Smooth Control Signal Research Articles

Sliding mode controller-observer pair for p53 pathway.

A significant loss of p53 protein, an anti‐tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild‐type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non‐linear technique is presented for the drug design of a control‐oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero‐dynamics is also proved. To make the model‐based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced‐order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in‐silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.

Global smooth sliding mode controller for flexible air-breathing hypersonic vehicle with actuator faults

A global smooth sliding mode controller (GSSMC) is proposed for flexible air-breathing hypersonic vehicle (FAHV) under actuator faults and parametric uncertainties, consisting of global fast finite-time integral sliding surface (GFFIS), generalized smooth second-order sliding mode reaching law (GSRL) and smooth fixed-time observer. Firstly, nonlinear control-oriented model of FAHV is processed using input/output feedback linearization with flexible effects and actuator faults modeling as lumped matched disturbances. Secondly, a GFFIS is established to ensure finite-time convergence of states without singularity based on a newly proposed fast finite-time high-order regulator (FFR). The FFR is improved from standard finite-time high-order regulator via dilation rescaling, which can accelerate response speed avoiding complicated parameters selection. Meanwhile, GFFIS can eliminate initial reaching phase to enhance robustness of system due to characteristic of global convergence. Thirdly, a GSRL is presented to ensure finite-time convergence of sliding mode vector and its derivative without chattering based on a generalized smooth second-order sliding mode control algorithm, the stability and finite convergence time of which is analyzed via Lyapunov criteria in detail. Then, a smooth fixed-time observer is applied to estimate lumped disturbances in fixed time and avoid effects of parametric uncertainties. With the three components, GSSMC can drive FAHV subject to actuator faults and parametric uncertainties to follow desired values in finite time with smooth control signals. Ultimately, three sets of simulations are performed to verify the effectiveness of the methods proposed.

Adaptive Fault-Tolerant Constrained Control of Cooperative Spacecraft Rendezvous and Docking

The relative pose control problem for spacecraft rendezvous and docking missions in the presence of control input constraints, actuator's partial failures, and unknown external disturbances is studied in this paper. A smoothly adaptive fault-tolerant constrained controller is developed based on the adaptive nonlinear state feedback method. Different from the traditional fault-tolerant saturated controllers, the proposed control approach explicitly accounts for the control input constraints with straightforward tuning parameters in controller. Meanwhile, the exact knowledge of the actuator failures is not required and uncertain failure information can be rejected. A smooth control signal containing simple saturation functions is designed, and the unknown bounded external disturbances can be rejected by the proposed method. The proposed controller can ensure ultimately, uniformly bounded stability of the closed-loop system, where relative pose and velocities converge to the small neighborhoods of zero. Numerical simulation results demonstrate the effectiveness of the proposed control approach.

Adaptive high order sliding mode controller/observer based terminal sliding mode for MIMO uncertain nonlinear system

ABSTRACT In this paper, an adaptive super twisting high order sliding mode controller observer is investigated for multi input–multi output uncertain system, with application to robotic manipulator based only on position measurement. First, a type-2 Takagi–Sugeno fuzzy system is used to model the original system. Next, by combining thefuzzy model with third order sliding mode observer, a novel fuzzy observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on super twisting algorithm the proposed controller generates a smooth control signal and guarantees the finite time stabilisation of second order sliding mode. The controller gains are generated based on adaptive estimation scheme, in which the gains overestimation problem and the prior knowledge of the upper boundaries of uncertainties can be avoided. The stability of proposed controller/ observer scheme is discussed using Lyapunov approach. Finally, the obtained simulation results for two link robot manipulator demonstrate the effectiveness of the proposed controller.

Reset control for synchronization of multi-agent systems

Standard approaches to synchronization problems in multi-agent systems apply local smooth control signals to achieve ultimate coherence. Most existing algorithms emphasize asymptotic behavior rather than transient performance. An alternative design framework based on reset control is presented to guarantee not only the asymptotic convergence but also a desired transient response. Specifically, the control protocol consists of a proportional integral (PI) compensator and a Clegg integrator (CI), where the integral term is reset to zero whenever the proportional term crosses zero. Numerical examples are included to illustrate the main result, and to compare the proposed reset control approach with the traditional static/dynamic state feedback control and the quasi-reset control methods.

