Control Signal Saturation Research Articles

A practical solution to the saturation problem in feedforward control for measurable disturbances

This paper treats the problem of control signal saturation caused by feedforward control from measurable load disturbances. An efficient feedforward compensator will often give significant peaks in the control signal at fast changes in the load disturbance. These peaks may cause the control signal to reach a saturation limit. In the paper, it is shown that the anti-windup function may cause unnecessarily sluggish responses in these cases. To overcome this problem, it is suggested to reduce the gain of the feedforward compensator during periods of control signal saturation. A method to calculate this gain reduction is presented, and several simulation examples show that this idea will result in a great performance improvement in cases of saturation problems. The proposed algorithm is also tested on a lab-scale temperature control system to demonstrate the noticeable practical capabilities.

A Novel Exploration-Exploitation-Based Adaptive Law for Intelligent Model-Free Control Approaches.

Model-free control approaches require advanced exploration-exploitation policies to achieve practical tasks such as learning to bipedal robot walk in unstructured environments. In this article, we first construct a comprehensive exploration-exploitation policy that carries quality knowledge about the long-term predictor and the control policy, and the control signal of the model-free algorithms. Therefore, the developed model-free algorithm continues exploration by adjusting its unknown parameters until the desired learning and control are accomplished. Second, we provide an utterly model-free adaptive law enriched with the exploration-exploitation policy and derived step-by-step using the exact analogy of the model-based solution. The obtained adaptive control law considers the control signal saturation and the control signal (input) delay. Performed Lyapunov stability analysis ensures the convergence of the adaptive law that can also be used for intelligent control approaches. Third, we implement the adaptive algorithm in real time on a challenging benchmark system: a fourth-order, coupled dynamics, input saturated, and time-delayed underactuated manipulator. The results show that the proposed adaptive algorithm explores larger state-action spaces and treats the vanishing gradient problem in both learning and control. Also, we notice from the results that the learning and control properties of the adaptive algorithm are optimized as required.

Real-Time Optimization of Social Distancing to Mitigate COVID-19 Pandemic Using Quantized Extremum Seeking

The application of extremum seeking control is investigated to mitigate the spread of the COVID-19 pandemic, maximizing social distancing while limiting the number of infections. The procedure does not rely on the accurate knowledge of an epidemiological model and takes realistic constraints into account, such as hospital capacities, the observation horizon of the pandemic evolution and the quantized government sanitary policy decisions. Based on the bifurcation analysis of a SEIARD compartmental model providing two possible types of equilibria, numerical simulation reveals the transient behaviour of the extremum of the constrained cost function, which, if rapidly caught by the algorithm, slowly drifts to the steady-state optimum. Specific features are easily incorporated in the real-time optimization procedure, such as quantized sanitary condition levels and long actuation (decision) periods (usually several weeks), requiring processing of the discrete control signal saturation and quantization. The performance of the proposed method is numerically assessed, considering the convergence rate and accuracy (quantization bias).

Performance Comparison Between Piezoelectrically Induced Stresses and Active Control for Aeroelastic Stability Augmentation

Recent works have addressed piezoelectrically induced stresses as a potential technique for aeroelastic stability augmentation of biclamped structures. Because active-control-based techniques are conventionally used for aeroelastic stabilization, this paper presents a comparative study on the effectiveness of piezoelectrically induced stresses and active control for aeroelastic stability augmentation. A finite-element-method-based piezoaeroelastic model is proposed employing two-node, eight-degree-of-freedom smart beam elements and an unsteady, strip-theory-based aerodynamic approach involving vertical gust components. A stability augmentation system was designed for stiffness control and used for comparison in a particular wing configuration. Analyses involving the stability margins, input signal energy, and the response to vertical gust were performed and discussed. The results showed that piezoelectrically induced stresses and active control can provide equivalent flutter speed increase for the two cases of gain margin considered. However, the system can become unstable due to control signal saturation when submitted to high-amplitude gusts, which was not observed when piezoelectrically induced stresses is used. On the other hand, it was observed that the active control required a much smaller amount of energy for stabilization. In general, it was noticed that the piezoelectrically induced stresses technique was not as effective as active control to increase the flight envelope of biclamped structures, because active control can provide equivalent aeroelastic stability improvement with smaller amount of energy. However, it is found to be a promising strategy to be used on emergency devices, where the aeroelastic stability of biclamped structures needs to be guaranteed in critical aerodynamic disturbance conditions.

