the remaining state variables remain bounded. Simulation results are presented which show that the derived modular control system accomplishes precise set point yaw angle control and turning maneuvers in spite of the uncertainties in the system parameters using only yaw angle feedback.

Feedforward control of flexural waves propagating in a rectangular panel

This paper is concerned with active wave control of a distributed parameter structure. It is the purpose of this paper to present the active wave control method of a rectangular panel and to clarify fundamental properties of the control system. Firstly, 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. It is also found that some phenomena different from the case of a beam-like structure appear under certain boundary conditions.

Forced dynamics control of an actuator with linear PMSM

The paper presents design and verification of Forced Dynamics Control of an actuator with linear permanent magnet synchronous motor. This control method is a relatively new one and offers an accurate realization of a dynamic speed response, which can be selected for given application by the user. In addition to this, the angle between stator current vector and moving part flux vector is maintained mutually perpendicular as it is under conventional vector control. To achieve prescribed speed response derived control law requires estimation of an external force, which is obtained from the set of observers. The first observer works in pseudo-sliding mode and observes speed of moving part while the second one has filtering effect for elimination of the previous one chattering. The overall control system is verified by simulations and experimentally. Preliminary experiments confirmed that the moving part speed response follows the prescribed one fairly closely.