Partial State Feedback Research Articles

Tracking control of robot manipulators actuated by brushless DC motors: Elimination of joint velocity measurements with a robust observer

AbstractThis work introduces an innovative robust partial state feedback controller designed for robotic manipulators actuated by brushless DC motors. The proposed controller/observer structure relies solely on actuator current and robot joint position measurements, while effectively compensating for dynamic uncertainties in both the electrical (actuator dynamics) and mechanical (robot's dynamical terms) subsystems. Specifically, a model–based robust observer, eliminating the need of joint velocity measurements, is combined with a backstepping‐type controller design. As opposed to the previous model based observers that depend on the actual model parameters, the proposed observer structure utilizes the best guest estimates of the system parameters supported with a robust compensation term. This approach eliminates the need for precise knowledge of system parameters of the observer design which is a significant improvement over most of the previous results. This approach ensures the semi‐global, uniformly ultimately bounded joint tracking error signal. The overall stability of the closed‐loop system is affirmed through Lyapunov‐based arguments. Experimental studies conducted on an in‐house‐built two‐link robotic manipulator, actuated by brushless DC motors, are presented to demonstrate the effectiveness and feasibility of the proposed method.

Fixed-time stabilization for lower-triangular nonlinear systems under the p-normal form

This article investigates the fixed-time stabilization (FTS) problem for lower-triangular nonlinear systems under the [Formula: see text]-normal form. Under suitable assumptions condition of the system’s nonlinearities, a novel fixed-time partial-state feedback (PSF) control law is designed using backstepping design method and adding a power integrator (API) technique. With the help of one appropriate Lyapunov function, it is shown that the partial-state of the corresponding closed-loop system is fixed-time stable. Numerical simulation is given to illustrate the potency of the suggested continuous partial-sate feedback controller.

A Model-Following Control Approach to Peaking Attenuation in High-Gain Partial State Feedback for Nonlinear Systems

We consider the model-following control (MFC) scheme for a class of nonlinear minimumphase systems in Byrnes-Isidori form using the nonlinear model in the model control loop (MCL). For the control design we apply partial state feedback in the process control loop (PCL). In particular we consider a high-gain feedback of the external state in the PCL to stabilise the system globally. For the proposed MFC design the typical peaking phenomenon of the high-gain feedback can be overcome if a sufficiently accurate estimate of the initial process state is available. We further establish that the control effort of the proposed MFC design is guaranteed less than that of a comparable stabilising high-gain design using a single-loop feedback only. We demonstrate the design capability of peaking attenuation by a numerical example.

Accurate voltage regulation for a DC microgrid using nonlinear state feedback controller

AbstractThe high penetration of distributed generation systems poses challenges in effectively managing both DC bus voltage and power‐sharing in DC microgrids (MGs). To ensure precise voltage regulation across various distributed generation systems and maintain overall system stability, this paper studies the modelling and control of an islanded DC MG described by a set of nonlinear‐nonaffine differential equations. In the proposed DC MG, a battery storage, a photovoltaic (PV) power plant, and a back‐end power converter with DC loads have been connected to a common DC bus. First, a dynamic model of a DC MG was developed. Then, to find the maximum power point of solar PV, a straightforward method based on an artificial neural net is employed. Afterward, a nonlinear local state feedback controller through output regulation theory is applied to achieve voltage stability, overcoming the drawbacks of droop‐based techniques. Moreover, partial state feedback capability simplifies controller design. To verify the effectiveness of the proposed approach, various scenarios, including sudden load variation, illumination change, and changes in the MG configuration, have been examined. Finally, numerical studies were carried out in a simulation environment to demonstrate the superiority of the proposed nonlinear control scheme over constant feedback control.

Robust Stabilization of Time-Varying Nonlinear Systems With Time-Varying Delays: A Fully Actuated System Approach.