Experimental Study of Command Governor Adaptive Control for Unmanned Underwater Vehicles

The control of unmanned underwater vehicles (UUV) is a complex problem mainly due to the nonlinear dynamics, uncertainty in model parameters, and external disturbances. Adaptive control is a promising solution to address these issues. Nevertheless, its full potential is yet to be realized, especially in underwater vehicle applications, mainly due to the compromise between the transient performance and a smooth control signal. The addition of a new command governor with standard model reference adaptive control (MRAC) named as a command governor adaptive control (CGAC) has been proposed as a promising solution to this trade-off. Nevertheless, the suitability of CGAC in underwater vehicle applications and its performance are yet to be verified. This paper fills this knowledge gap and experimentally validates the suitability and performance of CGAC in underwater vehicle applications. The standard MRAC is used as the baseline for performance comparison. Experimental results showed that CGAC achieves a low frequency control signal through low gain values and improves transient performance through modifications to the command signal. In addition, the ability of CGAC to overcome disturbances such as tether forces, and tolerate faults such as partial thruster failure was confirmed. Another interesting feature observed in these experiments is the ability of CGAC to operate despite the thruster dead zone, which standard MRAC is unable to perform without a dead-zone inverse. Therefore, according to the results CGAC performs better than standard MRAC and thus is a promising solution for future underwater vehicle applications.

A self-tuning robust full-state feedback control design for the magnetic levitation system

In this study, a self-tuning robust integral of signum of error (RISE) based controller is designed and used to control a magnetic levitation (maglev) system. In the control design, unlike the classical RISE controller, ‘tanh’ function is used instead of ‘signum’ function to obtain a more smooth control signal. The gains of the controller are updated according to a time-varying update rule. Convergence of the error under the closed-loop operation is proven via Lyapunov-based stability analysis. The controller is tested on an experimental maglev system and successful results are obtained.

Chattering free robust adaptive integral higher order sliding mode control for load frequency problems in multi‐area power systems

The aim of the article is to design a chattering free robust adaptive integral higher order sliding mode control for load frequency problems in multi-area hydro power systems using decentralised variable structure control methodology. The proposed controller assures change in frequency in all the areas due to load disturbance converge to zero in finite time. Results are compared with the performances obtained using integral sliding mode control (ISMC) and integral higher order sliding mode control (IHOSMC). The proposed controller helps in achieving finite time convergence of change in frequency due to load disturbances with chattering free and smooth control signal as compared to that obtained using ISMC and IHOSMC. Performance of the controller is tested for plant considered with non-linearities in power system such as generation rate constraints and governor deadband. The proposed controller is also validated against random load disturbances and IEEE large bus system (39-bus system).

Command-Filtered Integral Backstepping Control of Longitudinal Flapping-Wing Flight

The current work is concerned with longitudinal trajectory tracking control and simulation of a flapping-wing micro air vehicle. For the purpose of accurate simulation studies, a nonlinear and time-periodic dynamic model that accounts for the wings inertial effects is developed using Lagrange’s equations for quasi coordinates. Moreover, the aerodynamic loads are formulated, based on quasi-steady assumptions, taking into account the rotational circulation as well as the leading-edge vortex. Using the averaging method, the dynamic model is transformed to a time-invariant one that is the basis for controller design. Employing two control inputs, the flapping frequency and bias, an integral backstepping control law is synthesized. To ensure smooth oscillation-free control signals, a low-pass command filter is introduced in the control law. The choice of the control signals is based on Lyapunov stability criterion, while stability of the error dynamics is proved by the singular perturbation method. Simulation studies indicate that the proposed backstepping controller successfully achieves trajectory tracking. In addition, simulation results highlight the role of integral backstepping in achieving robust performance against model uncertainties and external disturbances and the importance of the command filter in maintaining smooth feasible control signals.

