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Articles published on Transient Response Time
- New
- Research Article
- 10.3390/a18110694
- Nov 3, 2025
- Algorithms
- Rui S Mendes + 1 more
Traditional heat diffusion systems are typically regulated using Proportional–Integral–Derivative (PID) controllers. PID controllers still remain the backbone of numerous industrial control applications due to their simplicity, robustness, and efficiency. However, traditional tuning methods—such as Ziegler–Nichols or Cohen–Coon—often exhibit limitations when applied to systems with nonlinear dynamics, time-varying behaviors, or parametric uncertainties. To address these challenges, Fuzzy Logic Controllers (FLC) have emerged as a promising hybrid strategy, by translating quantitative and imprecise linguistic inputs into quantitative control actions, thereby enabling more adaptive and precise regulation. This is achieved through the integration of fuzzy inference mechanisms that dynamically adjust PID gains in response to changing system conditions. This study proposes a fuzzy logic control strategy for a heat diffusion system and conducts a comparative analysis against conventional PID control. The methodology encompasses system modeling, design of the fuzzy inference system, and simulation studies. To improve transient response and address time delays, additional features such as Anti-Windup compensation and a Smith Predictor are integrated into the control scheme. The final validation step involves the introduction of simulated environmental disturbances, including abrupt temperature drops, to evaluate the controller’s robustness. Simulation results demonstrate that the proposed FLC provides superior dynamic performance compared to the conventional PID controller, achieving approximately 5–7% faster rise time and 8–10% lower settling time. The incorporation of an anti-windup mechanism did not yield significant benefits in this application. In contrast, the integration of a Smith Predictor further reduced oscillatory behavior and substantially improved disturbance rejection, tracking accuracy, and adaptability under simulated thermal variations. These results underscore the effectiveness of the FLC in handling systems with time delays and nonlinearities, reinforcing its role as a robust and adaptable control strategy for thermal processes with complex dynamics.
- New
- Research Article
- 10.1002/adma.202509314
- Nov 1, 2025
- Advanced materials (Deerfield Beach, Fla.)
- Miao Xiong + 14 more
Organic electrochemical transistors (OECTs) are crucial for next-generation (bio-)electronic devices but are often constrained by the use of aqueous electrolytes, which introduce crosstalk, hinder miniaturization, and limit circuit integration. Here, a photo-patternable solid-state electrolyte based on 𝜄-carrageenan (𝜄-CGN) and poly(ethylene glycol) diacrylate (PEGDA) is presented, enabling high-performance OECTs and complementary circuits. The 𝜄-CGN electrolyte exhibits high ionic conductivity (>10 mS cm-1), comparable to a 0.1 m NaCl aqueous electrolyte, while supporting precise patterning down to 15 µm, fast transient response times, minimal hysteresis, and excellent stability in both p- and n-type OECTs. Compact solid-state NAND/NOR gates (500 × 800 µm2), 4-input NAND gates (1600 × 800 µm2, 8 OECTs), and half-adders (2 × 1 mm2, 18 OECTs) are demonstrated, all exhibiting correct logic functions and low-voltage operation. To highlight its potential for implantable bioelectronics, solid-state spiking circuits, monolithically integrated with flexible cuff electrodes, are developed for vagus nerve stimulation in mice. These findings establish 𝜄-CGN-based solid-state electrolytes as a promising platform for scalable, implantable circuits, paving the way for next-generation bioelectronic devices.
- Research Article
- 10.1021/acsaelm.5c01214
- Sep 23, 2025
- ACS applied electronic materials
- Junghyun Lee + 5 more
Organic electrochemical transistors (OECTs) prepared from poly-(3,4-ethylenedioxythiophene) (PEDOT) doped with poly-(styrenesulfonate) (PSS) have been widely investigated, typically with films prepared by spin-casting and drying from aqueous commercially available suspensions. Electrochemical deposition of PEDOT makes it possible to more precisely control film thickness and counterion composition. Here, we examined the influence of channel thickness and counterion composition on the properties of OECTs fabricated using electrochemically polymerized PEDOT with p-toluene sulfonate (pTS) and PSS on interdigitated gold electrodes. While PEDOT:PSS films deposited with a particular charge density were somewhat thicker (with more PSS in the film), PEDOT:pTS films showed higher volumetric capacitances consistent with their more rough, irregular surface morphologies. The maximum transconductance (g m,max) (∼70 mS) and on-current levels barely changed over the examined range of channel thicknesses (100-800 nm) with both counterions. The device stability (current retention in ON/OFF cycling) and transient response times (∼10 ms) were enhanced with larger counterions, thinner channel films (∼100 nm), and lower applied drain voltages (under -0.1 V). These design insights were used to create channel-functionalized OECT-based label-free glucose sensors with high stability. These results demonstrate the ability to optimize and enhance the performance and stability of electrochemically deposited PEDOT-based interdigitated OECT devices.
