Full State Feedback Control Research Articles

Design and Simulation of an Automatic Alignment System for Ship Multi-Support Shafting

The current shafting alignment process primarily relies on manual adjustments, resulting in low efficiency and limited precision. This study designs an automatic alignment system for multi-support shafting to improve alignment efficiency and accuracy, advancing the development of intelligent systems. The overall design of the automatic alignment system is proposed, including the establishment of shafting and actuator models. The alignment performance of two control strategies under different shafting deviations is validated through simulations. The results indicate that both the full-state feedback control strategy and the model predictive control strategy can regulate bearing load errors to within 1%. Compared to manual alignment, both strategies demonstrate significantly higher efficiency. The proposed automatic alignment system is feasible and lays a foundation for the development of high-precision shafting alignment systems.

Real‐Time Implementation of Unknown Input Observer‐Based State and Unknown Disturbance Estimation for Series Active Filters

ABSTRACTSeries active filter (SAF) is generally utilized in compensating harmonic voltage source‐type loads. In this paper, a combined action of controller and observer is proposed for SAF. Full state feedback (SFB) and linear quadratic regulator (LQR) controllers are posited in order to estimate states, and fault. SFB utilizes the pole placement method, whereas LQR utilizes the tuning of matrices by Bryson's rule. Luenberger observer (LO), proportional–integral observer (PIO), and unknown input observer (UIO) were also designed. The efficacy of this scheme is illustrated through the simulations, in the presence of faults. The state dynamics of SFB‐ and LQR‐based control of SAF with LO, PIO, and UIO in different faulty cases are compared. It can be clearly seen through simulations that the state dynamic response of LQR‐based control of SAF is faster when compared to SFB‐based control of SAF in both cases. Further, LO and PIO established a steady‐state error between the actual state and its estimate, with reference to desired input, in the presence of a fault. UIO perfectly tracked the desired input, even in the presence of various unknown fault, when compared to LO and PIO. Furthermore, UIO also estimates the unknown faults better when compared to PIO. Finally, in a dynamic operating scenario, the effectiveness of the suggested control strategy has been assessed and verified using MATLAB/SIMULINK and the output of a real‐time simulator (OPAL‐RT OP4510).

Eksik Tahrikli Döner Ters Sarkaç Sisteminin Yukarı Yükseltilmesi için Enerji Tabanlı Doğrusal Olmayan Kontrol Algoritması ve Deneysel Doğrulaması

Bu çalışmada, döner ters sarkaç sistemi hareketli koluyla sınırlı bir bölge içinde, salınımı kontrol edilerek ve sarkaç enerjisi artırılarak, kararlı denge noktasından kararsız denge noktasına çıkarılması hedeflenmektedir. Döner ters sarkaç sisteminin doğrusal olmayan modeli ve denge noktalarındaki doğrusal modelleri verildikten sonra sarkaç yukarı yükseltme algoritması tanıtılmaktadır. Yukarı yükseltme algoritması, sarkaç salınırken belli noktalarda kol yardımıyla sarkaca enerji yüklemesine dayanmaktadır. Burada kol ivmelendirilmesi sabit bir ivme ile hareket ettirilmektedir. Yukarı yükseltme işlemindeki algoritma, sarkacın hızının en fazla olduğu yere yani kararlı denge noktasına ilerlerken ve periyodunu tamamlarken devreye girmektedir. Bu analizler hesaplanmış sınırlar dikkate alınarak yapılmaktadır. Sarkacın yukarı yükselmesi gerçekleştiğinde doğrusal model üzerinden elde edilmiş temel bir tam durum geri beslemeli kontrolcü devreye girmektedir ve sarkacı kararsız denge noktasında tutmaktadır. Böylece, anahtarlamalı bir kontrol yapısı elde edilmektedir. Önerilen kontrol algoritmasının doğrulaması için önerilen algoritma bir döner sarkacı üzerinde gerçek zamanlı olarak test edilmiştir. Farklı kol ivmelendirme değerleri ile elde edilen karşılaştırmalı sonuçlar sunulmuştur. Kol ivmesi ±32 rad/s2’den ±64 rad/s2’ye çıkarıldığında sarkacın yukarı yükselme süresi yaklaşık 9 s’den 5 s’ye düşmektedir. Bu sonuçlar, önerilen algoritmanın deneysel başarısını göstermektedir.