Terminal synergetic design of a nonlinear robot manipulator in the presence of disturbances

PurposeThe purpose of this paper is to design a synergetic controller to precisely and quickly track reference signals in robot manipulators. Having smooth control signal this controller enables the nonlinear robot system to track desired references in presence of disturbances in a finite time.Design/methodology/approachA new synergetic manifold is introduced here, followed by adding a nonlinear exponential term to it have a precise tracking within a finite time of the desired references with disturbances. Previously the nonlinear term was inserted in the main synergetic equation which makes it complicated due to its hard mathematical approach. Using Lyapunov function, the stability of the system in the presence of disturbances is proved. The validity of the resulted system is confirmed by simulating it in Simulink.FindingsUsing a terminal synergetic controller with new manifold proposed in this work enables system’s state variables to track desired reference signal in the presence of disturbances from any initial condition with proper precision and rate. Simulation results show that compared to similar methods it provides a more proper speed and a finite time convergence with high precision and speed.Originality/valueProviding fast and precise convergence, the proposed controller can be used in robot manipulator systems which need fast response and also have a precise performance such as in printing 3D objects and any industrial process.

Optimal Control via Reinforcement Learning with Symbolic Policy Approximation

Model-based reinforcement learning (RL) algorithms can be used to derive optimal control laws for nonlinear dynamic systems. With continuous-valued state and input variables, RL algorithms have to rely on function approximators to represent the value function and policy mappings. This paper addresses the problem of finding a smooth policy based on the value function represented by means of a basis-function approximator. We first show that policies derived directly from the value function or represented explicitly by the same type of approximator lead to inferior control performance, manifested by non-smooth control signals and steady-state errors. We then propose a novel method to construct a smooth policy represented by an analytic equation, obtained by means of symbolic regression. The proposed method is illustrated on a reference-tracking problem of a 1-DOF robot arm operating under the influence of gravity. The results show that the analytic control law performs at least equally well as the original numerically approximated policy, while it leads to much smoother control signals. In addition, the analytic function is readable (as opposed to black-box approximators) and can be used in further analysis and synthesis of the closed loop.

Wavelet neural network PID controller for a UAS transporting a cable-suspended load

A novel model-free Adaptive Wavenet PID (AWPID)-based controller for enabling an Unmanned Aircraft System (UAS) to transport a cable suspended load of unknown characteristics is presented. The control design enables the UAS to perform a trajectory tracking task, based solely on the knowledge of the UAS position. The methodology is based on a novel framework, which identifies inverse error dynamics using a Wavelet Neural Network (WNN) with daughter Mexican hat wavelets activation functions. A real-time load transportation task consisting of a multi-rotorcraft UAS carrying a cable suspended load of unknown characteristics validates the effectiveness of the trajectory tracking control strategy, showing smooth control signals even when the dynamic model of the UAS and the load characteristics are not known.

Analysis, control and design of speed control of electric vehicles delayed model: multi‐objective fuzzy fractional‐order controller

The purpose of this study is to suggest an optimal multi-objective fuzzy fractional-order controller (MOFFOPID) for the speed control of EV systems with time-delay. It is presumed that while the EV is in movement, the armature winding resistance of the direct current (DC) motor varies with time due to temperature changes and this makes it impossible to develop an accurate dynamic model for an EV system. Consequently, in order to have a fast and accurate tracking of the set-point, besides a smooth control signal, a new multi-objective stochastic optimisation is used for the online adjustment of the parameters of MOFFOPID controller. Moreover, a comparison is made between the results of the current study and those of some of the most recent studies on the same topic, which have used online multi-objective PI and online multi-objective fuzzy PI, to assess the efficiency of the suggested controller. Finally, the experimental results based on a TMS320F28335 DSP are implemented on a DC motor to verify the effectiveness of the proposed MOFFOPID controller in controlling the speed of the DC motor which has non-linear features. The results of the simulation confirm the desirable performance of suggested controller.

A Dual-Mode Control with a RBF Network

In this paper, a RBF network with Gaussians is adapted through a combination of switching and integral laws. The idea is taking the best features of each method. The hyperbolic tangent is used instead of signal function which reduces the chattering phenomenon. A hyperbolic secant is used to regulate the integral law, increasing its effects on steady state and reducing on transient. This method produces a smooth control signal with a significant chattering reduction or even its elimination, and a fast and less oscillatory system output. The process is in real time, and the error between the reference model and system outputs is the controlled variable. This strategy needs only measurements of input and output of the plant. Knowledge about parameters and disturbances is unnecessary too. A Lyapunov proof is presented for dual-mode method and comparisons through simulations.

