Control Input Energy Research Articles

Reentry vehicle fixed-time terminal guidance and attitude control with impact angle constraints

The motivation of this paper is to handle the terminal guidance and attitude control problem for the unpowered reentry vehicle in the diving phase, which is crucial for interception to the target. The most important objectives of this study are to intercept the maneuvering target with the miss distance and impact angle error as small as possible. First, the second-order derivatives of the aerodynamic angles are derived with the fin deflections as control input, which is objective to avoid the tracking of reentry vehicle body angle rate command in the traditional methods. Second, a novel fixed-time time-varying parameter nonsingular terminal sliding mode guidance law is proposed to improve the convergence speed of line-of-sight angle rate, which can avoid control input singularity without switching to the polynomial form when the error approaches the origin. Thirdly, a new global time-varying sliding mode is developed to design the attitude controller, with the predefined fixed convergence time and analytical solution. The system states are proved to be fixed-time convergence based on the Lyapunov stability theory. Six-degree-of-freedom flight simulations are conducted to validate the superiority of the proposed algorithm in terms of miss distance, impact angle error, intercepting time and control input energy.

Design concepts and control algorithm to minimize the control effort for earth-orbit-raising solar sails

This paper presents novel design concepts and a robust sliding mode control (RSMC) algorithm for a solar sail optimized for an Earth-orbit-raising demonstration mission. The design of the solar sail is focused on minimizing mission difficulty and control effort during the Earth-orbit-rising mission. To this end, a gravity-stabilized long boom and one-sided black-coating film are introduced in the solar sail system, and a reaction wheel is used as a control torque actuator. The strategic combination of these components modifies the attitude control task from 90° back-and-forth pitch motion control for maintaining the proper attitude for receiving solar radiation pressure (SRP) to that of stabilizing the sail attitude perturbed from gravity-stabilized equilibrium. This simplification of the control task can minimize the mission difficulty and control input energy because attitude control is required only for small deviations from the attitude equilibrium, while the one-sided black-coated film with a reflective surface on the opposite side ensures that SRP propulsion effectively pushes the sail toward the orbit-rising direction. Thus, the control torque of the reaction wheel size can be reduced. To validate the Earth-orbit-raising mission performance, a quaternion-based RSMC approach is established for the six degree-of-freedom dynamic model. The simulation results confirm that the proposed solar sail system can stabilize its attitude with minimal control torque energy of the reaction wheels during Earth-orbit-raising missions.

Will Fractional Order Model Based MPC Save Control Energy?

In real-world situations, many complex processes exhibit fractional order dynamic characteristics. In this context, the common integer order modeling methods may not appropriately capture the physics of these processes, leading to a less satisfactory controller design. This paper conducts a comparative analysis between the First order plus time delay (FOPTD) model and the Time Delay with Single Fractional Pole (TDWFP) model. These two modeling methods are employed to characterize a one-dimensional heat propagation process and two model predictive controllers are developed based on the models. The results demonstrate a better fitting performance in both time and frequency response with the TDWFP model. Furthermore, the TDWFP model-based Model Predictive Control exhibits reduced sensitivity to the prediction horizon and requires low control input energy. This indicates the potential of using fractional order model in MPC for improved control energy efficiency in practical applications.

Prescribed-Time Formation Control for a Class of Multiagent Systems via Fuzzy Reinforcement Learning

This paper concerns optimal prescribed-time forma- tion control for a class of nonlinear multi-agent systems (MASs). Optimal control depends on the solution of the Hamilton-Jacobi- Bellman equation, which is hard to be calculated directly due to its inherent nonlinearity. To overcome this difficulty, the rein- forcement learning strategy with fuzzy logic systems is proposed, in which identifier, actor, and critic are used to estimate unknown nonlinear dynamics, implement control behavior, and evaluate system performance, respectively. Different from the existing optimal control algorithms, a new performance index function considering formation error cost and control input energy cost is constructed to achieve optimal formation control of MASs within a prescribed time. The presented control strategy can ensure that the formation error converges to the desired accuracy within a prescribed time. Finally, the validity of the presented strategy is verified via a simulation example.

Prescribed Performance Adaptive Tracking Control With Small Overshoot for a Class of Uncertain Second-Order Nonlinear Systems

This brief investigates the problem of prescribed performance adaptive tracking control for a class of second-order nonlinear systems with uncertainties. First, a new performance function is defined to guarantee that the tracking error has small overshoot and converges to a predetermined region for a user-defined time. Then, to effectively diminish the control input energy consumption caused by the introduction of constraints, a novel coordinate transformation function is designed. Next, an improved fixed-time backstepping control framework is established to achieve the tracking control objective. According to the theoretical analysis, all signals of the closed-loop system are bounded, and the tracking error converges to a preset domain with small overshoot for a user-designed time. Finally, numerical simulations confirm the effectiveness of the presented control strategy.

