Guaranteed Cost Control Scheme Research Articles

Guaranteed cost control for dynamic positioning of marine surface vessels with input saturation

This paper investigates the dynamic positioning (DP) control problem of marine surface vessels (MSVs) suffering from external perturbations and input saturation. The linear Matrix Inequalities (LMI) based guaranteed cost control scheme is designed to obtain the satisfaction of the preset performance indicators. Aiming towards this purpose, the mathematical model of the MSV is first translated into a novel state-and-parameter-dependent (SPD) structure under small yaw angle variation. Furthermore, the performance indicator of the control scheme is derived for robustness against disturbances. With the application of LMI analysis method, the performance function will be transformed to a matrix inequality. Then, input saturation constraints are imposed to the control input, which will also be treated as a matrix inequality. Eventually, theoretical analysis shows that asymptotic stability will be endowed to the closed-loop system and input saturation constraints are also satisfied. Numerical simulation results are presented to demonstrate the advantage and validity of the proposed controller.

Hybrid iterative learning fault‐tolerant guaranteed cost control design for multi‐phase batch processes

AbstractA robust design of a hybrid iterative learning fault‐tolerant guaranteed cost control scheme is proposed for a class of multi‐phase batch processes under faults and disturbances. Firstly, based on an equivalent two‐dimensional Fornasini‐Marchesini (2D‐FM) switched system with actuator faults varying within an allowable range, a 2D robustly hybrid controller that includes a robust hybrid extended feedback control to ensure performance over time and a hybrid iterative learning control to improve the tracking performance from cycle to cycle is formulated to guarantee the closed‐loop convergence and the H∞ performance level with a cost function bearing the upper bounds for all admissible uncertainty and actuator failures. Secondly, 2D system theory and the average dwell time strategy are adopted to derive conditions for guaranteeing exponential stability of the corresponding system in terms of linear matrix inequalities (LMIs), where the suboptimal hybrid guaranteed cost controller, which minimizes the quadratic performance index and rejects external disturbances, is designed using a convex optimization under LMI constraints. Finally, the proposed method is further verified by simulation on an injection molding process in comparison with traditional methods.

Decentralized control for spacecraft formation in elliptic orbits

PurposeThis paper aims to address the problem of formation control for spacecraft formation in elliptic orbits by using local relative measurements.Design/methodology/approachA decentralized formation control law is proposed to solve the aforementioned problem. The control law for each spacecraft uses only its relative state with respect to the neighboring spacecraft it can sense. These relative states can be acquired by local relative measurements. The formation control problem is converted to n stabilization problems of a single spacecraft by using algebraic graph theories. The resulting relative motion model is described by a linear time-varying system with uncertain parameters. An optimal guaranteed cost control scheme is subsequently used to obtain the desired control performance.FindingsNumerical simulations show the effectiveness of the proposed formation control law.Practical implicationsThe proposed control law can be considered as an alternative to global positioning system-based relative navigation and control system for formation flying missions.Originality/valueThe proposed decentralized formation control architecture needs only local relative measurements. Fuel consumption is considered by using an optimal guaranteed cost control scheme.

The Optimal Guaranteed Cost Control of Tractor-semitrailer Steering Stability

The Gim tire model was adopted to set up the nonlinear dynamic model of tractorsemitrailer. Choosing the slip angle of tractor, the yaw velocity of tractor, the yaw velocity of semitrailer, and the angle between tractor and semitrailer as control variables, as well as considering the uncertain characteristic of the tire cornering stiffness, the optimal guaranteed cost control scheme was proposed. An optimal guaranteed cost controller of DYC for the tractor-semitrailer stability was developed based on model following technique. Based on the established nonlinear dynamic model, simulation in Matlab/Simulink software environment was described. The simulation results suggest that for the tractor-semitrailer with optimal guaranteed cost controller of DYC, the handling and stability performance on big slip angle is improved. The conclusion can be useful for the system design of tractor-semitrailer.

Optimal Guaranteed Cost Control of Four-Wheel Steering Vehicle with Three Degree-of-Freedom

A nonlinear model of 4WS vehicle with three degree-of-freedom is established, Considering the uncertain characteristic of the tire lateral stiffness, an guaranteed cost control scheme was proposed for vehicle stability control, the optimal guaranteed cost control laws is derived in terms of linear matrix inequalities (LMIs). The simulation results show that transient response amplitude of the yaw rate , center side-slip angle and lateral acceleration can be decreased greatly, a good steady-state response can be achieved at a high speed, which improves the driving safety and handling stability.

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞ performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.

Delay‐range‐dependent guaranteed cost control for batch processes with state delay

A guaranteed cost control scheme is proposed for batch processes described by a two‐dimensional (2‐D) system with uncertainties and interval time‐varying delay. First, a 2‐D controller, which includes a robust feedback control to ensure performances over time and an iterative learning control to improve the tracking performance from cycle to cycle, is formulated. The guaranteed cost law concept of the proposed 2‐D controller is then introduced. Subsequently, by introducing the Lyapunov–Krasovskii function and adding a differential inequality to the Lyapunov function for the 2‐D system, sufficient conditions for the existence of the robust guaranteed cost controller are derived in terms of matrix inequalities. A design procedure for the controller is also presented. Furthermore, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the optimal guaranteed cost controller that minimizes the upper bound of the closed‐loop system cost. The proposed control law can stabilize the closed‐loop system as well as guarantee H∞ performance level and a cost function with upper bounds for all admissible uncertainties. The results can be easily extended to the constant delay case. Finally, an illustrative example is given to demonstrate the effectiveness and advantages of the proposed 2‐D design approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2033–2045, 2013

Optimal Iterative Learning Fault‐Tolerant Guaranteed Cost Control for Batch Processes in the 2D‐FM Model

This paper develops the optimal fault‐tolerant guaranteed cost control scheme for a batch process with actuator failures. Based on an equivalent two‐dimensional Fornasini‐Marchsini (2D‐FM) model description of a batch process, the relevant concepts of the fault‐tolerant guaranteed cost control are introduced. The robust iterative learning reliable guaranteed cost controller (ILRGCC), which includes a robust extended feedback control for ensuring the performances over time and an iterative learning control (ILC) for improving the tracking performance from cycle to cycle, is formulated such that it cannot only guarantee the closed‐loop convergency along both the time and the cycle directions but also satisfy both the H∞ performance level and a cost function having upper bounds for all admissible uncertainties and any actuator failures. Conditions for the existence of the controller are derived in terms of linear matrix inequalities (LMIs), and a design procedure of the controller is presented. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the upper bound of the closed‐loop system cost. Finally, an illustrative example of injection molding is given to demonstrate the effectiveness and advantages of the proposed 2D design approach.

Delay-dependent guaranteed cost control for state-delayed system with disturbance and its application to engine idle speed control

This paper proposes a delay-dependent guaranteed cost control scheme for engine idle speed control (ISC) with induction-to-torque delay and external load disturbance. An augmented linearization model of engine at idle speed operating mode was developed based on physical principle and experiment data. To provide a compromise between disturbance rejection and other performance requirements of ISC, a multi-objective cost function upper bound was given, which can help us to take into account the fuel economy and disturbance rejection performance together in ISC. Poles constraint was added to the closed-loop system to guarantee convergence rates of state. The whole optimization solution to ISC can be solved under the framework of LMI. A commercial engine model was utilized to assess the performance of the controller. Simulation results on this model show us that designed controller can achieve desired performance.