- Research Article
- 10.1002/ese3.70229
- Jul 16, 2025
- Energy Science & Engineering
- Xinhao Bian + 5 more
ABSTRACTThe air supply system is regarded as a critical component in high‐power proton exchange membrane fuel cells (PEMFCs). Precise control of air mass flow rate and pressure is essential for improving system efficiency, durability, and output power stability. In this study, an 86 kW‐grade PEMFC engine was designed, and a feed‐forward PID‐based control strategy was developed, which achieves dynamic air pressure‐flow decoupling of the PEMFC and provides a quicker response to radically varying loads. Experiments were conducted under various load conditions to evaluate the system's performance. The results demonstrated that the proposed strategy achieved a short transient response time and stable tracking of air mass flow and cathode inlet pressure. Additionally, the voltage deviation between the minimum and average values of individual cells was maintained below 0.05 V, indicating excellent uniformity within the stack. This uniformity ensures the long‐term durability and reliability of the fuel cell stack.
- Research Article
- 10.1088/1742-6596/3046/1/012001
- Jul 1, 2025
- Journal of Physics: Conference Series
- Kang Wu + 1 more
Abstract In this paper, a DC-to-DC buck converter with slope compensation based on COT architecture is proposed for applications in walkie-talkies, portable power supplies, and cellular phones. Compared to the common COT-controlled DC-DC BUCK converter, which does not notice the feedback voltage jitter problem when the external input power fluctuates, or the load changes rapidly, the slope compensation function is proposed to be incorporated in the design. The feedback path of the voltage is changed by the superimposed ramp signal, which improves the system’s anti-jitter function. The principle is similar to the ramp compensation mode in the conventional current mode, but the implementation is different. The proposed design uses the eastern DP 180nmBCD process with an input voltage range of 6 V to 24 V, an output voltage range of 3 V to 5 V, and a transient response time of only 12.327us for a load from 6 A to 8 A.
- Research Article
- 10.1142/s0219455426503153
- May 30, 2025
- International Journal of Structural Stability and Dynamics
- Ali Karimian + 2 more
In this paper, nonlinear size-dependent vibrations and stability of clamped–clamped electrically actuated microbeams reinforced with uniformly distributed carbon nanotubes and bonded with piezoelectric layers have been investigated. The lower piezoelectric layer is supposed to be under a combination of a DC and AC voltage, considering the fringing field effect and Casimir force. The modified couple stress theory is considered to account for the size effect. Viscoelastic properties that may have a certain impact on nonlinear dynamics are studied based on the fractional Kelvin–Voigt constitutive model. The governing partial fractional differential equation of motion is derived using the extended Hamilton’s principle, utilizing the nonlinear von Karman stress–strain relationships within the Euler–Bernoulli beam model. This equation is then discretized to a nonlinear reduced order model (ROM) using Galerkin’s approach. The transient time response of the system is determined via a reformulation of the Newmark method employing fractional derivatives discretized by the Grünwald–Letnikov summation. Dynamic pull-in phenomena are examined by numerically integrating the ROM equation. Neglecting time-dependent terms, the pseudo-arclength continuation technique is also employed to inspect the static pull-in instability. A perturbation method, based on multiple time scales, is applied to study the primary resonance of the microbeam, considering a harmonic AC voltage with small amplitude. The influences of the order of fractional derivative, small-scale parameter, amplitude of AC excitation, and piezoelectric voltages on the hardening-type and softening-type behavior in frequency response curves are investigated. It is shown that just small increments in the values of the order of the fractional derivative, for example, from 0.15 to 0.25, can significantly reduce the amplitude of oscillations and also can change bifurcation characteristics of the microsystem. Also, the results indicate that small variations in the ratios of the length scale parameter to microbeam thickness, from 0 to 0.2, can cause large shifts in the resonance region of the frequency response curves.