Independent Pitch Adaptive Control of Large Wind Turbines Using State Feedback and Disturbance Accommodating Control

Wind turbines experience significant unbalanced loads during operation, exacerbated by external disturbances that challenge the stability of the pitch control system and affect output power. This paper proposes an independent pitch adaptive control strategy integrating state feedback and disturbance accommodating control (DAC). Initially, nonlinear wind turbine dynamics are globally linearized, and DAC is applied to mitigate the impact of wind disturbances dynamically. Subsequently, the entire range of wind speeds is segmented, and controllers are individually designed to optimize gain settings according to specific control objectives at each wind speed interval. Scheduling parameters such as collective pitch angle and tower fore-aft displacement are identified and trained using Radial Basis Function Neural Networks (RBFNN). Finally, based on the output gain values determined by RBFNN, the full-state feedback controller group is adaptively adjusted, and the optimal controller is selected for the final output. Simulations conducted on the NREL 5MW reference wind turbine model using FAST and Simulink demonstrate that compared to the ROSCO controller, the proposed strategy ensures smoother output power and effectively reduces blade and tower loads, thereby extending the turbine’s operational lifespan.

Improving the Step Response of Flexible Systems in the Presence of Real Nonminimum Phase Zeros

Abstract It is well known that real nonminimum phase (RNMP) zeros impose a tradeoff between the settling time and undershoot in the step response of flexible systems. Existing methods to alleviate this tradeoff predominantly rely on various advanced control strategies without delving into a broader mechatronic approach that combines physical system and control system design. To address this gap, this article proposes a proportional viscous damping-based physical system design in combination with feedback control and prefilter design. First, the effect of proportional viscous damping on RNMP zeros of flexible systems is established to propose a damping strategy that pushes all the RNMP zeros further away from the imaginary axis. Then, a step-by-step mechatronic system design process is presented to apply this damping strategy along with a full-state feedback control strategy and prefilter to a multi-degree-of-freedom (DoF) flexible system. The application of this design process yields simultaneous improvement in the settling time and undershoot in the step response of this flexible system.

Utilization and performance comparison of several HESSs with cascade optimal-FOD controller for multi-area multi-source power system under deregulated environment

Electric power system network is evolving rapidly towards a more flexible, robust and secured interconnected network which can provide better power quality within a competitive environment commonly known as deregulated power system (DPS). For safeguarding DPS, energy storage systems (ESSs) and an efficient control method are required to maintain equilibrium between load demand and generated power known as automatic generation control (AGC). This study highlights an attempt of performance comparison of several hybrid ESSs (HESSs) for AGC of multi-area multi-source power system under deregulated scenario. The considered system comprises of thermal, hydro and gas (THG) generating units in each area of a two-area DPS. A cascade optimal controller-fractional order derivative (COC-FOD) is suggested for AGC performance advancement and its performance is compared with optimal controller (OC). A nature inspired salp swarm algorithm (SSA) is utilized to optimise secondary FOD controller gains while primary OC is designed via full state feedback control approach. The time domain analysis and bode plot reveal the eminence of COC-FOD over OC by returning 66 % lower value of cost function, 24 % lower undershoot, 98 % lower overshoot, at least 24 % lesser rise time for area frequency deviation, and 30 % greater stability margins with comparable settling time and lesser number of oscillations. The performances of various HESSs like ultra-capacitor (UC) + redox flow battery (RFB), superconducting magnetic energy storage (SMES) + RFB and flywheel energy storage (FES) + RFB in the attendance of OC and COC-FOD controller are compared and performance of COC-FOD in the presence of SMES+RFB is found superior to other HESS combinations by giving 75 % lesser value of cost function and at least 43 % lesser undershoot for area frequency deviation compared to the scenario where COC-FOD is simulated without ESSs. To present a more realistic scenario, system nonlinearities are considered. Finally, COC-FOD controller proved its resilience and efficacy by providing satisfactory stabilized performance under wide variations in the system parameters.

