Polytopic Linear Parameter Varying Model Research Articles

Polytopic LPV modeling and gain scheduling [formula omitted] control of ball screw with position- and load-dependent variable dynamics

Ball screw drive (BSD) is a precision transmission mechanism widely used in high-precision positioning or tracking systems. The dynamic behavior of BSD varies with position and load, which causes tracking errors and poor robustness. Therefore, this paper proposes a polytopic linear parameter varying (LPV) model to express the varying dynamic behavior of BSD. The parameters of the LPV model are identified by the closed-loop frequency domain method and Levenberg–Marquardt iterative algorithm. Based on the polytopic LPV model, an LPV gain scheduling (GS) H∞ controller is proposed for the BSD with varying dynamics. Specifically, the controller is designed through polytope-based GS representation and mixed sensitivity synthesis. The most significant part is the proposal of a GS H∞ control algorithm to implement controller parameters that change with changing dynamics. Moreover, the stability of the closed-loop system is achieved by quadratic stabilization with state feedback. Finally, identification experiments and trajectory-tracking comparative experiments are carried out. The experimental results demonstrate that the proposed polytopic LPV modeling and GS H∞ control synthesis are effective in achieving accurate trajectory tracking and excellent robustness.

Tube-MPC Control via Notch Filter for Flexible Air-Breathing Hypersonic Vehicle with Actuator Fault

In this paper, the tube model predictive control (Tube-MPC) via notch filter is proposed for flexible air-breathing hypersonic vehicle with actuator fault. Firstly, considering the low-order flexible modes, the polytopic linear parameter varying (LPV) model of flexible air-breathing hypersonic vehicle is established using Jacobian linearization and tensor product. Actuator fault and parameter uncertainty are transformed into a lumped disturbance term. The baseline Tube-MPC trajectory tracking controller is developed by designing robust auxiliary feedback control law and nominal control law. In order to weaken the effect of flexibility, a notch filter is introduced to eliminate the frequency response peak of flexible modes. And the effect of notch filter on control performance and stability is analysed. Secondly, an alternative controller design strategy is proposed to ensure stability of the closed-loop system. The filter and the original nonlinear model are combined together such that the new polytopic LPV model is codesigned. On the basis, the adjustable Tube-MPC controller is developed to improve the control performance and ensure the stability of the system. Finally, the effectiveness of the two controllers is verified by simulations.

Development of an autonomous fog computing platform using control-theoretic approach for robot-vision applications

This paper presents the dynamic modelling and linear matrix inequality (LMI) based controller design of a distributed fog computing framework for real-time robot vision applications. A mobile robot vision system acquires the images from an application environment such as a warehouse, where articles are stacked in numerous racks. We characterise the mobile robot vision data (MRVD) using frames per second (FPS) and the image resolution. From the MRVD, object detection is performed by an open-source deep learning (DL) platform for detecting and localising various objects. However, with higher FPS together with high-resolution images, the processing time by the DL algorithm increases significantly. This necessitates the deployment of a distributed computing platform with several computing nodes. In this work, we deploy a distributed fog computing environment (DFCE) for the real-time object detection in an application environment.The processing time required to handle the MRVD is called the service time. However, for efficient auto-scaling performance, the mathematical model of the DFCE, taking into consideration the characteristics of the MRVD is necessary. In this context, we envisage the application of control theory to build the dynamic model of the DFCE. A Linear Parameter Varying (LPV) model is proposed for the DFCE with the service time as the output, the number of fog nodes as the input, and the characteristics of MRVD as the time-varying parameters. At first, an LPV model for the DFCE is derived using system identification, and the model is validated using the real-time test data. The LPV model is converted to a Polytopic LPV (PLPV) model for LMI based controller design. Finally, we develop and validate a Linear Matrix Inequality (LMI) based LPV controller to meet the service time constraints for a given application environment.For localisation and trajectory tracking with obstacle avoidance in the application environment, the mobile robot implements an Extended Kalman Filter (EKF) based simultaneous localisation and mapping (SLAM) and a bug-based path planning algorithm respectively. Finally, we present, detailed controller validation results illustrating the mobile robot navigation together with the auto-scaling control for the fog computing platform to modulate the service time.

