Data-Driven Composite Nonlinear Feedback Control for Semi-Global Output Regulation of Unknown Linear Systems With Input Saturation

This paper compares common PI controller with proximate time-optimal servomechanism (PTOS), composite nonlinear feedback (CNF) control law, and a mode switching control (MSC) scheme. The structure of PI controller is simple and easy to implement. The PTOS control law devotes to fast acceleration and deceleration, while the CNF control law consists of a linear feedback part for achieving fast response and a nonlinear feedback part for suppressing the overshoot caused by the linear part, so as to improve the transient performance in set-point tracking. The MSC scheme is proposed to achieve fast and precise set-point tracking in servo systems. The control scheme incorporates a CNF control law into PTOS control. These control laws were then applied to the position-velocity control loop in a permanent magnet synchronous motor (PMSM) servo system in simulation. The simulation results verify that the PTOS control is capable of tracking the target position fast, the CNF control can achieve the target position with a small overshoot and under the MSC scheme the servo system is able to track a wide range of target positions fast and accurately.

To improve the transient performance, the composite nonlinear feedback (CNF) control technique is introduced to solve the output regulation problem of linear systems with input saturation. Under the assumption that both the states of plant and exo-system are not measurable for feedback, an full state observer is designed to construct an output feedback CNF control law. The output feedback CNF controller is constructed based on a state feedback control law that solves the output regulation problem and the state observer. The solvability of the output regulation problem by output feedback CNF control is established which shows that the nonlinear feedback part does not change the solvability condition of the output regulation problem. The introducing of nonlinear feedback part in the CNF control law provides an extra degree of freedom to improve the transient performance. By appropriately choosing the linear feedback gain and the nonlinear feedback gain in the CNF control law can significantly improve the transient performance of the controlled output which is illustrated by a disturbance rejection problem.

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper investigates the design of the composite nonlinear feedback (CNF) control law for multivariable linear systems with input saturation. In the existing design procedure of the CNF control for multivariable systems, the nonlinear function is given by an m dimensional matrix in a diagonal form, where m is the number of system inputs. However, the inputs and the outputs of the system are coupled heavily in many cases. Thus, it is very difficult to tune the nonlinear functions of the diagonal matrix in the design of the CNF control. This paper proposes a more efficient design procedure for the CNF control by using the structure information of the system in a special coordinate basis (SCB) form. The proposed design procedure gives a clear map on how to select the structure of the nonlinear feedback gain, and how to tune the nonlinear functions in the CNF control.

The general design procedure of composite nonlinear feedback (CNF) control does not consider the structure information of the system. As a result, the tuning of the nonlinear feedback gain is very difficult, especially for nonminimum phase systems. In this paper, a novel design method is proposed to construct a CNF control law by using the structure information of the system in a special coordinate basis (SCB) form. First, the system is transformed into the SCB form, in which the system is divided into three parts, i.e., stable zero dynamics part, unstable zero dynamics part, and integration part. For a nonminimum phase linear system, a virtual linear feedback gain is designed to stabilize the unstable zero dynamics. With this virtual gain, the system can be transformed to an integration system which is connected to a stable system. Then, the CNF control law is tuned only for the integration part of the system. Since the target system is an integration system, the proposed method simplifies the tuning of the nonlinear function in the CNF design.

COMPOSITE NONLINEAR FEEDBACK CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH INPUT SATURATION

SummaryThis paper considers output tracking of nonstep reference signals for multi‐input multi‐output singular systems subject to actuator saturation and external disturbances. Singularity of the system alongside the actuator saturation constraint and external disturbances adds more complexity to stability analysis and controller design than normal systems. Moreover, the problem of output tracking of nonstep reference signals in singular systems via the composite nonlinear feedback (CNF) control law is not studied so far in the literature, and this article will investigate this problem for the first time by proposing the modified CNF control law. For this purpose, first, a singular reference generator system is constructed to produce the desired nonstep reference signal. Then, the dynamical error system is obtained by defining a new state vector as the tracking error and augmenting it to the main system. Different parts of the modified CNF control law are designed afterwards. Due to complexities caused by the singularity of the system and the saturation constraint, detailed mathematical calculations are done. In this regard, a theorem is given that guarantees the tracking problem for three different cases of the saturation function. Moreover, the given theorem will investigate the uniform ultimate boundedness analysis of the tracking error in the face of external disturbances. Finally, the theoretical results are affirmed by computer simulations through three examples to verify the performance and applicability of the proposed control law.

ABSTRACTThis paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.

