Robust Linear Quadratic Sliding-Mode Control for BLDC Motor Positioning System

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.

In this paper we present a new state space model based linear quadratic fault-tolerant tracking control scheme for batch processes with unknown disturbances and partial actuator faults. To develop the linear quadratic fault-tolerant control, the batch process is first treated with a new state space representation that incorporates both the state and the output tracking error dynamics. Then relevant concepts of the subsequent linear quadratic control are formulated, where improved closed-loop control performance is achieved even with unknown disturbances and actuator faults compared with traditional linear quadratic control. Application to injection velocity control shows that the proposed scheme achieves the design objective well with performance improvement.

Combined iterative learning and delta-operator adaptive linear quadratic Gaussian control of a commercial rapid thermal processing system

From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.

This study investigates the longitudinal motion control of unmanned aerial vehicles through a simulation in MATLAB. The linear model of an unmanned aerial vehicle is applied to controllers to explicate the longitudinal motion of the unmanned aerial vehicle. The ideal performance for an unmanned aerial vehicle is to achieve the desired response instantly with 100% precision. However, currently available controllers need further improvements. Thus, a proportional-derivative linear quadratic regulator controller is developed and compared with a proportional-integral-derivative controller, a linear quadratic regulator controller, and a proportional linear quadratic regulator controller. The proportional-derivative linear quadratic regulator controller enhances the response of the system by reducing settling time by more than 95% compared with other available controllers. Additionally, the proportional-derivative linear quadratic regulator improves the root mean square error by almost 50% compared with the proportional linear quadratic regulator controller and improves rise time by almost 96% with reasonable overshoot.

This study discusses the quantised linear quadratic Gaussian (LQG) control problem for linear stochastic systems. A symmetric channel that connects the sensor and the controller is considered. Given a quantiser that is applied on the most recent innovation of the measurement, it is shown that the well-known separation principle remains valid. Based on a quantised innovations Kalman filter, a suboptimal LQG controller is given in terms of the solutions of two Riccati difference equations associated, respectively, with the state estimation and the standard linear quadratic regulator control. The corresponding approximate suboptimal cost is also derived. An illustrative example is included to demonstrate the effectiveness of the proposed controller.

The linear quadratic optimal control problem under quadratic constraints is an optimization problem over a generally non-convex set. Yakubovich [8] and Megretski [4] have studied this problem, and they show how it may be translated into a two-stage, convex optimization problem. In this paper we study the linear quadratic control problem under quadratic constraints for generalized first-order systems. As in the state-space case the linear quadratic control problem without quadratic constraints may be solved in terms of a linear matrix inequality. Subsequently, we use the results from [8] to derive a linear matrix inequality characterizing the linear quadratic optimal behaviour under quadratic constraints.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

An 8-DOF three-axle vehicle model with semi-active suspension is built in this paper, of which the accuracy is verified through simulations and experiments. Based on the optimal control theory, the linear quadratic Gaussian controller for semi-active suspension is designed with 10 evaluation indicators. Considering the deficiency of linear quadratic Gaussian control weight coefficients based on experience, analytic hierarchy process is employed to determine the weight coefficients of each indicator. The control effect is analyzed through MATLAB/Simulink. The adaptability of proposed control strategy under 25 driving conditions is analyzed with different road grades and speeds. The driving condition of “70 km/h travel speed on the road of grade B” is selected, under which the comparison of vehicle responses between semi-active suspension and passive suspension is made. Results show that the vertical vibration is effectively diminished by using semi-active suspension with linear quadratic Gaussian controller. Compared with passive suspension, the riding comfort is improved and the adverse effect on handling stability is eliminated. The three-axle vehicle with semi-active suspension has good adaptability to various working conditions.