Observer based pitch control for load mitigation and power regulation of floating offshore wind turbines

Abstract Most commercial wind turbines use proportional-integral (PI) collective blade-pitch control to regulate rotor speed in the above-rated wind speed regime. A significant drawback of this type of controller is that it assumes that the blades have identical structural properties and are subject to similar aerodynamic loads, which is seldom the case. Also, these controllers are designed to regulate the rotor speed and are not designed for structural vibration/load reduction. However, it is well known that blade pitch control can reduce structural loads on wind turbines. This opens up the possibility of designing controllers that use existing actuators and sensors like the blade pitch actuators to reduce structural loads/vibrations while maintaining the required rotor speed. Recent studies have investigated individual blade pitch control (IPC) to address these shortcomings. However, the vast majority of studies published in the literature depend on the availability of state measurement. Although sensors are commonly placed on all wind turbines, and some information is readily available, the measurement required by the typical state-feedback controllers is usually not available. Displacements and velocities of the blade, the tower and the floating platform are difficult to measure. This paper develops an observer-based individual blade pitch controller for load mitigation and power regulation of floating offshore wind turbines. We propose to use a Kalman filter to estimate the state from the accelerometer and strain gauge measurement for use in the state-feedback controller. The state-feedback controller was proposed previously by the authors that showed excellent performance. This paper extends the capability of the state-feedback controller by designing an observer (Kalman filter) to estimate the state from limited measurements. The proposed observer based controller is compared against a baseline proportional integral collective blade pitch controller and full state-feedback controllers to evaluate its performance. Numerical results show that the proposed output feedback controller offers performance improvements over the baseline controller, similar to the full state-feedback controller.

Optimal quadratic full state feedback control of nonlinear affine systems

The solution of the optimal quadratic full-state feedback closed-loop control of a nonlinear affine system problem is presented and solved. This solution uses the State-Dependent Coefficient (SDC) form of a nonlinear system and the Calculus of Variations. Further, it is shown that this solution enables the computation of the value function associated with the respective Hamilton-Jacobi-Bellman equation thus satisfying the necessary and sufficient conditions for optimality. The use of the SDC form representation in the optimal solution for a nonlinear affine system results in an explicit and exact full-state feedback closed-loop control implementation as opposed to the existing open-loop solutions of the optimal control. This solution, like for the linear case, is non-causal and thus cannot be solved in real-time. The closed-loop application involves precomputing a time-varying full-state feedback matrix. The optimal feedback is a linear combination of the current state. The time-varying gain matrix is the backward solution of a non-symmetric matrix Riccati equation. Conditions for the stability of the full-state feedback are presented. This new representation of the optimal solution gives a well-understandable algorithm that enables implementation in the closed loop of the optimal feedback control of a non-linear system which is not possible with the existing optimal open loop representations.

Design of Static Output Feedback Suspension Controllers for Ride Comfort Improvement and Motion Sickness Reduction

This paper presents a method to design a static output feedback active suspension controller for ride comfort improvement and motion sickness reduction in a real vehicle system. Full-state feedback controller has shown good performance for active suspension control. However, it requires a lot of states to be measured, which is very difficult in real vehicles. To avoid this problem, a static output feedback (SOF) controller is adopted in this paper. This controller requires only three sensor outputs, vertical velocity, roll and pitch rates, which are relatively easy to measure in real vehicles. Three types of SOF controller are proposed and optimized with linear quadratic optimal control and the simulation optimization method. Two of these controllers have only three gains to be tuned, which are much smaller than those of full-state feedback. To validate the performance of the proposed SOF controllers, a simulation is carried out on a vehicle simulation package. From the results, the proposed SOF controllers are quite good at improving ride comfort and reducing motion sickness.

The chemostat reactor: A stability analysis and model predictive control

This contribution develops the model predictive control for an unstable chemostat reactor. Initially, we analyze the system’s model — a nonlinear first-order hyperbolic partial integro-differential equation (PIDE) — and carry the model linearization around an unstable operating condition. Employing the structure-preserving Cayley–Tustin transformation, we obtain a discrete-time model representation of the continuous model. Subsequently, we solve the operator Ricatti equations in the discrete-time setting to derive a full state feedback controller that stabilizes the closed-loop and design a Luenberger observer for state reconstruction given the system output measures. Finally, we formulate a dual-mode MPC ensuring constraint satisfaction and optimality, integrating the gain-based unconstrained full-state feedback optimal control obtained from the Ricatti equation. This dual-mode strategy describes an optimization problem where the predictive controller acts only if constraints become active within the control horizon. Simulation studies validate the controller performance, where the MPC only takes action if the constraints are predicted to be active within the control horizon while also guaranteeing closed-loop stabilization under only output feedback. This type of controller can be easily implemented with other control strategies and significantly decreases the computational costs of solving the optimal control problems when compared to other MPC approaches.