Development of on-line neural network based adaptive fractional-order sliding mode robust controller on electromechanically actuated engine cooling system

The reduction of temperature fluctuations around desired reference and control input energy for cooling actuators are among the most important aims of engine thermal management system. However, maintaining of engine/radiator outlet temperature within certain limits is a challenging process in different engine operating conditions due to unknown in-cylinder variable heat transfer rate in terms of the control theory. For this purpose, the thermodynamic model is obtained by dividing into two subsystems, such as the engine and the radiator subsystem in the presence of unknown heat transfer rate, external disturbance, and uncertainties in this study. To increase system robustness, tracking engine inlet/outlet temperature control of engine cooling components is performed using the adaptive fractional-order sliding mode control structure. Moreover, the disturbances acting on the system and unknown heat transfer dynamics of the system are estimated with a radial basis function on-line neural network estimator. The efficiency of proposed controller strategy for electromechanically actuated engine cooling system is compared by proportional–integral–derivative and classical integral sliding mode control under the NEDC (New European Driving Cycle) and WLTP (Worldwide Harmonized Light Vehicles Procedure) transient operating conditions. The temperature error tracking performance is tested by paying attention integral square error, integral absolute error, integral time-weighted absolute error along to the driving cycles. The obtained results showed that the adaptive fractional-order sliding mode control–based engine cooling system outperforms compared to the optimally gain tuned proportional–integral–derivative and integral sliding mode control schemes in terms of reducing of tracking error and engine cooling actuators energy consumption for all engine operating cycles.

Design of fixed-time adaptive super twisting controllers for perturbed nonlinear systems

ABSTRACT In this paper a design methodology of fixed-time adaptive super twisting control is proposed for a class of multi-input nonlinear systems with matched and unmatched perturbations to solve the fixed-time regulation problems. The sliding surface is firstly designed, and then the super twisting controller is designed accordingly. The perturbation estimation and adaptive mechanisms are also embedded in the proposed control scheme, so that there is no need to know the upper bounds of perturbations as well as perturbation estimation error in advance. Hence applying excessive control input energy to systems is also avoided due to utilisation of perturbation estimator. Moreover, choosing appropriate design parameters is also addressed in detail in order to meet the required fixed-time convergent time. Finally, a numerical example is given for demonstrating the feasibility of the proposed control strategy.

LQR control on multimode vortex-induced vibration of flexible riser undergoing shear flow

Under the actions of ocean currents and/or waves, deep-sea flexible risers are often subject to vortex-induced vibration (VIV). The VIV can lead to severe fatigue and structural safety issues caused by oscillatory periodic stress and large-amplitude displacement. As flexible risers have natural modes with lower frequency and higher density, a multimode VIV is likely to occur in risers under the action of ocean currents, which is considered as shear flow. To decrease the response level of the VIV of the riser actively, a multimode control approach that uses a bending moment at the top end of the riser via an LQR optimal controller is developed in this study. The dynamic equations of a flexible riser including the control bending moment in shear flow are established both in the time and state-space domains. The LQR controllers are then designed to optimize the objective function, which indicates the minimum cost of the riser's VIV response and control input energy based on the Riccati equation of the closed-loop system under the assumption that the lift coefficient distribution is constant. Finally, the VIV responses of both the original and closed-loop systems under different flow velocities are examined through numerical simulations. The results demonstrate that the designed active control approaches can effectively reduce the riser displacement/angle by approximately 71%–89% compared with that of the original system. Further, for multimode control, the presented mode-weighted control is more effective than the mode-averaged control; the decrease in displacement is approximately 1.13 times than that of the mode-averaged control. Owing to the increase in flow velocity as more and higher-order modes are excited, the VIV response of the original system decreases slightly while the frequency response gradually increases. For the closed-loop system, the response becomes smaller and more complicated, and the efficiency of the controller becomes lower at a certain flow velocity.

최적 절환 초평면을 갖는 슬라이딩 모드에 의한 DC모터의 강인한 속도제어

This paper deals with robust speed servo control for DC motors based on a sliding mode control (SMC). SMC is well known for its robust control performance against external disturbances including motor parameter variations. An optimum switching plane, a key issue for SMC, is designed to minimize control error and input energy in a state space model. Voltage command which is an output of the sliding mode controller is induced to satisfy the Lyapunov’s second method for critical stability. The robust control performance of the suggested sliding mode control is evaluated by two experiments such as a load test and parameter variation test. The external load test was conducted by applying 100% and 80% of the rated torque using a powder brake. The parameter variation experiment was conducted by increasing nominal parameters of the motor used in the controller by 3 times. Moreover, the effectiveness of SMC is clarified by comparing with the PI control experimental results. The experimental results showed that SMC has stronger control performance against the disturbance and parameter changes than the PI controller.