The composite nonlinear feedback (CNF) control problem with event-triggered strategy for saturated systems with measurement feedback is considered in this paper. Both the full-order measurement and the reduced-order one are investigated to ensure the satisfactory performance of the closed-loop saturated systems under the proposed event-triggered mechanism. Generally speaking, the CNF control is divided into the linear control part and the nonlinear control part, which are designed separately. The purpose of the former is to shorten the rise time, while the latter aims at reducing the overshoot caused by the former. In this paper, a co-design method of linear and nonlinear control parts is proposed such that the control output tracks the reference input asymptotically with a good transient performance. Moreover, the parameter of CNF is applied to the construction of event-triggered mechanism which can efficiently reduce the communication burden. In order to avoid Zeno behavior, the minimum event-triggering time interval is explicitly formulated. Finally, an example of fighter aircraft is given for illustration.

A composite nonlinear feedback (CNF) control with dynamic event‐triggered strategy for saturated systems is considered in this paper. The CNF control is introduced to improve the system response speed and reduce the overshoot under disturbances. The dynamic event‐triggered mechanism (DETM) is utilized to save more communication resources. The focus of this paper is to achieve the asymptotic tracking of saturated systems by combining DETM with CNF control. A criterion is presented to guarantee that the system can track the reference input signal asymptotically. Zeno behavior is eliminated by proving the minimum time interval is greater than zero. Finally, simulations are carried out to verify the correctness of the proposed results.

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

This paper proposes Composite Nonlinear Feedback (CNF) controller application for yaw rate tracking control of active front steering (AFS) for vehicle equipped by Steer-by-Wire (SBW). CNF controller is used in AFS system to achieve a fast tracking response of yaw rate according to the desired response and to generate correction steer angle input to enhance vehicle maneuverability. A 2-DOF linear vehicle model is used to design the controller and as the vehicle plant for the simulation evaluation. In order to analyze the proposed control strategy performance, the designed controller was simulated using J-curve and lane change maneuvers conditions and then compared with conventional Proportional Integral Derivative (PID) controller. The results show CNF has a fast yaw rate tracking capability and manage to improve vehicle maneuverability compared to conventional.

The purpose of controlling the vehicle handling is to ensure that the vehicle is in a safe condition and following its desire path. Vehicle yaw rate is controlled in order to achieve a good vehicle handling. In this paper, the optimal Composite Nonlinear Feedback (CNF) control technique is proposed for an Active Front Steering (AFS) system for improving the vehicle yaw rate response. The model used in order to validate the performance of controller is nonlinear vehicle model with 7 degree-of-freedom (DOF) and a bicycle model is implemented for the purpose of designing the controller. In designing an optimal CNF controller, the parameter estimation of linear and nonlinear gain becomes very important to produce the best output response. An intelligent algorithm is designed to minimize the time consumed to get the best parameter. To design an optimal method, Multi Objective Particle Swarm Optimization (MOPSO) is utilized to optimize the CNF controller performance. As a result, transient performance of the yaw rate has improved with the increased speed of in tracking and searching of the best optimized parameter estimation for the linear and the nonlinear gain of CNF controller.

To enhance the dynamic performance and robustness of the voltage control system of islanded microgrid inverters, a new control strategy combining integral sliding mode (ISM) control and composite nonlinear feedback (CNF) control is proposed. In ISM control, firstly, a new reaching law is designed to improve movement quality in the reaching phase by improving the power term and introducing the inverse tangent function. Then, to improve disturbance observation accuracy, a variable gain extended state observer is designed by improving the regulation mechanism of the state variables according to deviation control. Using the idea of variable damping, linear and nonlinear feedback are combined into CNF control. Specifically, linear feedback provides a small damping ratio for faster system response, while nonlinear feedback increases the damping ratio to improve steady‐state performance. Simulation results show that the integral sliding mode‐composite nonlinear feedback (ISM‐CNF) control strategy cam balances convergence speed and chattering better and achieves higher steady‐state accuracy than conventional strategies. Moreover, ISM‐CNF control has better robustness to reference voltage variations and disturbances caused by sudden load changes. Therefore, the ISM‐CNF control strategy can accomplish voltage control of islanded microgrid inverters quickly and steadily, effectively suppressing system disturbances and enhancing stability and power quality. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

A two term composite nonlinear feedback (2TCNF) control technique is developed here for nonlinear time delay systems in presence of input saturation. The proposed controller consists of two terms that are conventional composite nonlinear feedback (CNF) control and delay state control. CNF control has advantage of fast transient response and delay state control improves damping characteristics. The proposed controller thus has both these advantages and it tracks the reference smoothly. The closed loop asymptotic stability is guaranteed via Lyapunov–Krasovskii analysis. The efficiency of the proposed controller is tested on exothermic chemical reactor and validated through simulation results. Its performance is compared with the conventional CNF control. The superiority of 2TCNF is established in terms of less overshoot, fast transient response and reduced steady state error.