- Research Article
- 10.1007/s13369-025-10265-z
- May 21, 2025
- Arabian Journal for Science and Engineering
- Noor Lina Ramli + 3 more
Abstract Tidal energy is a highly predictable and sustainable resource with significant potential to meet global energy demands. This study proposes an adaptive optimum relation-based (A-ORB) maximum power point tracking algorithm to enhance the efficiency, stability, and adaptability of tidal energy conversion systems. The A-ORB algorithm integrates the optimum relation-based (ORB) approach with Hill Climb Search (HCS), along with an adaptive gain adjustment mechanism that dynamically tunes the parameter K based on power variation (ΔP). This hybrid strategy enables faster convergence, improved responsiveness to tidal fluctuations, and reduced power oscillations. The novelty of the proposed method lies in the combination of ORB and HCS with adaptive gain tuning, which collectively improves MPPT performance under variable tidal conditions. Simulation results show that A-ORB outperforms conventional techniques such as small step perturb and observe (SS-PO), small step incremental conductance (SS-InC), and bio-inspired particle swarm optimization (BI-PSO) in both tracking accuracy and power output. Specifically, A-ORB achieves a convergence time of 0.32 s and a maximum power output of 4833 W, compared to 4658 W (0.41 s) for SS-PO, 4561 W (0.5 s) for SS-InC, and 4699 W (0.37 s) for BI-PSO. Moreover, A-ORB exhibits significantly lower power oscillations (3.9 W) compared to 17.88 W (SS-PO), 21.96 W (SS-InC), and 10.4 W (BI-PSO). These findings demonstrate the potential of A-ORB to enhance MPPT efficiency, reduce transient response time, and improve adaptability in dynamic tidal energy environments.
- Research Article
- 10.21303/2461-4262.2025.003444
- Mar 28, 2025
- EUREKA: Physics and Engineering
- Hoang Dang Danh + 1 more
VIOLATION OF PUBLISHING ETHICSTRMS finds applications across various fields, including aerospace, robotics, education, and research. In control system development field, TRMS provides an excellent platform for developing and testing control algorithms due to its nonlinear and coupled dynamics. This research aims to develop a robust tracking control approach for twin rotor multiple-input multiple-output system (TRMS). First, the model of TRMS is written in the space state of uncertain fully-actuated mechanical form with additive disturbances caused by existence of measurement errors, payload variations, and external disturbances. The robust controller is then designed using the sign function and auxiliary controller to ensure that the closed system including TRMS system and robust controller is always adjusted so that the position-tracking errors tend to the origin, the closed-loop system is globally robust and stable with the lumped system uncertainties caused by modeling errors, the aerodynamic coupling between the vertical and horizontal movements, and friction forces that affect the motions of TRMS. The advantages of this method are a fast transient period, high precision, and strong robustness, and without the adaptive mechanism, it can be applied widely to practical applications such as high nonlinear systems, robotic manipulators, and rigid spacecraft attitude control systems. Finally, to show the advantages this control method is applied to the angles tracking control problem of TRMS which has high nonlinear characteristics, input torque disturbances, and the coupling between the vertical and horizontal movements. The experimental results are presented with the choosing of parameters as nominal parameters that validate the proposed solution. The prominent advantages of this method include a zero percent overshoot, a transient response time of approximately 1s for the yaw angle and 1.5 s for the pitch angle, and superior impulse disturbance rejection compared to linear control. Specifically, the proposed controller stabilizes the pitch angle to its desired initial value within 1s, while the stabilization time for the yaw angle is also 1 s.
