Robust minimax optimal control of nonlinear uncertain systems using feedback linearization with application to hypersonic flight vehicles

The purpose of this study is to build a two-stage Kalman filter (TSKF) for estimating the actuator control effectiveness factors of an unmanned aerial vehicle (UAV). The actuator faults can be determined and isolated using controller effectiveness factor estimates. A linear quadratic regulator (LQR) controller is designed for the modelled UAV. The control matrix is identified by the TSKF. In the case of actuator faults, LQR controller can be reconfigured for the identified control distribution matrix. For faulty actuator scenarios (change in elevator, throttle, aileron control effectiveness factors are taken into account), the designed system is tested, and the success of TSKF is shown. The closed-loop systems which include LQR-type controllers in the longitudinal and lateral dynamics are considered and simulations are done in this system to estimate the true states and the control effectiveness factors. True values of the effectiveness factors are estimated, and it is shown that the estimation of the states can be done effectively using TSKF for lateral and longitudinal models.

One of the well-known methods for improving the lateral stability of a vehicle is to utilize an active steering controller. Common active steering systems use feedback signals from a yaw rate sensor and side-slip angle estimation. However, in some driving conditions, skilled drivers can prevent vehicle rollover using the steering angle of the vehicle. Hence, the effect of an active front-steering controller on the roll angle of the vehicle is studied in this paper. For this study, a three-degree-of-freedom linear model of a vehicle which has the lateral motion, the yaw motion and the roll motion as the degrees of freedom is derived. The effectiveness of the active steering controller on the roll stability of the vehicle is examined by simulations in a wide range of longitudinal velocities of the vehicle using a linear quadratic regulator controller. The results obtained indicate that the active steering controller increases the roll stability of the vehicle only at low vehicle speeds and also that consideration of the roll degree of freedom in the design of the active steering controller is not effective at high vehicle speeds. Therefore a two-degree-of-freedom bicycle model is sufficient for active steering controller design. Another part of this paper is dedicated to designing a practical active steering controller for a vehicle with time-varying and uncertain parameters. In fact, designing a controller which guarantees the stability of the vehicle with simultaneous uncertainties in the cornering stiffnesses of the tyres and in the time-varying velocity is the main goal of this paper. Another important advantage of the proposed controller is its simplicity and static structure. In fact, this controller design is carried out offline and can be implemented for use in a real vehicle. This simple and powerful controller is a robust linear quadratic regulator controller. For designing a robust linear quadratic regulator controller, a polytopic model of the two-degree-of-freedom vehicle is obtained, which considers the uncertainty in the parameters. In addition, a linear matrix inequality is used to design a linear quadratic regulator controller for an uncertain or parameter-varying system. Finally, the performance of the designed robust linear quadratic regulator controller was studied by simulating the vehicle responses in some manoeuvres. A sport utility vehicle model is used for simulation purposes. This non-linear vehicle model has eight degrees of freedom and its tyres are assumed to be both linear and non-linear. The performance of the robust linear quadratic regulator controller was studied for vehicles with both linear and non-linear Pacejka tyres. The proposed controller guarantees robust stability of the closed-loop system in the presence of 50% variation in the vehicle speed and 20% uncertainty in the stiffnesses of the tyres.

The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.

This paper intends to compare controllers used for non-isolated (transformer less) interleaved double dual boost (IDDB) converter which provide high voltage gain and can be used for high-power applications. A control subsystem is required to improve dynamic behaviour of converter and to have a better output response. In most cases small signal model of converter is obtained which are linearized at an operating point to derive a controller which cannot take uncertainties into consideration. Robust control and Nonlinear control methods are probably areas which can handle uncertainties and non-linearities effectively. Conventional linear quadratic regulator (LQR) controller cannot assure stability if system is highly uncertain. A convex model of converter dynamics is obtained taking uncertainties into account. To apply LQR control in uncertain converter case linear matrix inequalities(LMIs) are used to optimize the performance index. A comparative study of LMI-LQR control, LQR Controller and PID controller is done.

In this paper, the differences between decoupled and coupled control of bank-to-turn (BTT) missiles have been studied in detail from three aspects: stabilizability, linear quadratic regulator (LQR) control and tracking control. It is found that for some parameters the BTT missile can be controlled by a decoupled way, especially for stabilizability and LQR control. However, for some others, the BTT missile cannot be decoupled and a coupled control method is needed. Therefore, for a practical flight control system, the decouplability should be studied before giving a decoupled control method. In addition, in order to avoid the disadvantages of LQR control method, an improved H∞ controller design method is given. Combined with tracking control problem, a new H∞ control method is established for trajectory tracking.

This paper presents a scheme to design a tracking controller for a class of uncertain nonlinear systems using a robust feedback linearization approach. The scheme is composed of two steps. In the first step, a linearized uncertainty model for the corresponding uncertain nonlinear system is developed using a robust feedback linearization approach. In this step, the standard feedback linearization approach is used to linearize the nominal nonlinear dynamics of the uncertain nonlinear system. The remaining nonlinear uncertainties are then linearized at an arbitrary point using the mean value theorem. This approach gives a multi-input multi-output (MIMO) linear uncertain system model with a structured uncertainty representation. In the second step, a minimax linear quadratic regulation (LQR) controller is designed for MIMO linearized uncertain system model. In order to demonstrate the effectiveness of the proposed method, it is applied to a velocity and altitude tracking control problem for an air-breathing hypersonic flight vehicle.