Aggressive Maneuver Oriented Robust Actuator Fault Estimation of a 3-DOF Helicopter Prototype Considering Measurement Noises

This article presents a robust actuator fault estimation strategy design for a three-degree of freedom (3-DOF) helicopter prototype which can be adapted to aggressive maneuvers. First, considering large pitch angle condition during flight, nonlinear coupling characteristic of the helicopter system is exploited. As the pitch angle can be measured in real time, a polytopic linear parameter varying (LPV) model is developed for the helicopter system. Furthermore, considering measurement noises in the actual helicopter system, the dynamical model of helicopter system is modified accordingly. Then, based on the modified polytopic LPV model, a robust unknown input observer is developed for the helicopter system to realize actuator fault estimation, in which both measurement noises and large pitch angle are considered. Robust performance of proposed fault estimation approach is guaranteed by using energy-to-energy strategy. And the observer gains are calculated by using linear matrix inequalities. Finally, based on a 3-DOF helicopter prototype, both simulations and experiments are conducted. The effects of measurement noises and large pitch angle on the fault estimation performance are sufficiently demonstrated. And effectiveness as well as advantages of the proposed observer is verified by using comparative analysis.

Robust Controller Designing for an Air-Breathing Hypersonic Vehicle with an HOSVD-Based LPV Model

This paper focuses on the linear parameter varying (LPV) modeling and controller design for a flexible air-breathing hypersonic vehicle (AHV). Firstly, by selecting the measurable altitude and velocity as gain-scheduled variables, the original longitudinal nonlinear model for AHV is transformed into the LPV model via average gridding division, vertex trimming, Jacobian linearization, and multiple linear regression within the entire flight envelope. Secondly, using the tensor product model transformation method, the obtained LPV model is converted into the polytopic LPV model via high-order singular value decomposition (HOSVD). Third, the validity and applicability of the HOSVD-based LPV model are further demonstrated by designing a robust controller for command tracking control during maneuvering flight over a large envelope.

Piece‐wise ellipsoidal set‐based model predictive control of linear parameter varying systems with application to a tower crane

AbstractIn this paper, a model predictive control algorithm for polytopic linear parameter varying (LPV) systems is proposed, which is based on an offline calculated sequence of robust one‐step controllable sets. At each sampling instant, a finite‐time optimal control problem is solved subject to a stabilizing constraint on the first state to ensure stability and recursive feasibility guarantees independent of the length of the prediction horizon and the cost function. An algorithm is proposed to compute a sequence of piece‐wise ellipsoidal one‐step controllable sets. The systematic application of the developed algorithm is possible via tensor product model transformation to a class of nonlinear systems. The size and shape of each set depend on the vertices of the polytopic LPV system and influences the control performance. By using the tensor product model transformation, different vertex representations can be obtained automatically. Furthermore, a trade‐off between model complexity and accuracy can be chosen, and the computational effort of the set calculation can be influenced. The developed method is applied to a tower crane system. The tower crane is modeled in a cascaded form with three separate subsystems. The couplings between the subsystems are treated as varying parameters. Each subsystem of the crane is transformed into a polytopic LPV system using the tensor product model transformation. By discarding the nonzero singular values, the complexity of the polytopic LPV model is reduced in terms of the number of vertices.

Design and Experimental Validation of an LPV Pure Pursuit Automatic Steering Controller

This paper addresses the problem of designing control systems for steering an autonomous vehicle, for varying speed, ensuring stability and sustaining performance, taking into account comfort and safety. A novel automatic lateral control architecture is proposed combining Linear Parameter Varying (LPV) control theory and the Pure-Pursuit algorithm. The response of the robust controller is investigated for tracking a reference trajectory. The implementation is based on the reduction of the polytopic LPV model. In addition, to illustrate the results, the synthesized controller has been tested first in simulations, and then to an automated electric Renault Zoe in a test track providing encouraging results.

Active Vibration Control of a Convertible Structure based on a Polytopic LPV Model Representation

This paper deals with modeling and control of lightweight convertible structures for the application in civil and structural engineering. Such structures are prone to vibrations due to their lightweight design. In addition, they exhibit transformation state dependent dynamic behavior. In order to guarantee a reliable operation, the use of active vibration control (AVC) is an effective means. For the example of a simplified convertible structure, modeling is demonstrated using the linear parameter-varying (LPV) framework. Based on local linear time-invariant (LTI) models, derived from a finite element model of the convertible structure, a polytopic LPV model is established. This LPV model is then utilized to design a polytopic LPV output-feedback controller for AVC during the structure’s transformation. The effectiveness of the designed controller is validated in simulation.

An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems

Abstract The linear parameter varying (LPV) approach has proved to be suitable for controlling many non-linear systems. However, for those which are highly non-linear and complex, the number of scheduling variables increases rapidly. This fact makes the LPV controller implementation not feasible for many real systems due to memory constraints and computational burden. This paper considers the problem of reducing the total number of LPV controller gains by determining a heuristic methodology that combines two vertices of a polytopic LPV model such that the same gain can be used in both vertices. The proposed algorithm, based on the use of the Gershgorin circles, provides a combinability ranking for the different vertex pairs, which helps in solving the reduction problem in fewer attempts. Simulation examples are provided in order to illustrate the main characteristics of the proposed approach.