Experimental implementation of MIMO model predictive controller-based second order divided difference filter for nonlinear systems

In this paper, we propose an experimental implementation of a nonlinear predictive controller based on the second order divided difference filter (DDF2) which is a derivate-free estimator. The used state estimator avoids the determination of Jacobian matrices required with the extended Kalman filter (EKF) for an easy implementation with nonlinear systems. In addition, the second order Stirling's interpolation of the estimator allows a more accurate a priori state prediction. A constrained nonlinear predictive controller-based DDF2 is designed to control a multivariable three-tank system. In order to generate the control signals, the controller solves a nonlinear objective function. To overcome the offset output error that appeared due to the inaccuracy of the system model, an internal state model correction scheme is adopted at each iteration. Practical results show the reliability of the proposed method in state estimation, setpoint tracking, and smooth control signal generation. The proposed controller outperforms the model predictive control based on linear state space model derived from the linearisation of the system model around the same setpoint trajectory.

Experimental Fuzzy/Split-Range Control: Novel Strategy for Biodiesel Batch Reactor Temperature Control

With respect to environmental concerns, biofuels have been used around the world, such as biodiesel, and any improvement in the biodiesel production process is desirable. This paper proposes three different control systems based on fuzzy logic and output control signal split-range. Regulating reaction temperature with low settling time and process variable oscillation are the process control aims, and smooth output control signal for actuators protection is also desired. An automated biodiesel production prototype was used and the experimental results demonstrate that a fuzzy/split-range structure with three input variables showed the best performance, resulting in process variable regulation in set-point value with small settling time and actuators premature wearing prevention.

Characterization and adaptive fuzzy model reference control for a magnetic levitation system

This paper shows the implementation of a fuzzy controller applied for magnetic levitation, to make this, the characterization of the magnetic actuator was computed by using ANSYS® analysis. The control law was a Mamdani PD implemented with two microcontrollers, to get a smooth control signal, it was used a model reference. A learning scheme was used to update the consequents of the fuzzy rules. Different reference signals and disturbances were applied to the system to show the robustness of the controller. Finally, LabVIEW® was used to plot the results.

Ultra-Stable Non-Isolated Brillouin Fiber Laser Using Real-Time Control

We present and demonstrate a highly stabilized non-isolated single-mode Brillouin fiber laser utilizing a novel, simple, and inexpensive approach for locking the cavity length. Our scheme is based on an intuitive control algorithm programmed into an embedded microcontroller and is characterized by smooth control signals. The laser cavity length is controlled in real-time using a piezoelectric actuator according to the pump level inside the cavity. Using this control scheme, we demonstrate ultra-stable, non-isolated, Brillouin fiber laser with power variations of ∼4% and lasing frequency drift of few hundreds of kilohertz. To the best of our knowledge, this is the first comprehensive report on the frequency stability properties of controlled BFLs. We compare the stability of our laser to non-controlled cavities, investigate the impact of minimal isolation and discuss various parameters that affected the achievable stability and govern the laser short and long term stabilities. The demonstrated approach is highly attractive for real-life, out-of-the-lab applications where sufficient thermal and mechanical isolation is difficult and expensive to obtain.

Adaptive smooth second-order sliding mode control method with application to missile guidance

This paper proposes an adaptive smooth second-order sliding mode control law for a class of uncertain non-linear systems. The key point of this control law is ensuring a smooth control signal considering parametric uncertainty and disturbances with unknown bounds. The proposed control method is obtained by introducing a continuous function under the integral and using adaptive gains. The switching function and its derivative are forced to zero in finite time. This is achieved using a smooth control command and without the prior knowledge of upper bound parameters of uncertainties. The finite-time stability is proved based on a quadratic Lyapunov approach and the reaching time is estimated. This structure is used to create a homing guidance law and the efficiency is evaluated via simulations.

A new observer-based chattering-free sliding mode guidance law

This paper proposes a new observer-based sliding mode guidance law to intercept maneuvering targets in terminal phase. In order to satisfy the interception, the line of sight angular rate is considered as sliding variable based on parallel navigation idea. For this sliding variable reach to zero in finite time, the guidance law is designed using a new chattering-free observer-based sliding mode control. This algorithm consists of the target acceleration estimation using a new extended state observer. Therefore, with the availability of this estimation, switching function of the sliding mode control is replaced with a smooth function to generate smooth control signal. Also, the stability of closed-loop system is proven by using Lyapunov method. Numerical simulations are presented to illustrate the proposed guidance law potential.