This chapter presents the results of experiments comparing different computationally efficient model predictive control (MPC) methods applied to a laboratory device, demonstrating the active vibration control (AVC) of lightly damped mechanical structures. Because of the combination of long prediction horizons, short sampling times and large actuator-disturbance asymmetry, the implementation of the predictive control strategy on lightly damped vibrating structures is highly demanding. The vibration damping effect and online timing properties of model predictive control algorithms such as infinite horizon cost dual-mode quadratic programming based MPC (QPMPC), pre-computed explicit multi-parametric programming based MPC (MPMPC), minimum-time MPMPC and the very efficient but suboptimal Newton–Raphson based MPC (NRMPC); all with guaranteed stability and constraint feasibility are analyzed in different disturbance and loading scenarios. All MPC methods along with the baseline linear quadratic (LQ) controller decrease vibration settling to equilibrium by an order of magnitude time. The damping effect of all investigated MPC strategies is comparable with a slight decrease in performance for the suboptimal minimum-time MPMPC and NRMPC controllers. Due to the excessive online computational needs of QPMPC, it is a very unlikely candidate for lightly damped vibrating systems given currently available hardware. The online timing analysis presented here demonstrates that MPMPC provides significantly shorter online execution times, however its suboptimal minimum-time version does not bring a convincing improvement. NRMPC can provide online execution times on par with linear quadratic controllers; however, its suboptimality becomes excessive with increasing prediction model orders.

In this study, the design procedure and the performance analysis of a linear quadratic gaussian controller (LQGC) are presented. The controller is expected to regulate the production–inventory process of a manufacturing system along a pre-determined trajectory within the plant hierarchical control system; the hierarchical control structure is also described briefly in this chapter. The LQGC is based on a dynamic, discrete-time, and a stochastic model, aggregating products, and production processes. The simulation results show that the LQGC is well -suited for the intended purpose.

This chapter introduces a robust control scheme of load frequency control (LFC) of a micro-grid system integrated with a wind energy system. The control scheme is based on H∞ and linear quadratic Gaussian techniques. The main idea of the control design is to be stable against the parameter’s uncertainties and the load disturbance. A complete model of the power system with the DFIG has been linearized. This model has been utilized to design both controllers of H∞ and linear quadratic Gaussian. The H∞ is designed by optimal selecting of the weighting functions to ensure the robustness and to enhance the overall performance. Also, the full states considering the frequency deviation are assessed based on the standard Kalman filter method. Moreover, the states of the system are applied with the linear quadratic Gaussian feedback optimal control performance under normal and abnormal operating conditions. Simulation tests are applied with the purpose of validation of the overall controllers’ performance. The results proved the superiority of the planned integration of the wind energy system with the micro-grid.KeywordsRobust controlLoad frequency controlLinear quadratic gaussianH∞Wind energy system

Future grids will consist of many small and large subgrids that will require complex control for grid interaction as well as tracking of operation. This paper presents the design of a robust integral linear quadratic Gaussian (ILQG) controller for damping and tracking control of subgrid voltage of hybrid microgrid. The design of ILQG is carried out by augmenting the subgrid dynamics with an integrator that takes power from the DC bus connecting with AC and PV based DC grid. The subgrid consists of a parallel combination of several uncertain and unknown loads that may produce the voltage oscillation. The performance of ILQG is evaluated for various load dynamics and compared with the LQG, LQR, and integral controller in terms of bandwidth. The robustness of proposed controller is studied by considering a number of uncertainties within subgrid model. Results show that the proposed ILQG controller provides improved robust performance than others.

Stability is the first demand of the feedback control design. The parametrization of all stabilizing controllers is standard theory. The stabilizing controller has some free parameters which can be used for further optimization. Linear Quadratic (LQ) control and Dead Beat control are standard algorithms for optimal control of discrete time models of real systems. The dead beat control results in very large input signals which are not realizable. The LQ control is widely used, because enables to tune the criterion to our requirements. In this paper the combination of both tuning algorithms is presented. The dead beat control algorithm has a unique solution. To enlarge number of steps gives us free parameters which can be used for the optimization of LQ criterion.

We present the parameter robust risk-sensitive control theory to deal with the parameter uncertainties of a system. In this synthesis, the parameter uncertainties are decomposed into three parts, and are reflected in the cost function and the noise models. This new method improves the tolerance of a controller to parameter uncertainties in a system. We apply the newly developed method to satellite structure attitude control application. The linearized version of the satellite structure attitude model is derived for the attitude hold mode. To determine the performance of the parameter robust risk-sensitive control method, the steady-state mean square histories of the state and input variables are calculated by finding the covariance matrices. Moreover, the performance robustness of parameter robust risk-sensitive control is compared with the classical linear quadratic Gaussian control. Finally, as an application of this parameter robust risk-sensitive control, we consider commercially operating remote sensing satellite. The numerical simulations show that the parameter robust risk-sensitive control method has better performance and stability characteristics than the classical linear quadratic Gaussian control method, especially when the parameter uncertainties are large.