Full State Feedback Research Articles

Policy Iteration-Based Learning Design for Linear Continuous-Time Systems Under Initial Stabilizing OPFB Policy.

Policy iteration (PI), an iterative method in reinforcement learning, has the merit of interactions with a little-known environment to learn a decision law through policy evaluation and improvement. However, the existing PI-based results for output-feedback (OPFB) continuous-time systems relied heavily on an initial stabilizing full state-feedback (FSFB) policy. It thus raises the question of violating the OPFB principle. This article addresses such a question and establishes the PI under an initial stabilizing OPFB policy. We prove that an off-policy Bellman equation can transform any OPFB policy into an FSFB policy. Based on this transformation property, we revise the traditional PI by appending an additional iteration, which turns out to be efficient in approximating the optimal control under the initial OPFB policy. We show the effectiveness of the proposed learning methods through theoretical analysis and a case study.

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).

Energy-saving cruise control method for heavy-duty transport vehicle based on pump-valve coordinated drive

In order to realize the dual-goal of the improvement in the cruise performance and fuel economy of the heavy-duty transport vehicle (HDTV) for the transfer of the prefabricated box-girder in the construction of high-speed railway, a pump-valve parallel coordinated drive scheme is designed on the basis of the hydrostatic drive system of the HDTV, which combines the load-sensing valve control system and hydrostatic pump control system. Furthermore, the pump-valve coordinated controller (PVC) is also proposed to ensure the cooperation of the two systems, which adopts power following control strategy to control engine speed, the pump and motor displacement respectively, thus achieving the rough adjustment of the cruise velocity. The linear quadratic regulator (LQR) based on the full-state closed-loop feedback is introduced in PVC to control the proportional direction-valve (EPDV) and compensate for the velocity errors, thus realizing the fine adjustment of cruise velocity. A semi-physical experimental test-platform for the HDTV is established to conduct contrast tests between the rule-based controller (RBC) and the proposed PVC under different operating conditions. The results indicate that the PVC effectively reduces the velocity error, the total error is decreased by 80.6% and that of the maximum error is 43.4% under empty-load conditions, and under heavy load conditions, the total error is lowered by 82.1% and that of the maximum error is 46.8%. Moreover, the PVC also brings down the fuel consumption rate of the HDTV, with a maximum reduction of 27.6% and a minimum of 11.4%.

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.

Mean-square exponential stabilization of mixed-autonomy traffic PDE system

Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and Autonomous Vehicles (AVs) coexist on the road has gained increasing attention over the recent decades. This paper addresses the boundary stabilization problem for mixed traffic on freeways. The traffic dynamics are described by uncertain coupled hyperbolic partial differential equations (PDEs) with Markov jumping parameters, which aim to address the distinctive driving strategies between AVs and HVs. Considering that the spacing policies of AVs vary in mixed traffic, the stochastic impact area of AVs is governed by a continuous Markov chain. The interactions between HVs and AVs such as overtaking or lane changing are mainly induced by impact areas. Using backstepping design, we develop a full-state feedback boundary control law to stabilize the deterministic system (nominal system). Applying Lyapunov analysis, we demonstrate that the nominal backstepping control law is able to stabilize the traffic system with Markov jumping parameters, provided the nominal parameters are sufficiently close to the stochastic ones on average. The mean-square exponential stability conditions are derived, and the results are validated by numerical simulations.

Meta-heuristic optimization-based robust [formula omitted] controller design for active suspension systems subject to actuator saturation

This study focuses on designing robust H∞ controllers to mitigate actuator saturation-related issues of active suspension systems. Two design methods are presented: one utilizing full-state feedback and the other relying on measurable output feedback. The H∞ state-feedback control incorporates actuator saturation directly into the design, representing the control input with the saturation function in the state-space model. The resulting optimization-based design problem, derived from theoretical stability analyses, poses a non-convex NP-hard problem under bilinear matrix inequality (BMI) constraints. To address this challenge, the study proposes a meta-heuristic optimization-based technique, providing a straightforward yet effective method to manage the BMI problem. The scope extends to practical implementation considerations, where suspension systems may only utilize measurable output variables. The H∞ static output-feedback control case is explored by extending the design of a full-order state-feedback controller. Despite the BMI-related challenges entailed in this scenario, the proposed meta-heuristic optimization-based design technique demonstrates flexibility in managing BMI conditions, thus eliminating the need to modify the controller design methodology. A noteworthy contribution of this study is its consistent application of the same meta-heuristic optimization-based technique for designing both H∞ state-feedback and static output-feedback controllers. Experimental results validate the effectiveness of the proposed robust H∞ control strategies.