A general time-varying nonlinear uncertain system with time-varying delays is proposed, which is composed of two subsystems: one is an uncertain fully actuated subsystem representing the controllable part in the system, the other is an isolated globally uniformly asymptotically (GUA) stable autonomous subsystem which represents the uncontrollable part in the system. Both the single-order fully actuated system (FAS) and the multiorder FAS representations of the controllable subsystem are introduced. The problem of robust stabilization of such a compound system with full-state feedback can be converted into an input-to-state GUA stabilization problem of the fully actuated subsystem, which is solved for both types of single- and multiorder FASs with very general assumptions on the uncertain perturbed functions. Under certain conditions, the solution reduces to that for robust stabilization with partial-state feedback, and naturally reduce to that for robust stabilization of FASs. Two illustrative examples demonstrate both the effect and the application procedure of the proposed robust stabilization approach.

Encrypted distributed model predictive control with state estimation for nonlinear processes

This research focuses on encrypted distributed control architectures, aimed at enhancing the operational safety, cybersecurity and computational efficiency of large-scale nonlinear systems, where only partial state measurements are available. In this setup, a distributed model predictive controller (DMPC) is utilized to partition the process into multiple subsystems, each controlled by a distinct Lyapunov-based MPC (LMPC). To consider the interactions among different subsystems, each controller receives and shares with the other controllers control inputs computed for its particular subsystem. As full state feedback is not available, we integrate an extended Luenberger observer with each LMPC, initializing the LMPC model with complete state estimate information provided by the observer. Furthermore, to enhance cybersecurity, wireless signals received and transmitted by the controllers are encrypted. Guidelines are established to implement this proposed control structure in any large-scale nonlinear chemical process network. Simulation results, conducted on a specific nonlinear chemical process network, demonstrate the effective closed-loop performance of the encrypted DMPC with state estimation, utilizing partial state feedback with sensor noise. This is followed by a comprehensive comparison of the closed-loop performance, control input computational time, and suitability of encrypted centralized, decentralized, and distributed MPC frameworks.

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.

Motor Current Feedback-Only Active Damping Controller With High Robustness for LCL-Equipped High-Speed PMSM

This paper proposes a flexible active damping method for LCL-equipped high-speed permanent magnet synchronous motor. The damping ratio of the LCL resonance can be freely designed by the proposed high-order partial-state (virtual output voltage and the capacitor current) feedback. Moreover, a coefficient selection method is developed to complete the design of the damping system quickly and efficiently. As the main contribution, the proposal can easily apply to single-sensor (motor current feedback-only) applications to eliminate the sensor of the capacitor current with high parameter robustness. The experimental results of a 72kr/min test motor verify the stability and robustness of the proposed control strategy.

Model reference adaptive disturbance rejection control using partial-state feedback

In this paper, we propose a partial-state feedback model reference adaptive control strategy for uncertain linear time-invariant systems with unmatched disturbances. The new control design is based on parametrization and observer technique. The control structure and output matching of nominal partial-state feedback disturbance rejection are presented. The adaptive partial-state feedback disturbance rejection scheme guarantees closed-loop system stability and asymptotic output tracking. A simulation example indicates the effectiveness of the presented adaptive partial-state feedback control design.

Positive effects of time delays on the stability of switched control systems with partial state feedback information

In this paper, a novel state-dependent switching controller with delayed positive partial state feedback is proposed to stabilise a controlled system with insufficient state information. At first, the controlled system is converted to a single-degree-of-freedom vibrational system by using an invertible transform and a second-order Taylor approximation for the time delay term. Then, appropriate control gain parameters and a state-dependent switching rule are designed via the physical meaning of the resulting vibrational system. By combining the advantages of delayed positive position feedback with the state-dependent switching mechanism, we find that the time delay can considerably improve the asymptotic stability of the controlled system. Finally, three numerical examples show that the proposed controller is effective and that time delay indeed plays a prominent positive role in switched control systems.

Partial State Feedback Adaptive Disturbance Rejection Control

A unified disturbance rejection problem based on model reference adaptive control (MRAC) technique is addressed. When the full-state vector is not operational in feedback, we use partial-state signal y(t) to design a disturbance rejection controller. The parametrization and disturbance compensation techniques are necessary for designing adaptive control strategy to deal with systems uncertainties and unknown disturbances. This scheme guarantees the desired system performances, including closed-loop system stability as well as asymptotic output tracking. The proof progress of system stability is elaborated.

