Barrier Lyapunov function-based adaptive prescribed performance control of the PMSM used in robots with full-state and input constraints

The permanent magnet synchronous motor is extensively used in robots due to its superior performances. However, robots mostly operate in unstructured and dynamically changing environments. Therefore, it is urgent and challenging to achieve high-performance control with high security and reliability. This paper investigates an accelerated adaptive fuzzy neural prescribed performance controller for the PMSM to solve chaotic oscillations, prescribed output performance constraint, full-state constraints, input constraints, uncertain time delays, and unknown external disturbances. First, for ensuring the permanent magnet synchronous motor with higher security, faster response speed, and lower tracking error simultaneously, a novel unified prescribed performance log-type barrier Lyapunov function is proposed to handle both prescribed output performance constraint and full-state constraints. Subsequently, a continuous differentiable constraint function-based model is introduced for solving input constraints nonlinearity. The Lyapunov–Krasovskii functions are utilized to compensate the uncertain time delays. Besides, a type-2 sequential fuzzy neural network is exploited to approximate unknown nonlinearities and unknown gain. For the “explosion of complexity” associated with backstepping, a tracking differentiator is integrated into this controller. Furthermore, a speed function is introduced in the backstepping technique for accelerated convergence. On the basis of above works, the accelerated adaptive backstepping controller is achieved. And the presented controller can ensure that all the closed-loop signals are ultimate boundedness, and all state variables are restricted in the prespecified regions and the permanent magnet synchronous motor successfully escapes from chaotic oscillations. Finally, the simulation results verify the effectiveness of the proposed controller.

A Novel Method of Prescribed Constraint Control Without Initial Condition of Nonlinear Systems

A novel constraint control strategy without initial condition of constrained variables is investigated based on backstepping technique for nonlinear systems. In this paper, the novel constraint control strategy is presented for a class of strict-feedback nonlinear systems with actuator saturation and external disturbances by using a nonlinear mapping and a novel performance constraint function. In this control strategy, there are two prescribed constraint functions, the design of these functions is not related to the initial conditions of the constrained variables. Unlike the existing constraint control method without initial condition, the proposed method gives a new solution. It can guarantee that the constraint variable gets into a prescribed constraint region from any initial value no later than a setting time. And the setting time is a design parameter, it can be set arbitrarily. A prescribed performance constraint tracking controller is designed in this paper. It can make that the tracking error of the nonlinear system is constrained to a given region no later than the given setting time, and the transient and steady state performance of the system are ensured. Finally, the proposed method is compared with the existing method, the effectiveness and superiority of the proposed method are demonstrated by two practical examples.

COBREXA.jl: constraint-based reconstruction and exascale analysis

COBREXA.jl is a Julia package for scalable, high-performance constraint-based reconstruction and analysis of very large-scale biological models. Its primary purpose is to facilitate the integration of modern high performance computing environments with the processing and analysis of large-scale metabolic models of challenging complexity. We report the architecture of the package, and demonstrate its scalability by benchmarking the task distribution overhead incurred when performing analyses of many variants of multi-organism community models simultaneously.

Robust H ∞ Feedback Compensator Design for Linear Parabolic DPSs with Pointwise/Piecewise Control and Pointwise/Piecewise Measurement

In this paper, a robust H ∞ control problem of a class of linear parabolic distributed parameter systems (DPSs) with pointwise/piecewise control and pointwise/piecewise measurement has been investigated via the robust H ∞ feedback compensator design approach. A unified Lyapunov direct approach is proposed in consideration of the pointwise/piecewise control and point/piecewise measurement based on the distributions of the actuators and sensors. A new type of Luenberger observer is developed on the continuous interval of space domain to track the state of the system, and an H ∞ performance constraint with prescribed H ∞ attenuation levels is proposed in this paper. By utilizing Lyapunov technique, mathematical inequalities, and integration theory, a sufficient condition based on LMI for the exponential stability of the corresponding closed-loop coupled system under an H ∞ performance constraint is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.

Performance Improvement of a Two-Stage Proportional Valve With Internal Hydraulic Position Feedback

The present research concentrates on the performance improvement of a two-stage proportional valve with internal hydraulic position feedback which is named as the Valvistor valve. In this paper, the performance constraint of this valve is identified and a novel electronic closed-loop control strategy with an integral-separation fuzzy proportional-integral-derivative controller is proposed to improve the valve performance, including the static characteristics and the dynamic characteristics. The results show that in the Valvistor valve, the comparison point and the feedback loop for the internal hydraulic position feedback is only in the main stage, while the input is in the pilot stage. This leads to the poor performance of this valve. The control strategy is very effective and the performance of the Valvistor valve is improved. With the control strategy, the error of the poppet displacement is reduced from 4.9% to 2.1% by adjusting the spool displacement in the pilot stage in real-time and the flow error is reduced from 5.3% to 2.3%. The dead zone of the poppet displacement and the flow is eliminated. The hysteresis is reduced from 5.3% to 2.6% and the linearity is improved. The overshoot is reduced from 0.06 to 0.02 mm and the settling time is reduced from 0.5 to 0.2 s. Moreover, the bandwidth is increased from 8 to 16 Hz.

Appointed-Time Integral Barrier Lyapunov Function-Based Trajectory Tracking Control for a Hovercraft with Performance Constraints

This paper develops a totally new appointed-time integral barrier Lyapunov function-based trajectory tracking algorithm for a hovercraft in the presence of multiple performance constraints and model uncertainties. Firstly, an appointed-time performance constraint function is skillfully designed, which proposes to pre-specify the a priori transient and steady performances on the system tracking errors. Secondly, a new integral barrier Lyapunov function is constructed, which combines with the appointed-time performance constraint function to guarantee that the performance constraints on the system tracking errors are never violated. On this basis, an adaptive trajectory tracking controller is derived using the appointed-time integral barrier Lyapunov function technique in the combination of neural networks. According to Lyapunov’s stability theory, it can be shown that the proposed controller is capable of ensuring transient and steady performances on the output tracking errors. In particular, the position and speed tracking can be fulfilled in a user-appointed time without requiring complex control parameters selection. Finally, results from a comparative simulation study verify the efficacy and advantage of the proposed control approach.