State Feedback Via Judicious Pole Placement and Linear Quadratic Regulator – Application to Rotary Inverted Pendulum

In the control system regulatory concept, placing closed loop poles too far from the origin in the stability region produces fast regulation time but requires huge forcing energy as a trade-off. As such, stabilizing an unstable system with minimum energy is needed, though this presents a challenge to the designer. At the design phase, the designer may ponder the optimized energy while compromising the possibility of catastrophic stabilization phenomena due to minimal forcing thrust towards the poles. In this manuscript, a simple Linear Quadratic Regulator (LQR) is proposed as an alternative to full state feedback (FSF) with judicious pole placement. The efficacy of both approaches was observed by exploiting a Rotary Inverted Pendulum (RIP) as a testbed. Beforehand, the RIP system dynamics were developed in the time domain. RIP is an under-actuated mechanical system that is inherently nonlinear and unstable. The main control objectives of RIP are swing-up control, stabilization control, switching control, and trajectory control. The methodology involved the appearance of weighted matrices that were necessary for the minimum cost function. The Riccati and Lyapunov criteria are also exploited to facilitate design. The result shows the comparative transient performances of the two approaches, where the LQR outperforms the FSF in many aspects.

Secondary voltage regulation based on full-state feedback — performance assessment with Dyna[formula omitted]o

This paper discusses the performance assessment of new secondary voltage regulators currently under study in France to address challenges posed by the energy transition. With renewable integration and increasing cross-border interconnections, power flow variations surge across the network. Coupled with the historical SVRs’ relatively slow response, operational since the late 1970s, recent observations show higher voltage volatility. Prior research has already highlighted the potential of two novel regulators: the Average Q-SVR and the LQ-SVR, in mitigating these issues. Our focus here centres on the latter and begins by discussing the implications of control design hypotheses on closed-loop system performance. These include linearisation, neglecting communication delays, and assuming uniform dynamic behaviour across all resources. We then propose a two-step control design, leveraging Linear Quadratic Regulator (LQR) and eigenstructure placement methods and demonstrate that this approach surpasses the LQR method alone in terms of transient reactive power tracking.

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.

LQR control strategy for virtual synchronous generator adapted to stiff grid

Virtual synchronous generators (VSG) exhibit good small-signal stability in low short-circuit ratio (SCR) grids. However, the small-signal stability of the grid decreases as its SCRs increase, and there is even a risk of sub-synchronous resonance (SSR). The VSG sequence impedance model considering the frequency coupling effect is developed. The reasons for SSR caused by VSG integration into a stiff grids are analyzed using the sequence impedance analysis method and the Nyquist criterion. To enhance the grid-connected stability of VSG under stiff grids conditions, a linear quadratic regulator (LQR) control strategy with full-state feedback was proposed. The control strategy of LQR can effectively improve the phase margin of VSG output impedance in the low-frequency region, and it also exhibits strong robustness to variations in grid short-circuit ratios. It can also significantly improve the stability margin of the grid-tied system consisting of VSG and stiff grid, and effectively suppress the occurrence of SSR. Finally, the effectiveness and reliability of LQR control strategy are verified by OPAL-RT experimental platform.

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.

Input saturated [formula omitted] optimal control to mitigate DTMB 5415 combatant roll motion using anti roll gyro stabilizer

Despite technological advances, rolling motion is the most critical motion for the stability and survivability of ships. This study examines the possibility of using Anti Roll Gyrostabilizer System (ARGS) as a control actuation system to mitigate the roll motion of the DTMB 5415. In the scope of conceptual study, state space model of the DTMB 5415 Combatant Warship has been obtained. Then, ARGS dynamics have been integrated into the roll motion dynamics. Parameters of the DTMB 5415 and actuator are identified from the literature. Comparing experimental and numerical studies in the literature have also expanded the damping term parameters in the equation of roll motion. However, a Monte Carlo analysis is carried out to define the preliminary parameters of ARGS. An actuator-saturated Linear Matrix Inequality (LMI) Full State-Feedback H∞ Optimal Controller is tested for this design iteration. The results are also contrasted with the requirements that military ships must meet. Ship roll amplitudes have significantly decreased (over 95% for various sea conditions) and have complied with STANAG 4154 standards. The 1 radian Precession Angle limit has not been overshot. Continuous and discrete-time control rules are implemented, thus demonstrating the applicability of this actuation and control method are shown.

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.

Practical System Identification and Incremental Control Design for a Subscale Fixed-Wing Aircraft

An incremental differential proportional integral (iDPI) control law using eigenstructure assignment gain design is tested in flight on a subscale platform to validate its suitability for fixed-wing flight control. A kinematic relation for the aerodynamic side-slip angle rate is developed to apply a pseudo full state feedback. In order to perform the gain design and assessment, a plant model is estimated using flight test data from gyro, accelerometer, airspeed and surface deflection measurements during sine-sweep excitations. Transfer function models for the actuators and surface deflections are identified both in-flight and on the ground for several different actuators and control surfaces using hall sensor surface deflection measurements. The analysis reveals a large variation in bandwidth between the different types of servo motors. Flight test results are presented which demonstrates that the plant model estimates based on tests with good frequency excitation, high bandwidth actuators and surface deflection measurements can be used to reasonably predict the closed-loop dynamic behavior of the aircraft. The closed-loop flight test results of the iDPi control law show good performance and lays the groundwork for further development.

Adaptive Stabilization of Uncertain Linear System With Stochastic Delay by PDE Full-State Feedback

Adaptive Stabilization of Uncertain Linear System With Stochastic Delay by PDE Full-State Feedback