Design of Active Suspension Controller for Ride Comfort Enhancement and Motion Sickness Mitigation

This paper presents a method for designing an active suspension controller for ride comfort enhancement and motion sickness mitigation. For this, it is necessary to design an active suspension controller, which aims to reduce the vertical acceleration and pitch rate of a sprung mass in a vehicle. A half-car vehicle model was selected. For the controller design, a static output feedback (SOF) control was selected instead of a full-state feedback control because it is hard to measure all state variables in real vehicles. With the available signals, three types of SOF controller were proposed. To determine the gains of the SOF controllers, a linear quadratic optimal control methodology and a simulation-based optimization method were adopted. To validate the proposed method, a simulation was carried out using vehicle simulation software. The simulation results show that the proposed method is quite effective for ride comfort enhancement and motion sickness mitigation.

Design and Control of the Rehab-Exos, a Joint Torque-Controlled Upper Limb Exoskeleton

This work presents the design of the Rehab-Exos, a novel upper limb exoskeleton designed for rehabilitation purposes. It is equipped with high-reduction-ratio actuators and compact elastic joints to obtain torque sensors based on strain gauges. In this study, we address the torque sensor performances and the design aspects that could cause unwanted non-axial moment load crosstalk. Moreover, a new full-state feedback torque controller is designed by modeling the multi-DOF, non-linear system dynamics and providing compensation for non-linear effects such as friction and gravity. To assess the proposed upper limb exoskeleton in terms of both control system performances and mechanical structure validation, the full-state feedback controller was compared with two other benchmark-state feedback controllers in both a transparency test—ten subjects, two reference speeds—and a haptic rendering evaluation. Both of the experiments were representative of the intended purpose of the device, i.e., physical interaction with patients affected by limited motion skills. In all experimental conditions, our proposed joint torque controller achieved higher performances, providing transparency to the joints and asserting the feasibility of the exoskeleton for assistive applications.

Trajectory control of Mars probe based on fuzzy variable parameter theory

The longitudinal dynamics model of the Mars probe's entry phase is a time-varying and nonlinear model. The study of time-varying nonlinear systems is complex. When the system is processed with a T–S fuzzy system, there is a limitation that the number of fuzzy rules increases dramatically. In this paper, the dynamic model of the Mars probe in the entry phase is treated with a fuzzy variable parameter system to overcome this shortcoming. By the process of local linearisation, a fuzzy variable parameter model of the Mars probe is established according to the time-varying characteristics of atmospheric density. Next, the full-state feedback and dynamic output feedback gain-scheduling controllers are designed based on the quadratic Lyapunov stability theory. Finally, Simulink simulation verifies that the fuzzy variable parameter system of the Mars probe's entry phase can be asymptotically stabilised by the designed controllers.

Output regulation and tracking for linear ODE-hyperbolic PDE–ODE systems

This paper proposes a constructive solution to the output regulation — output tracking problem for a general class of interconnected systems. The class of systems under consideration consists of a linear 2 × 2 hyperbolic Partial Differential Equations (PDE) system coupled at both ends with Ordinary Differential Equations (ODEs). The proximal ODE system, which represents actuator dynamics, is actuated. Colocated measurements are available. The distal ODE system represents the load dynamics. The control objective is to ensure, in the presence of a disturbance signal (regulation problem), that a virtual output exponentially converges to zero. By doing so, we can ensure that a state component of the distal ODE state robustly converges towards a known reference trajectory (output tracking problem) even in the presence of a disturbance with a known structure. The proposed approach combines the backstepping methodology and frequency analysis techniques. We first map the original system to a simpler target system using an invertible integral change of coordinates. From there, we design an adequate full-state feedback controller in the frequency domain. Following a similar approach, we propose a state observer that estimates the state and reconstructs the disturbance from the available measurement. Combining the full-state feedback controller with the state estimation results in a dynamic output-feedback control law. Finally, existing filtering techniques guarantee the closed-loop system robustness properties.