Trajectory tracking of a quadrotor using a robust adaptive type-2 fuzzy neural controller optimized by cuckoo algorithm

This paper proposes an adaptive and robust adaptive control strategy based on type-2 fuzzy neural network (T2FNN) for tracking the desired trajectories of a quadrotor. The designed methods can control both the position and the orientation of a quadrotor. Contrary to common sliding mode controllers (SMCs), the robust adaptive trajectory tracking scheme presented here is based on SMC with exponential reaching law; which helps reduce the phenomenon of chattering. Moreover, parameters including the gains of sliding surfaces, are optimized by cuckoo optimization algorithm (COA), and the results are compared with those obtained by genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO). The designed methods in this study are called adaptive T2FNN controller and the exponential SMC (ESMC)-T2FNN. The law for updating the T2FNN is obtained online by using the Lyapunov stability theory. Considering undesired factors such as uncertainties, external disturbances and control signal saturation, the results of our controllers are compared with those of the adaptive type-1 fuzzy neural network controller (T1FNN) and ESMC-T1FNN. The extensive simulations demonstrate the effectiveness of the proposed COA-based ESMC-AT2FNN approach compared to the other tested techniques (i.e. GA, PSO and ACO) in terms of the improved transient and steady-state trajectory-tracking performance. The mean and standard deviation values concerning the COA are obtained through statistical analyses at 0.00006173 and 0.000092, respectively. This paper also examines the complexity of COA in optimizing the trajectory tracking control of quadrotor and investigates the effects of COA parameters on optimization results. The stable performance of the cuckoo algorithm is demonstrated by varying its parameters and analyzing the obtained results. These results also show the convergence of COA for the considered problem.

Speed control of DC motor based on wireless networked control system with time delay and saturation parameters

The integration of a wireless network in a closed-loop control system can provide several benefits such as flexibility, installation, and maintenance. However, the presence of time delay in the network system can reduce the control performance. On the other hand, control signal saturation is also the problem that must be overcome in designing a controller. This study aims to design a DC motor speed control by integrating wireless network in its closed-loop system. This concept is known as the Wireless Networked Control System (WNCS). The network parameter used in this study is focused on the time delay. In the controller side, we use a saturation parameter which usually occurs due to limitations of the input signal. The PI-AW controller is used due to having the ability to overcome the saturation of the control signal. The simulation results show that the PI-AW controller can produce the best responses if compared with PI linear and PI saturated with settling time under 1.5 seconds and overshoot less than 8% for three constant values of time delay. The control signal generated also does not exceed the maximum limit of 12 V.

Switched Control Design with Guaranteed Cost for Uncertain Nonlinear Systems Subject to Actuator Saturation

Abstract This manuscript proposes a robust switched controller design with minimization of an upper bound of a quadratic performance index (guaranteed cost) related to the system output for a class of uncertain nonlinear systems with actuator saturation described by Takagi-Sugeno (TS) fuzzy models. The switched control eliminates the necessity of finding or estimating the membership functions, which can be uncertain or complex to obtain. In most practical implementations, systems and actuators have physical limitations. Therefore, in order to approximate the theoretical switched controller design closer to its implementation, it will be considered that the system has an operating region and control signal saturation. The proposed switched controller design will be implemented in a bench active suspension system considering actuator saturation with uncertain mass and actuator fault. A comparison will be shown between robust single-gain and switched controller with the same design parameters.