Global Stabilization for Stochastic Continuous Cascade Nonlinear Systems Subject to SISS Inverse Dynamics and Time-Delay: A Dynamic Gain Approach

This article is devoted to the global continuous control for stochastic low-order cascade nonlinear systems with time-varying delay and stochastic inverse dynamics. Compared with existing results, the nature of only continuous, but nonsmooth, is unfolded since the power of the stochastic cascade system is of low order; and all the traditional growth conditions on unknown drift and diffusion nonlinearities and local Lipschitz condition are quitted, which largely extends the scope of application. Combining with stochastic input-to-state stability, two new lemmas are developed with rigorous proofs to deal with uncertain nonlinear terms and unmeasurable stochastic inverse dynamics. A continuous control scheme consisting of a delay-independent partial state feedback controller and a serial of dynamic update laws is proposed to guarantee the globally asymptotical stability of the closed-loop system.

Partial-state feedback adaptive stabilization for a class of output-constrained nonlinear cascaded systems

This paper presents a robust adaptive stabilizing control scheme via partial-state feedback for a class of nonlinear cascaded systems with a time-varying output constraint. Different from the existing achievements, the nonlinear parameterization and unmeasured zero-dynamics are considered in this paper. The notion of input-to-state stability (ISS) and ISS-Lyapunov function are used to describe the zero-dynamics. The time-varying barrier Lyapunov function (TVBLF) is employed to ensure the output constraint satisfaction and the changing supply rates technique is used to deal with the unknown cascaded zero-dynamic states. It is shown that all the signals in the closed-loop system are bounded, and the asymptotic stabilization is achieved without violation of the output constraint. The performance of the proposed control scheme is illustrated through a simulation example.

Composite‐observer‐based adaptive robust control of electrical‐optical gyro‐stabilized platform with largely unknown modeling uncertainties and partial state feedback

AbstractIn this article, a desired compensation version of the output feedback controller (DOFCESO) without using velocity measurement signal is proposed for precise tracking control of the three‐axis electrical‐optical gyro‐stabilized platform in the presence of largely unknown matched and mismatched modeling uncertainties. The proposed controller takes into account not only the system parametric deviations as well as the unmeasurable signal and external disturbances. To further handle the unmeasurable signal and the external disturbances, the composite extended state observer and nonlinear disturbance observer are constructed simultaneously via integrating adaptive nonlinear feedback tracking control design. To address the uncertainties arising from parametric deviations and external disturbances, the parameter adaptation mechanism is incorporated into the composite observer design to estimates of both the unmeasurable signal and the mismatched disturbance in the adaptive backstepping design. The tracking differentiator design is introduced here to estimate the derivative of the virtual control, leading to a much simpler control structure and reduced implementation costs. Furthermore, the proposed controller guarantees final tracking accuracy in the presence of time‐invariant modeling uncertainties and preserves the performance results of both control methods while overcoming their practical performance limitations. Extensive comparative experimental results are obtained to verify the high‐performance nature of the proposed control strategy.

Partial state feedback sliding mode control for double-pendulum overhead cranes with unknown disturbances

In this paper, a novel sliding mode controller which requires partial state feedback is proposed for double-pendulum overhead cranes subject to unknown payload parameters and unknown external disturbances. Firstly, it is theoretically proved that the hook and payload tend to their respective equilibrium points concurrently. Secondly, a decoupling transformation is performed on the original nonlinear dynamics of double-pendulum overhead cranes. The novel sliding mode controller that does not require the prior information and motion signals of the payload is designed based on the decoupled nonlinear dynamics. Then, the asymptotic stability of the equilibrium point of double-pendulum overhead cranes is proved by rigorous analysis. Finally, several simulations are conducted to validate the effectiveness and robustness of the proposed controller.