- Research Article
- 10.18196/jrc.v6i2.24409
- Mar 11, 2025
- Journal of Robotics and Control (JRC)
- Suad Ali Aessa + 2 more
In communications systems, a group of technologies can be linked into one system. Each technology has a function, and each system has stages. Therefore, it can be said that the input stage can have one or multiple inputs. MIMO techniques suffer from a large-scale linear dynamic problem, it will be easy to adjust the (PID) of a continuous system, and any system is considered vulnerable to disturbances during the operation process. Therefore, a state of instability can occur in it, which requires developing solutions to modify the behavior of the it. Systems need control units to handle transient states as a result of changing operating conditions of the system. Expert and intelligent systems can be used to adjust the traditional controllers and make them adapt to the operating conditions of the proposed system. Work must be done to make the proposed approach capable of ensuring stability for the system. Work can be done to reduce the time for the transient state and the speed of response to the stable state. The behavior of the system can be clarified through simulation results and show the difference between the methods. Proposed to test the feasibility and effectiveness of the work and verify it using the MATLAB program to design a highly accurate and efficient model. The current study reviews This work displays the tuning of the PID controller for MIMO systems utilizing a statistical FPA and evaluated by objective function as integral time absolute error (ITAE). A combination of ITAE combined with the FPA reduction method is adopted to reduce the steady-state transient time responses between the higher-order initial scheme and the unit amplitude It also aims to conduct simulation and develop the appropriate and proposed design model with different. It is possible to compare the control of the system using a traditional control unit and another that adjusts using the modern technology of the Flower pollination algorithm FPA-PID. It also showed that the results of the simulation process were clear that the optimization process using FPA-PID was superior to the other traditional case (PID).
- Research Article
- 10.1002/adc2.70004
- Feb 25, 2025
- Advanced Control for Applications
- Nattapong Suksabai + 1 more
ABSTRACTIn industrial overhead cranes, inverters and motors are used to control motor position, velocity, and acceleration. However, higher‐order derivatives depend on load characteristics, leading to inconsistent jerk profiles and deviations in circular path. Payload sway further contributes to path deviation, and although sway suppression techniques are beneficial, they extend the transient response time. This paper proposes a position feedback control technique based on extended state observers to compensate for the higher‐order dynamics, and address uncertainties in the driven unit through disturbance rejection. A command smoother is analyzed to provide an equation used for path deviation prediction. The trapezoidal trajectory, expressed as a function of sine and cosine, is analyzed to use in this circular path study. A command smoother with feedforward control, is used to mitigate payload sway, demonstrating advantages over existing techniques by enabling smoother and faster motion. Several experiments were conducted on an industrial‐grade overhead crane to evaluate the effects of different high‐order dynamics and the effect from utilizing the sway suppression technique. The extended state observers parametrically compensate for the high‐order dynamics of the trolley, resulting in better path deviation. With the proposed controller, the percent overshoot was measured as 2.1%, compared to 16.8% without the controller. The equation used to predict path deviation in circular paths is proposed. In conclusion, the use of extended state observers significantly improves circular path deviation in overhead crane applications. The proposed equation highlights the tradeoff between path deviation and rapid motion in curved paths.
- Research Article
- 10.31763/ijrcs.v5i2.1684
- Feb 4, 2025
- International Journal of Robotics and Control Systems
- Manal Kadhim Oudah + 2 more
Large Scale Multiple Input Multiple Output (MIMO) technology is a promising technology in wireless communications, and it is already at the heart of many wireless standards. MIMO technologies provide significant performance improvements in terms of data transfer rate and reduction the interference. However, MIMO techniques face large-scale linear dynamic problems such as system stability and it will be possible to overcome this problem by tuning the proportional integral derivative (PID) in continuous systems. The aim of this paper is to design an efficient model for MIMO based on Adaptive Neural Inference System (ANFIS) controller and compare it with a traditional PID controller. and evaluated by objective function as integral time absolute error (ITAE). ANFIS is used to train fuzzy logic systems according to the hybrid learning algorithm. The training involves the fuzzy logic parameters through simulating the validation data to represent a model to know the correctness and effectiveness of the system. It is optimizes the system performance in real time, however, to avoid potential problems such as easy local optimality. In the proposed approach stability is guaranteed as the initial steady-state scheme. ITAE is combined with ANFIS to minimize the steady-state transient time responses between the high-order initial pattern and unit amplitude response. The proposed ANFIS self-tuning controller is evaluated by comparing with the conventional PID. MATLAB simulink is used to illustrate the results and demonstrate the possibility of adopting ANFIS controller. The simulation results showed that the performance of ANFIS controller is better than the PID controller in terms of settling time, undershoot and overshoot time.