Control of a Multiphase Buck Converter, Based on Sliding Mode and Disturbance Estimation, Capable of Linear Large Signal Operation

Power-hardware-in-the-loop systems enable testing of power converters for electric vehicles (EV) without the use of real physical components. Battery emulation is one example of such a system, demanding the use of bidirectional power flow, a wide output voltage range and high current swings. A multiphase synchronous DC-DC converter is appropriate to handle all of these requirements. The control of the multiphase converter needs to make sure that the current is shared equally between phases. It is preferred that the closed-loop dynamic model is linear in a wide range of output currents and voltages, where parameter variations, control signal limits, dead time effects, and so on, are compensated for. In the case presented in this paper, a cascade control structure was used with inner sliding mode control for phase currents. For the outer voltage loop, a proportional controller with output current feedforward compensation was used. Disturbance observers were used in current loops and in the voltage loop to compensate mismatches between the model and the real circuit. The tuning rules are proposed for all loops and observers, to simplify the design and assure operation without saturation of control signals, that is, duty cycle and inductor current reference. By using the proposed control algorithms and tuning rules, a linear reduced order system model was devised, which is valid for the entire operational range of the converter. The operation was verified on a prototype 4-phase synchronous DC-DC converter.

New optimal controller tuning method for an AVR system using a simplified Ant Colony Optimization with a new constrained Nelder–Mead algorithm

In this paper, an optimal gain tuning method for PID controllers is proposed using a novel combination of a simplified Ant Colony Optimization algorithm and Nelder–Mead method (ACO-NM) including a new procedure to constrain NM. To address Proportional-Integral-Derivative (PID) controller tuning for the Automatic Voltage Regulator (AVR) system, this paper presents a meta-analysis of the literature on PID parameter sets solving the AVR problem. The investigation confirms that the proposed ACO-NM obtains better or equivalent PID solutions and exhibits higher computational efficiency than previously published methods. The proposed ACO-NM application is extended to realistic conditions by considering robustness to AVR process parameters, control signal saturation and noisy measurements as well as tuning a two-degree-of-freedom PID controller (2DOF-PID). For this type of PID, a new objective function is also proposed to manage control signal constraints. Finally, real time control experiments confirm the performance of the proposed 2DOF-PIDs in quasi-real conditions. Furthermore, the efficiency of the algorithm is confirmed by comparing its results to other optimization algorithms and NM combinations using benchmark functions.

Disturbance Compensation Algorithm Under Saturation of Control Signal

The disturbance compensation algorithm for control of multi-input multi-output (MIMO) plant is proposed. The plant is described by the linear differential equation with unknown parameters and external bounded disturbances. The algorithm ensures the small difference between plant output and reference signal under the saturation of control signal. It is shown that the algorithm can be applied for plant with unknown dynamical order. The simulations illustrate the efficiency and robustness of the designed control system.

A novel method for fuzzy scale factors scheduling in fuzzy PD+I with anti-windup system controllers

The adjustment of scale factors in fuzzy controllers is a key factor in their correct functioning. In two-inputs fuzzy PID controllers, such as fuzzy PI+D (FPI+D) and fuzzy PD+I (FPD+I), the adjustment of scale factors is directly related to the adjustment of the gains of a PID controller using some of the traditional methods of adjustment. In systems that have control signal saturation, fuzzy PID controllers require anti-windup systems (AW) that limit the controller’s integral action. In these situations, the adjustments of scale factors are not directly related to the adjustment of gains of a PID controller. Its use increases the overall gain system and creates an unbounded controller, which causes a faster response in the transient state but an oscillatory behavior and even critical stability in the steady state of the response. A solution to this problem is to reduce the output scale factor, to create a bounded controller, in which the tracking time constant is augmented. Consequently, the system presents more bounded oscillations in the steady state, but the transient response is slower. The main motivation of this research was to develop an approach for adjusting fuzzy PD+I controllers with an anti-windup system (FPD+I AW) with faster response in the transient state and without oscillatory behavior in the steady state. This approach uses a second fuzzy controller, which adjusts the output scale factor and the tracking time constant according to the actual system error. To verify the effectiveness of the proposed approach, a fuzzy PD+I controller with an AW system based on tracking back calculation and fuzzy scale factor scheduling (FPD+I AW-FSFS) was implemented and used to control the speed in a direct current motor with control signal saturation and was compared with the responses of FPD+I unbounded and FPD+I bounded controllers with AWs based on tracking back calculation, thereby proving the effectiveness of the proposed method.