Heterogeneity-Aware Graph Partitioning for Distributed Deployment of Multiagent Systems.

In this work, we examine the distributed coverage control problem for deploying a team of heterogeneous robots with nonlinear dynamics in a partially known environment modeled as a weighted mixed graph. By defining an optimal tracking control problem, using a discounted cost function and state-dependent Riccati equation (SDRE) approach, a new partitioning algorithm is proposed to capture the heterogeneity in robots dynamics. The considered partitioning cost, which is a state-dependent proximity metric, penalizes both the tracking error and the control input energy that occurs during the movement of a robot, on a straight line, to an arbitrary node of the graph in a predefined finite time. We show that the size of the subgraph associated with each robot depends on its resources and capabilities in comparison to its neighbors. Also, a distributed deployment strategy is proposed to optimally distribute robots aiming at persistently monitoring specified regions of interest. Finally, a series of simulations and experimental studies is carried out to demonstrate the viability and efficacy of the proposed methodology in deploying heterogeneous multiagent systems.

New results on the trade-off performance of LTI system with colored noise and encoder-decoder strategy

This paper studies the trade-off performance between tracking performance and control input energy of the multi-input multi-output(MIMO), linear and time-invariant(LTI) system over an additive coloured Gaussian noise(ACGN) channel and the encoder-decoder strategies. The restriction that filter in the encoder-decoder strategy must be diagonal matrix is not necessary. And some new results are derived according to the inner-outer factorization. The results show that the trade-off performance is correlated to the unstable pole, non-minimum phase zero of the system. Also new poles and zeros generated by the non-diagonal encoder-decoder strategies may affect the trade-off performance. At last, two examples with different filters and different encoder-decoder strategies are discussed to validate the conclusions. The various encoder-decoder strategies revealed by the simulations may enhance or deteriorate the trade-off performance proposed in this paper.

Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

A fuzzy α-cut optimization analysis for vibration control of laminated composite smart structures under uncertainties

As a high performance and specific mechanically tailored material, composite structures present high structural behavior sensitivity to small variations in geometry or material properties. Some of these uncertainties are intrinsically related to the manufacturing process but others are usual uncertainty in material properties. A fuzzy interval analysis methodology is proposed in this paper in order to evaluate the structural behavior of laminated composite smart structures under vibration control and uncertain parameters. A Particle Swarm Optimization algorithm is used to search for input parameters in order to minimize and maximize system outputs by an anti-optimization and thus build their envelopes. Each input parameter has interval values defined by α-cut levels and interpolated by the Fuzzy reasoning. This methodology is applied to a smart structure of laminated composite material with attached piezoelectric patches and controlled by an optimal control regulator. System's interval outputs like natural frequency, mechanical vibration, and electric control input energy are investigated taking into account uncertainties in the composite and piezoelectric material properties, ply angles and layer thickness. Finally, it is concluded that these uncertainties may affect the control performance since it was found significant modifications in the dynamic behavior and therefore this should be accounted in the design stages.

Stabilization and set-point regulation of underactuated mechanical systems

Mechanical systems are referred to as underactuated if the number of independent actuators are fewer than the number of degrees of freedom, a general encountered problem in engineering applications. The considered mechanical systems belong to the class of Euler- Lagrange systems where both kinetic energy and potential energy are modeled in their most general form and energy dissipation is modeled according to the dissipation function of Rayleigh, i.e. viscous damping forces are assumed. The control objectives are stabilization and set-point regulation. The structure of the controller is a parallel combination of static output feedback with dynamic output feedback where nonlinear amplifiers are included. An energy based approach with Liapunov functions and the Kalman-Yacubovich-Popov main lemma yields alternative stability theorems. A number of conditions are introduced with respect to the controller's structure in order to guarantee stability. However, sufficient design freedom is left to choose a proper tuning principle and obtain the specified control objectives such as fast convergence to a set-point combined with disturbance rejection. A restriction on the control input energy can be incorporated as well. The applicability of the method will be illustrated with planar manipulators. The main contribution is that a methodology is developed which incorporates many controllers and tuning facilities.

Trade-off performance analysis of LTI system with channel energy constraint

In this paper, the trade-off performance between tracking error, control input energy and channel input power is studied. By modelling the communication channel as the additive coloured Gaussian noise channel (ACGN) with limited bandwidth, a new performance index is proposed and minimized over all stabilizing two-degree-of-freedom controllers. The results show that the trade-off performance is correlated to the intrinsic characteristics of the plant, including the locations and directions of the unstable pole, non-minimum phase zero. However it is unrelated to the non-minimum phase zeros of filter because of the two-degree-of-freedom controller. We also demonstrated that ACGN may degenerate the tracking performance. Finally, a typical example is given to validate the theoretical results.