A recurrent dynamic neural network (RDNN) based on Hopfield model is applied to linear quadratic regulator controller of an irrigation canal. The Saint-Venant equations of open-channel flow are linearized using the Taylor series and a finite difference approximation of the original nonlinear, partial differential equations. Using the linear optimal control theory, a Linear Quadratic Regulator (LQR) controller is developed for an irrigation canal with a single pool. A Hopfield recurrent dynamic neural network is applied to solution of Riccati equation for calculating the LQR control gains. The main advantage of Hopfield neural network model is its robustness and flexibility when dealing with unknown perturbations and parameters. The results of this study shows that an RDNN based LQR controller (RDNN/LQR) for irrigation canals offers an alternative to traditional LQR controller when dealing with the disturbances in the irrigation canals.

The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar. In this paper, two multi-objective optimization methods are developed using invasive weed optimization (IWO). The first method is the weighted criteria method IWO (WCMIWO) and the second method is the fuzzy logic IWO hybrid (FLIWOH). The two optimization methods were used to investigate the optimum diagonal values for the Q matrix of the linear quadratic regulator (LQR) controller that can balance the Robogymnast in an upright configuration. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated, but this time with disturbance applied to the Robogymnast states to develop another set of two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance evaluated. The results show that all four controllers are able to balance the Robogymnast with varying accuracies. It has also been observed that the controllers trained with disturbance achieve faster settling time.

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

Inverted pendulum systems, such as double or single, rotational or translational inverted pendulums are non-linear and unstable, which have been the most dominant approaches for control systems. The double inverted pendulum is one kind of a non-linear, unstable system, multivariable, and strong coupling with a wide range of control methods. To model these types of systems, many techniques have been proposed so that motivating researchers to come up with new innovative solutions. The Linear Quadratic Regulator (LQR) controller has been a common controller used in this field. Meanwhile, the Artificial Bee Colony (ABC) technique has become an alternative solution for employing Bee Swarm Intelligence algorithms. The research solutions of the artificial bee colony algorithm in the literature can be beneficial, however, the utilization of discovered sources of food is ineffective. Thus, in this paper, we aim to provide a double inverted pendulum system for stabilization by selecting linear quadratic regulator parameters using a bio-inspired optimization methodology of artificial bee colony and weight matrices Q and R. The results show that when the artificial bee colony algorithm is applied to a linear quadratic regulator controller, it gains the capacity to autonomously tune itself in an online process. To further demonstrate the efficiency and viability of the suggested methodology, simulations have been performed and compared to conventional linear quadratic regulator controllers. The obtained results demonstrate that employing artificial intelligence (AI) together with the proposed controller outperforms the conventional linear quadratic regulator controllers by more than 50 % in transient response and improved time response and stability performance

Inverted pendulum mounted on a cart is an inherently unstable system which requires control effort to stabilize it at its upright position. In this single input multi output system the pendulum is balanced by controlling the horizontal motion of the cart. Various controller design techniques have been developed to control such systems like PID controllers, LQR controllers, Neural networks etc. The performance of the system for controlling methods of PD (Proportional Derivative) controller and LQR (Linear Quadratic Regulator) controller are compared by simulating in MATLAB SIMULINK and the results are validated through results obtained from a real inverted pendulum system.

Purpose – This paper aims to present the design of a stability augmentation system (SAS) in the longitudinal and lateral axes for an unstable helicopter. Design/methodology/approach – The feedback controller is designed using linear quadratic regulator (LQR) control with full state feedback and LQR with output feedback approaches. SAS is designed to meet the handling qualities specification known as Aeronautical Design Standard (ADS-33E-PRF). A helicopter having a soft inplane four-bladed hingeless main rotor and a four-bladed tail rotor with conventional mechanical controls is used for the simulation studies. In the simulation studies, the helicopter is trimmed at hover, low speeds and forward speeds flight conditions. The performance of the helicopter SAS schemes are assessed with respect to the requirements of ADS-33E-PRF. Findings – The SAS in the longitudinal axis meets the requirement of the Level 1 handling quality specifications in hover and low speed as well as for forward speed flight conditions. The SAS in the lateral axis meets the requirement of the Level 2 handling quality specifications in both hover and low speed as well as for forward speed flight conditions. The requirements of the inter axis coupling is also met and shown for the coupled dynamics case. The SAS in lateral axis may require an additional control augmentation system or adaptive control to meet the Level 1 requirements. Originality/value – The study shows that the design of a SAS using LQR control algorithm with full state and output feedbacks can be used to meet ADS-33 handling quality specifications.

In this paper, we introduced the principle of using fast steering mirror (FSM) in compound-axis systems. Based on the modeling of a fast steering mirror, the linear quadratic regulator (LQR) controller design process is demonstrated. Several simulation experiments were done using the LQR controller that was designed, and the results were compared with two commonly used classical control theory controllers. The result of comparison and system analysis shows the effectiveness of the LQR algorithm.

The work incorporates the control strategies in closed loop control of quadratic boost converter based four bus micro grid using –HC (hysteresis controller) and LQR (linear quadratic regulator) controllers. The suggested LQR controls the voltage and current at load buses by using Hybrid Power Flow Controlled system. This work deals with the comparison of closed loop four bus system using HC/LQR controller. Simulation is done for 4 bus system & the outcomes are compared in terms of settling time and steady state error. The outcomes represents that the superior performance of LQR controlled 4 bus system compared to HC controlled 4 bus systems.