Design of Lyapunov Based Nonlinear Position Control of Electrohydraulic Servo Systems

This paper studies the nonlinear closed loop control of an electrohydraulic servo system. The control strategy is developed based on Lyapunov theory of nonlinear systems using integrator backstepping approach. Highly nonlinear nature of electrohydraulic servo system is well known. Main reasons for nonlinear and non-differentiable mathematical description of systems dynamics are the fluid compressibility, leakage flows, friction forces and nonlinear fluid flow through servo valve orifices. These nonlinear terms influence also the dynamic errors of the control system. Two different nonlinear design procedures are employed feedback linearization and integrator backstepping. Backstepping is used here because it is a powerful and robust nonlinear strategy. These techniques are used for construction of nonlinear control algorithm. The effectiveness of it, to stabilize any operating point of the system is proved by computer simulation. The systems error dynamics significantly depends on tuning parameters of the controller. The wrong selection of these parameters may lead to saturation or chattering of control signals. All derived results are validated by computer simulation of a nonlinear mathematical model of the system. The results are also compared to these obtained with a conventional P controller to prove that classic linear controllers fail to achieve a good tracking of the desired output, especially, when the hydraulic actuator operates at the maximum load. The research studies represented in the paper shows big potential of Lyapunov based nonlinear controller design procedures, to obtain desired control objectives.

Model-free constrained data-driven iterative reference input tuning algorithm with experimental validation

This paper presents the design and experimental validation of a new model-free data-driven iterative reference input tuning (IRIT) algorithm that solves a reference trajectory tracking problem as an optimization problem with control signal saturation constraints and control signal rate constraints. The IRIT algorithm design employs an experiment-based stochastic search algorithm to use the advantages of iterative learning control. The experimental results validate the IRIT algorithm applied to a non-linear aerodynamic position control system. The results prove that the IRIT algorithm offers the significant control system performance improvement by few iterations and experiments conducted on the real-world process and model-free parameter tuning.

Mu-Synthesis robust control of 3D bar structure vibration using piezo-stack actuators

This paper presents an idea for the Mu-Synthesis robust control of 3D bar structure vibration with using a piezo-stack actuators. A model of the 3D bar structure with uncertain parameters is presented as multi-input multi-output (MIMO) dynamics. Nominal stability and nominal performances of the open-loop 3D bar structure dynamic model is developed. The uncertain model-based robust controller is derived due to voltage control signal saturation and selected parameter perturbations. The robust control performances and robustness of the system due to uncertainties influence is evaluated by using singular values and a small gain theorem. Finally, simulation investigations and experimental results shown that system response of the 3D bar structure dynamic model with taken into account perturbed parameters met desired robust stability and system limits. The proposed robust controller ensures a good dynamics of the closed-loop system, robustness, and vibration attenuation.