Adaptive optimal output regulation of linear discrete-time systems based on event-triggered output-feedback

This paper presents novel event-triggered control approaches to solve the adaptive optimal output regulation problem for a class of linear discrete-time systems. Different from most existing research on output regulation problems, the developed adaptive optimal control approaches are based on (1) output-feedback instead of full-state or partial-state feedback, (2) adaptive dynamic programming (ADP) which provides approximate solutions of the optimal control problem without requiring the precise knowledge of the plant dynamics, and (3) an event-triggering mechanism that reduces the communication between the controller and the plant. It is shown that the system in closed-loop with the developed controllers is asymptotically stable at an equilibrium of interest, and the tracking errors asymptotically converge to zero. Moreover, the suboptimality of the closed-loop system is directly determined by the relative threshold, which is a ratio between the triggering threshold and the actual state. A numerical simulation example is employed to verify the effectiveness of the proposed methodologies.

Effect of delayed resonator on the vibration reduction performance of vehicle active seat suspension

The combination of dynamic vibration absorber and partial state feedback with time-delay is called delayed resonator. In order to suppress the seat vibration caused by uneven road surface and improve ride comfort, the delayed resonator is applied to the seat suspension to realize active control of the seat suspension system. The dynamic model of the half-vehicle suspension system is established, and the time-delay differential equation of the system under external excitation is solved by the precise integration method. The root mean square of the time-domain vibration response of seat displacement, seat acceleration and vehicle acceleration are selected as the objective function. Then, the optimal time-delay control parameters are obtained by particle swarm optimization algorithm. The frequency sweeping method is used to obtain the critical time-delay value and time-delay stable interval of the system. Finally, an active seat suspension model with delayed resonator is established for numerical simulation. The results show that the delayed resonator can greatly suppress the seat vibration response regardless of the road simple harmonic excitation or random excitation. Compared with dynamic vibration absorber, it has a better vibration absorption effect and a wider vibration reduction frequency band.

A Robust Vector Current Controller with Negative-Sequence Current Capability for Grid-Connected Inverters

This paper presents a vector current controller (in the synchronous reference, or the dq, frame) with negative-sequence current injection capability for three-phase grid-connected converters. This capability is desired for the operation of the converter during unbalanced conditions and also for a certain type of islanding detection. The proposed controller first determines the double-frequency current references and then uses a sixth-order two-input two-output proportional-integral-resonance (PIR) structure, which is optimally designed. Compared with the existing similar approaches, the proposed controller has a simpler structure and more robust performance, e.g., against system parameter uncertainties and weak grid conditions. The proposed controller is developed for converters with both the L-type and LCL-type filters. For the LCL-type converter, a suboptimal partial state feedback control is also proposed to achieve robust stability and active damping of resonance poles without requiring additional sensors. Detailed experimental results are presented to illustrate the properties and performances of the proposed controller.

Dynamic Analysis and Degenerate Hopf Bifurcation-Based Feedback Control of a Conservative Chaotic System and Its Circuit Simulation

A novel conservative chaotic system with no equilibrium is investigated in this study. Various dynamics such as the conservativeness, coexistence, symmetry, and invariance are presented. Furthermore, a partial-state feedback control scheme is proposed, and the stable domain of control parameters is analyzed based on the degenerate Hopf bifurcation. In order to verify the numerical simulation analysis, an analog circuit is designed. The simulation results show that the output of the analog circuit system can reproduce the numerical simulation results and verify the correctness of the theoretical analysis.

Partial-state feedback adaptive stabilization for a class of nonlinear systems with uncertainties

This paper studies the adaptive asymptotically stabilizing control problem for a class of uncertain nonlinear systems by the partial-state feedback. The input-to-state stability (ISS) is used to describe the dynamic uncertainties, and a novel Nussbaum function is resorted to counteract the unknown identical control directions. The damping terms with the estimates of unknown disturbance bounds are inserted in control design to handle the nonvanishing external disturbances. It can be seen that all signals in closed-loop are bounded and the system states converge to zero asymptotically in spite of the uncertainties. Finally, a simulation example is introduced to show the effectiveness of the presented control scheme.