Excitation control of a synchronous generator using a novel fractional‐order controller

Fractional calculus (FC) is widely used in a variety of fields, such as science and engineering. FC is recognised for its ability to produce a superior modelling and control in dynamical systems. Fractional controllers are known to be more efficient. In this paper, fractional-order control systems are studied with regard to control input energy efficiency, which is a noteworthy issue in designing control systems. In this study, improved tilt-integral–derivative (I-TID) is proposed. To validate the proposed controller, its results were compared with that of proportional–integral (PI) controller, fractional PI (F-PI) controller, and conventional tilt-integral–derivative (TID) controller. A genetic algorithm was used to tune the parameters of the aforementioned controllers. Simulation results revealed that the proposed controller is not only energy efficient, but also fast. The results also indicated that the performance of I-TID is much better than PI, F-PI, and conventional TID.

Distributed event-triggered consensus strategy for multi-agent systems under limited resources

The paper proposes a distributed structure to address an event-triggered consensus problem for multi-agent systems which aims at concurrent reduction in inter-agent communication, control input actuation and energy consumption. Following the proposed approach, asymptotic convergence of all agents to consensus requires that each agent broadcasts its sampled-state to the neighbours and updates its control input only at its own triggering instants, unlike the existing related works. Obviously, it decreases the network bandwidth usage, sensor energy consumption, computation resources usage and actuator wears. As a result, it facilitates the implementation of the proposed consensus protocol in the real-world applications with limited resources. The stability of the closed-loop system under an event-based protocol is proved analytically. Some numerical results are presented which confirm the analytical discussion on the effectiveness of the proposed design.

Minimized Tracking Error Randomness Control for Nonlinear Multivariate and Non-Gaussian Systems Using the Generalized Density Evolution Equation

In this technical note, a new stochastic control algorithm is presented for nonlinear and non-Gaussian continuous-time systems. Based on the recently developed generalized density evolution equation, which is more tractable than the classical Liouville equation, the relationship is established among the probability density function (PDF) of tracking error, control input and disturbances. An improved performance index is then constructed for this stochastic control strategy, which includes quadratic information potential of the tracking error, mean value of squared tracking error and constraints on the control input energy. By minimizing the performance index, a recursive optimal control algorithm is obtained using the gradient descent method. Moreover, the statistical linearization technique is adopted to formulate the boundedness condition of the closed-loop system. An illustrative example is given to demonstrate the validity and efficiency of the proposed stochastic optimal control methodology.

Degree of controllability for linear unstable systems

The degree of controllability is a measure to check how controllable a given system is, which makes up for the weak points of traditional methods for checking controllability. There are many definitions of the degree of controllability, and the most widely used measure is represented by controllability Gramian. This measure has physical meaning of minimum input energy to change the states. However, it is hard to use this method for unstable systems because the steady-state value of Gramian cannot be defined. Therefore, the degree of controllability for unstable systems is proposed in this paper. The definition of the measure is minimum control input energy to change the state from an arbitrary initial condition to an arbitrary final condition. The derivation result shows that the measure is the sum of two terms, one represented by Gramian of a stable subsystem and the other represented by Gramian of a subsystem that has mirror image poles of an anti-stable subsystem. These Gramians can be obtained by solving two Lyapunov equations. A simple numerical example shows the usefulness of the proposed measure of degree of controllability.

Linear Parameter-Varying Controller Design for Four-Wheel Independently Actuated Electric Ground Vehicles With Active Steering Systems

This paper presents a linear parameter-varying (LPV) control strategy to preserve stability and improve handling of a four-wheel independently actuated electric ground vehicle in spite of in-wheel motors and/or steering system faults. Different types of actuator faults including loss-of-effectiveness fault, additive fault, and the fault makes an actuator's control effect stuck-at-fixed-level, are considered simultaneously. To attenuate the effects of disturbance and address the challenging problem, a novel fault-tolerant (FT) robust linear quadratic regulator (LQR)-based $H_{\infty}$ controller using the LPV method is proposed. With the LQR-based $H_{\infty}$ control, the tradeoff between the tracking performance and the control input energy is achieved, and the effect from the external disturbance to the controlled outputs is minimized. The eigenvalue positions of the system matrix of the closed-loop system are also incorporated to tradeoff between the control inputs and the transient responses. The vehicle states, including vehicle yaw rate, lateral and longitudinal velocities, are simultaneously controlled to track their respective references. Simulations for different fault types and various driving scenarios are carried out with a high-fidelity, CarSim®, full-vehicle model. Simulation results show the effectiveness of the proposed FT control approach.