A new approach for adjusting scale factor in fuzzy PD+I controllers with anti-windup

In fuzzy controllers, the adjusting of scale factors, both input and output, is critical to the performance of the plant being controlled. The adjustment of scale factors in Fuzzy PD+I controllers (FPD+I) is well documented; however, in systems that have control signal saturation, FPD+I requires anti-windup systems (AW) that limit the controller's integral action. The adjustment procedure for FPD+I controllers cannot be used in Fuzzy PD+I controllers with anti-windup system (FPD+I AW), as it increases the overall gain system, which causes oscillatory behaviour and even critical stability in the controlled variable. The main motivation of this research was to have an approach for adjusting Fuzzy PD+I controllers with anti-windup system (FPD+I AW) without having oscillatory behaviour. In order to verify the proposed approach, both the input and output scale factors of a FPD+I AW controller were adjusted and used to control speed in a direct current motor with control signal saturation and were compared with the responses of conventional PID, Adaptive Neuro Fuzzy Inference System (ANFIS) and Fuzzy sliding controllers, all with AWs based on tracking back calculation, thereby demonstrating the effectiveness of the proposed approach.

Filtered Smith predictor with feedback linearization and constraints handling applied to a solar collector field

Feedback linearization (FL) has recently been used to control the temperature in a solar field using the water flow rate as the manipulated variable. Nevertheless, the system shows undesirable control signal oscillation caused by a delay uncertainty. In this paper, the dynamics resulting from applying the FL transformation to the nonlinear process model is approximated by a first-order model plus dead-time, and a filtered Smith predictor (FSP) is proposed as the control strategy. This controller deals with dead-time errors but also includes control signal saturation caused by flow rate constraints. Simulations demonstrate the robustness of the FSP structure in comparison to a simple PID and a Smith predictor (SP) approach when a faster closed-loop is required in a system with delay uncertainties. Real experimental results included show the improved behavior of the proposed control scheme.

Filtered Smith predictor with feedback linearization and constraints handling applied to a solar collector field

Abstract Recently, the feedback linearization (FL) technique was proposed to control the temperature in a solar field using the water flow rate as the manipulated variable. Nevertheless, the system shows non-desirable control signal oscillations caused by a delay uncertainty. In this paper, the resulting dynamics obtained after applying the FL transformation over the process nonlinear model is approximated by a first-order model plus dead time, and a filtered Smith predictor (FSP) is proposed as control strategy. This controller deals with dead-time errors but also includes control signal saturation caused by flow rate constraints. Simulations demonstrate the robustness of the FSP structure in comparison to a simple PID when a faster closed-loop is required in a system with delay uncertainties.

A family of smooth controllers for swinging up a pendulum

The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach.

Reduced-order Robust Multivariable Control of a Double-beam Cantilever Structure

Vibration control of a two-dimensional smart structure is presented. The least squares identification technique and a novel pole identification method are used to obtain accurate plant models. Comparable accuracy is achieved with a significantly lower model order using the latter method. A multivariable multi—input multi—output (MIMO) generalized minimum variance control scheme is used to address robustness issues of plant mismodeling, unmodeled modes/dynamics and control signal saturation. The controllers are tested for robustness to spillover problems. Results are further supported with the use of sensitivity response functions.

Robust multivariable control of a double beam cantilever smart structure

The uncertain surrounding environment in which smart structures are employed meansthat a fixed reference base with which to operate sensing/actuation devices cannot beassumed. The distributed placement of piezoceramic devices has made them the mostpopular choice for such an application. The limited available output force makes it essentialto consider the problems of control signal saturation on the robustness of resultingcontrollers. Much previous work has considered smart structural control in a singledimension. The current work looks at the vibration control of a two-dimensional smartstructure. Actuation is applied by means of two pairs of piezoactuators capable ofapplying moments with a controllable phase and amplitude difference allowing acontrollable ratio of bending and torsion motion. The design process of a multivariable(multi-input multi-output) generalized minimum variance control system is discussed.Application to an experimental double cantilever beam system is shown to result inrobust closed-loop control. Comparisons to the benchmark of multi-loop controldemonstrate numerous advantages of the multivariable system. Results are furthersupported with the use of sensitivity functions showing the response of the closed-loopsystems to frequencies of interest, particularly the important vibrational modes.