- Research Article
- 10.1177/13835416241308184
- Feb 1, 2025
- International Journal of Applied Electromagnetics and Mechanics
- Qingjun Yang + 3 more
A high-speed on-off ball valve with fast transient response is a crucial hydraulic element of the clutch shift system, which is provides exact and reliable control of the shift. In the present investigation, an analysis of the transient response and thermal loss characteristics of the novel high-speed on-off ball valves (HSBVs) with a permanent magnet radial ring was conducted using the finite-element method (FEM). The impacts of permanent magnet radial ring on the transient characteristics of HSBV have been inspected. The simulation results indicated that the radiation ring changes the magnetic induction intensity inside the ball. Compared with the conventional HSBV, the transient response time of a novel HSBV with permanent magnetic ring is shortened from 3.75 ms to 1.35 ms, which is 64% shorter. Moreover, the novel HSBV improves the utilization ratio of mechanical energy from 14.6% to 27.8% and effectively reduces the iron loss from 37.3% to 28.6%. The analysis also confirmed that the increase of thickness and length of the radiation ring are positively related to the improvement of dynamic response of HSBV, which could enlarge the transformation ratio of mechanical energy and weaken the eddy current loss. The influence of coercivity of permanent magnet ring with five different materials was also analyzed. It was noticed that the HSBV with permanent magnet ring made by N45H has the fast dynamic response because of its high coercivity.
- Research Article
- 10.1021/acs.analchem.4c03696
- Jan 27, 2025
- Analytical chemistry
- Xiaoqing Wu + 5 more
Nanofluidic iontronics, including the field-effect ionic diode (FE-ID) and field-effect ionic transistor (FE-IT), represent emerging nanofluidic logic devices that have been employed in sensitive analyses. Making analyte recognitions in predefined nanofluidic devices has been verified to improve the sensitivity and selectivity using a single ionic signal, such as ionic current amplification, rectification, and Coulomb blockade. However, the detection of analytes in complex systems generally necessitates more diverse signals beyond just ionic currents. Here, we demonstrated that dual ionic signals, steady ionic switching ratio, and transient response time (ts) act as detection signals modulated by dual-split gate voltages along the nanochannel for the detection of charged analytes. With an increase in gate voltage, the switching ratio decreases in both FE-ID and FE-IT, whereas the response time exhibits an exponential increase specifically in the FE-ID. Moreover, the response time shows no significant correlation with the external transmembrane voltage in the FE-IT. These results contribute to the optimization of reconfigurable iontronics through gate voltage modulation, providing a theoretical foundation for multiple ionic signal detection.
- Research Article
- 10.1039/d5mh00293a
- Jan 1, 2025
- Materials horizons
- Eyal Stein + 6 more
Organic mixed ionic-electronic conductors (OMIECs) are extensively utilized in bioelectronics, serving as essential components for converting biological signals into electronic ones. In the realm of ambipolar OMIECs, which support the transport of both electrons and holes, recent studies have introduced a novel blend approach to simplify fabrication and enhance tunability. However, these systems remain scarce, and the urge to advance blend-based OMIEC research is still emerging. Here, we present an extensive investigation of a polymer-fullerene ambipolar system, revealing the remarkable relationship between blend microstructure and system performance. Our results demonstrate that the capacitance and mobility of the blend components exhibit synergistic enhancements, surpassing the values observed in pristine materials. Additionally, the transient response time indicates a significant advantage for blends over pristine materials. These findings are elucidated through a schematic illustration of the blend morphology, providing profound insights into the properties of this system. This comprehensive study paves the way for the improved design of ambipolar OMIECs for use in bio-interfaces, advanced sensing applications, and innovative electronic devices.
- Research Article
3
- 10.1016/j.oceaneng.2024.119149
- Sep 4, 2024
- Ocean Engineering
- Zhengyu Chen + 4 more
Torsional vibration analysis and fuzzy adaptive PID control optimization of underwater vector propulsion shaft systems
- Research Article
3
- 10.3390/app14167092
- Aug 13, 2024
- Applied Sciences
- Haoran Xue + 2 more
In this paper, a novel intelligent controller for the trajectory tracking control of a nonholonomic mobile robot with time-varying parameter uncertainty and external disturbances in the case of tire hysteresis loss is proposed. Based on tire dynamics principles, a dynamic and kinematic model of a nonholonomic mobile robot is established, and the neural network approximation model of the system’s nonlinear term caused by many coupling factors when the robot enters a roll is given. Then, in order to adaptively estimate the unknown upper bounds on the uncertainties and perturbations for each subsystem in real time, a novel adaptive law employed online as a gain parameter is designed to solve the problem of inter-system coupling and reduce the transient response time of the system with lower uncertainties. Additionally, based on improved gray wolf optimizer and fuzzy system techniques, an adaptive algorithm using the gray wolf optimizer study space as the output variable of the fuzzy system to expand the search area of the gray wolves is developed to optimize the controller parameters online. Finally, the efficacy of the proposed intelligent control scheme and the feasibility of the proposed algorithm are verified by the 2023a version of MATLAB/Simulink platform.