Robust Predictive Control Algorithm Based on Parameter Variation Rate Information of Functional-Coefficient ARX Model

Considering the conservativeness caused by the polytopic linear parameter varying (LPV) model, which is constructed using only the upper and lower bound information of the state-dependent auto-regressive model with eXogenous input and radial basis function network type coefficients (RBF-ARX model). In this paper, a robust predictive control (RPC) algorithm based on the parameter variation rate information of the RBF-ARX model is proposed. By using the information, the size of the convex polytopic sets used to wrap the system's polytopic LPV model is compressed greatly. Thus, it improves greatly the control performance and reduces the conservativeness of the subsequent RPC algorithm. The conversion from the RBF-ARX model to the polytopic LPV state space model just uses the RBF-ARX model itself, and the derived LPV model is a special quasi-LPV autoregressive model. So, it is not necessary to assume that the time varying parameters and/or the bounds of the parameter variation rate in the polytopic LPV model must be known or measured. An example of a widely used continuous stirred-tank reactor process control is studied to illustrate the effectiveness of the proposed approach in terms of using parameter variation rate information of the RBF-ARX model to improve step response control performance and anti-jamming performance.

Interpolation Model Predictive Control of Nonlinear Systems Described by Quasi-LPV Model

This paper investigates the interpolation model predictive control (MPC) algorithm for nonlinear discrete-time systems, which can be represented by affine linear parameter varying (LPV) model. The general nonlinear model is transformed into the quasi-LPV model, then the equivalent polytopic LPV model and disturbed Linear time-invariant (LTI) model are obtained. Therefore, a finite-horizon interpolation MPC algorithm based ellipsoidal invariant set (EIS) is proposed. For comparison, the existing zero-horizon interpolation MPC algorithm, based on EIS, is also described to display the advantages of proposed algorithm. By virtue of the finite-horizon technique, the feasible region of proposed algorithm is much larger than zero-horizon interpolation MPC algorithm. An illustrative example is given to verify the effectiveness of proposed algorithms.

Reliability-based linear parameter varying robust non-fragile control for hypersonic vehicles with disturbance observer

In this paper, the linear parameter varying (LPV) reliable non-fragile control for the hypersonic vehicle (HV) is studied in case of disturbance and controller gain variations. Due to the dramatic and complex change of the HV longitudinal dynamics, a polytopic LPV model is constructed for the HV system stability analysis and controller design in a large flight envelope. Then, a disturbance observer (DOB)-based non-fragile controller for HV system with disturbance and unknown controller uncertainty is designed to guarantee the closed-loop stability and control performance under an adequate level of reliability, which is formed with two parts. One part is a DOB to compensate the uncertain dynamics and disturbance. The other is a robust non-fragile controller, which is designed based on a novel robust reliability method to deal with controller uncertainties, and obtained by carrying out reliability-based linear matrix inequality optimization. The presented controller for HV can provide the robustness as well as an excellent performance under the condition that the prescribed reliability degree is satisfied. Finally, numerical simulation for an HV demonstrates the effectiveness of the proposed method.

Output feedback polytopic LPV Tube-RMPC control for air-breathing hypersonic vehicles

This paper proposes an output feedback tube-based robust model predictive control (Tube-RMPC) scheme for air-breathing hypersonic vehicles. Firstly, the polytopic linear parameter varying (LPV) model is established by Jacobian linearisation and tensor-product (T-P) modelling for the longitudinal dynamics. Secondly, a robust polytopic state observer is designed to estimate the attack angle, pitch angle and pitch rate by utilising the limited information of altitude and velocity. Then, the Tube-RMPC controller satisfying all vertices of polytopic LPV model is presented. Wherein, estimation error and control error are bounded by two robust positively invariant sets respectively. The Tube-RMPC controller ensures that actual states lie in a tube centred with the nominal states. The input constraints of original system are guaranteed by employing tighter constraints for nominal system. Finally, simulation results show the feasibility and effectiveness of the proposed method for hypersonic vehicles.

Dynamic decoupling tracking control for the polytopic LPV model of hypersonic vehicle

The dynamic decoupling problem of the hypersonic flight vehicle (HFV) is considered in this paper. The Linear Parameter-Varying (LPV) model of the HFV is firstly obtained and smoothly transformed into a polytopic form by the Tensor-Product (TP) model transformation method. After that, a dynamic decoupling control method is derived by minimizing the H∞ norm of a virtual system, which is composed by the controlled system and the no coupling reference model. The necessary and sufficient condition for the existence of the controller is derived based on Linear Matrix Inequalities (LMIs). Next, the decoupling controller for the polytopic LPV model of HFV is designed. And the simulation results show that the proposed method has perfect performance in terms of dynamic decoupling.