DC-link Voltage Control Using Battery-side Controller in a Hybrid System

This work aims to model the PV-Battery hybrid system as well as design a controller used to stabilize the voltage at the DC-link for the load. It is intended to make the voltage between the battery and PV system stable, or it can be said that the voltage at the load becomes stable. The input system used is battery current and PV current is considered as a disturbance because of its characteristics that cannot be controlled when generating maximum power. Therefore, a full order state feedback controller with integrator is designed to reduce the steady state error. In addition, an algorithm is needed to estimate the PV current and at the same time reduce sensor utilization. This work utilizes Disturbance Observer to estimate these parameters as well as disturbance rejection. To verify the proposed system, there are three scenarios. The first scenario tests the system with constant PV load and current. The second scenario tests the system with varying PV current, and finally tests the system with varying load and current. From the scenarios, the system performed well with output voltage RMSE values equal to 0.003 in the first scenario, 0.4 in the second scenario, and 0.481 in the third scenario.

State-feedback control of a grid-tied cascaded brushless doubly-fed induction machine

The cascaded brushless doubly-fed induction machine (CBDFIM) is the developed version of a classic slip-ring doubly-fed induction machine (DFIM). Deprived of the main DFIM disadvantage - the slip-ring connection, the cascaded brushless doubly-fed induction machine has better durability and lower maintenance costs. Structurally it is realized by the presence of control stator and main stator working with a common rotor shaft. However, this type of electrical machine is characterized by much higher control inertia and larger dq control axis coupling, in comparison to DFIM. This fact makes problematic obtainment good dynamic performance and stability of the controlled system for classic control schemes. In the paper presented cascaded brushless doubly-fed induction machine state-feedback control schemes, based on CBDFIM full and reduced state-space model. Proposed algorithms allow control of CBDFIM generated active and reactive power components in a grid-tied operation and offer great possibilities of obtaining the desired dynamics parameters and stability of the controlled system. The main paper goal is to prove that reduced order state feedback control can be equally effective than full state feedback control in terms of obtained closed loop system dynamics and reduces influence of the couplings between the controlled variables.

Lyapunov stability of cable-driven manipulators with synthetic fibre cables regulated by non-linear full-state feedback controller

Robotic manipulators provide advantages in working environments regarding efficiency and safety, which is further increased in the case of elastic joint manipulators, whose mechanical compliance reduces the energy involved in collisions with workers. Cable-driven manipulators are elastic joint manipulators particularly suitable for industrial inspection thanks to the relocation of actuators outside hostile environments, increasing the manipulator payload-to-weight ratio. Recently, synthetic fibre cables are substituting steel cables due to their better-performing mechanical properties, but their visco-elastic behaviour must be compensated in the controller design. The key novelty of this work is using the four elements model, which includes the viscous behaviour, to design a non-linear full-state feedback controller for cable-driven manipulators. Furthermore, the mathematical proof of the closed-loop Lyapunov stability is provided.

Evaluation and Comparison of SEA Torque Controllers in a Unified Framework

Series elastic actuators (SEA) with their inherent compliance offer a safe torque source for robots that are interacting with various environments, including humans. These applications have high requirements for the SEA torque controllers, both in the torque response as well as interaction behavior with its environment. To differentiate state of the art torque controllers, this work introduces a unifying theoretical and experimental framework that compares controllers based on their torque transfer behavior, their apparent impedance behavior, and especially the passivity of the apparent impedance (i.e., their interaction stability) as well as their sensitivity to sensor noise. We compare classical SEA control approaches such as cascaded PID controllers and full state feedback controllers with advanced controllers using disturbance observers, acceleration feedback and adaptation rules. Simulations and experiments demonstrate the trade-off between stable interactions, high bandwidths and low noise levels. Based on these trade-offs, an application-specific controller can be designed and tuned, based on desired interaction with the respective environment.

Stability-assured design of a full state feedback controller for a three-phase grid-connected converter using disk margin analysis

The paper proposes a tuning procedure for a multioscillatory current controller in a three-phase three-wire grid connected converter operating under distorted voltage conditions. The control system should provide high quality sinusoidal currents. This is achieved by implementing internal models of expected disturbances — multioscillatory terms. Tuning of such systems is challenging if the objective is to guarantee a certain level of stability margins. The multiloop disk margin analysis may be a perfect candidate solution. This analysis combined with a global optimization produces controller gains that can be transferred to the physical system. The paper provides the first complete experimental verification of the multioscillatory full state feedback grid current control system with a designer specified stability margin in the form of disk radius.

Solid Boundary Output Feedback Control of the Stefan Problem: The Enthalpy Approach.

By taking enthalpy-an internal energy of a diffusion-type system-as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.