- Research Article
1
- 10.1145/3633457
- Jul 10, 2024
- ACM Transactions on Modeling and Computer Simulation
- Giuliano Casale + 3 more
Layered queueing networks (LQNs) are an extension of ordinary queueing networks useful to model simultaneous resource possession and stochastic call graphs in distributed systems. Existing computational algorithms for LQNs have primarily focused on mean-value analysis. However, other solution paradigms, such as normalizing constant analysis and mean-field approximation, can improve the computation of LQN mean and transient performance metrics, state probabilities, and response time distributions. Motivated by this observation, we propose the first LQN meta-solver, called LN, that allows for the dynamic selection of the performance analysis paradigm to be iteratively applied to the submodels arising from layer decomposition. We report experiments where this added flexibility helps us to reduce the LQN solution errors. We also demonstrate that the meta-solver approach eases the integration of LQNs with other formalisms, such as caching models, enabling the analysis of more general classes of layered stochastic networks. Additionally, to support the accurate evaluation of the LQN submodels, we develop novel algorithms for homogeneous queueing networks consisting of an infinite server node and a set of identical queueing stations. In particular, we propose an exact method of moment algorithms, integration techniques for normalizing constants, and a fast non-iterative mean-value analysis technique.
- Research Article
- 10.1049/tje2.12399
- Jul 1, 2024
- The Journal of Engineering
- Yutao Yang + 4 more
Abstract A temporary frequency response test and measurement error prediction method of direct current voltage transformer (DCTV) based on artificial intelligence (AI) is proposed. Firstly, the frequency characteristic of direct current (DC) side voltage of DCTV is analyzed. On this basis, a DCTV transient Frequency Response testing method based on transient alternating current (AC) & DC superposition was developed. Then, the method of voltage sudden change and phase correction is used to achieve transient process DCTV response time testing. Finally, the ant colony optimization (ACO) algorithm was improved by combining an adaptive inertia weight improvement strategy, achieving accurate prediction of the Measurement Error of DCTV. The proposed AI based DCTV transient Frequency Response testing and Measurement Error prediction method were compared and analyzed with the other three methods through simulation experiments. Compared to the other three comparison methods, the maximum transformation error in the evaluation indicators of mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE) decreased by 0.006, 0.0119, and 0.0085, respectively, while the maximum phase error decreased by 0.2794, 0.3004, and 0.2823, respectively.
- Research Article
5
- 10.1063/5.0206657
- Jul 1, 2024
- APL Photonics
- Rui He + 10 more
The monolithically integrated self-driven photoelectric detector (PD) with the light-emitting diode (LED) epitaxial structure completely relies on the built-in electric field in the multi-quantum wells region to separate the photogenerated carriers. Here, we propose a novel superlattices–electron barrier layer structure to expand the potential field region and enhance the detection capability of the integrated PD. The PD exhibits a record-breaking photo-to-dark current ratio of 5.14 × 107, responsivity of 110.3 A/W, and specific detectivity of 2.2 × 1013 Jones at 0 V bias, respectively. A clear open-eyed diagram of the monolithically integrated chip, including the PD, LED, and waveguide, is realized under a high-speed communication rate of 150 Mbps. The obtained transient response (rise/decay) time of 2.16/2.28 ns also illustrates the outstanding transient response capability of the integrated chip. The on-chip optical communication system is built to achieve the practical video signals transmission application, which is a formidable contender for the core module of future large-scale photonic integrated circuits.
- Research Article
- 10.1016/j.jfranklin.2024.107034
- Jun 26, 2024
- Journal of the Franklin Institute
- Marly T.A Cabrera + 2 more
Optimal switching boundary control for two-dimensional piecewise linear dynamical systems