Linear Parameter Varying Switching Attitude Tracking Control for a Near Space Hypersonic Vehicle Via Multiple Lyapunov Functions

AbstractThis article deals with the problem of linear parameter varying (LPV) switching attitude tracking control for a near space hypersonic vehicle (NSHV). Firstly, nonlinear attitude dynamics of the NSHV is modeled as a slow‐fast loop polytopic LPV model by using Jacobian linearization and Tensor‐Product (TP) model transformation approach. Secondly, for less conservative controller design purpose, the flight envelope is divided into four sub‐regions. Slow loop and fast loop LPV controllers are designed for each sub‐region. Based on switching character function, these slow loop and fast loop LPV controllers are then switched in order to guarantee the closed‐loop NSHV system to be asymptotically stable and satisfy a specified performance criterion. The existed conditions of the desired LPV switching controller are deduction by linear matrix inequations (LMIs) and the system stability analysis is given by multiple Lyapunov functions (MLPs), therefore, compared with existing switching control scheme, the proposed LPV switching control method is less conservative. Finally, numerical simulations demonstrate the effectiveness of the proposed method.

Non-fragile switching tracking control for a flexible air-breathing hypersonic vehicle based on polytopic LPV model

This article proposes a linear parameter varying (LPV) switching tracking control scheme for a flexible air-breathing hypersonic vehicle (FAHV). First, a polytopic LPV model is constructed to represent the complex nonlinear longitudinal model of the FAHV by using Jacobian linearization and tensor-product (T-P) model transformation approach. Second, for less conservative controller design purpose, the flight envelope is divided into four sub-regions and a non-fragile LPV controller is designed for each parameter sub-region. These non-fragile LPV controllers are then switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a specified performance criterion. The desired non-fragile LPV switching controller is found by solving a convex constraint problem which can be efficiently solved using available linear matrix inequality (LMI) techniques, and robust stability analysis of the closed-loop FAHV system is verified based on multiple Lypapunov functions (MLFs). Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.

Polytopic LPV modeling and gain-scheduled switching control for a flexible air-breathing hypersonic vehicle

A novel gain-scheduled switching control method for the longitudinal motion of a flexible air-breathing hypersonic vehicle (FAHV) is proposed. Firstly, velocity and altitude are selected as scheduling variables, a polytopic linear parameter varying (LPV) model is developed to represent the complex nonlinear longitudinal dynamics of the FAHV. Secondly, based on the obtained polytopic LPV model, the flight envelope is divided into four smaller subregions, and four gain-scheduled controllers are designed for these parameter subregions. Then, by the defined switching characteristic function, these gain-scheduled controllers are switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a given tracking error performance criterion. The condition of gain-scheduled switching controller synthesis is given in terms of linear matrix inequalities (LMIs) which can be easily solved by using standard software packages. Finally, simulation results show the effectiveness of the presented method.

Slow–fast loop gain-scheduled switching attitude tracking control for a near-space hypersonic vehicle

This article develops a slow–fast loop polytopic linear parameter-varying model and proposes a systematic gain-scheduled switching attitude tracking control scheme for a near-space hypersonic vehicle. First, the dynamics of near-space hypersonic vehicle is modeled as a slow–fast loop polytopic linear parameter-varying model using the Jacobian linearization and tensor-product model transformation approach. Open-loop simulation verification illustrates that the developed polytopic linear parameter-varying model captures the local nonlinearities of the original nonlinear system; therefore, it is suitable for model-based control. Second, for less conservative controller design purpose, the flight envelope is divided into smaller subregions, a family of slow loop and fast loop gain-scheduled controllers are designed, and each of them is suitable for a specific parameter subspace; the slow loop and fast loop gain-scheduled controllers are then switched in order to guarantee the closed-loop near-space hypersonic vehicle system to be asymptotically stable and satisfy a specified performance criteria. The resulting slow loop and fast loop gain-scheduled switching controllers are found by solving a convex constraint problem that can be efficiently solved using available linear matrix inequality techniques. Finally, numerical simulations have demonstrated the effectiveness of the proposed method.

On modeling and control of a flexible air-breathing hypersonic vehicle based on LPV method

This article develops a polytopic linear parameter varying (LPV) model and presents a non-fragile H2 gain-scheduled control for a flexible air-breathing hypersonic vehicle (FAHV). First, the polytopic LPV model of the FAHV can be obtained by using Jacobian linearization and tensor-product (TP) model transformation approach, simulation verification illustrates that the polytopic LPV model captures the local nonlinearities of the original nonlinear system. Second, based on the developed polytopic LPV model, a non-fragile gainscheduled control method is proposed in order to reduce the fragility encountered in controller implementation, a convex optimisation problem with linear matrix inequalities (LMIs) constraints is formulated for designing a velocity and altitude tracking controller, which guarantees H2 control performance index. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.