5.LITERARTURE SURVEYManyworks have been done in the area of reducing the computational time of MPCamong which A.
G Wills, Dale Bates, Andrew J Fleming, Brett Ninness, and S.O. RMoheimani 3 suggests the use of explicit controller. It has good results athigh sampling rate. Depending on the longitudinal dynamics operating region oflateral dynamics varies. Explicit control law defined for a specificlongitudinal state, here longitudinal velocity, may not be valid for otherregions. This problem could be addressed by exploring the state space and findingset of explicit control laws.A, Bicycle ModelVelocity at each wheel is in the direction of thewheel at higher vehicle speeds, that the can no longer be made.
In this case,instead of a kinematic model, a dynamic model for lateral vehicle motion mustbe developed. A “bicycle” model of the vehicle with two degrees offreedom is considered. A method forelectronic stability control (ESC) based on model predictive control (MPC)using the bicycle model with lagged tire force to reflect the lagged characteristicsof lateral tire forces on the prediction model of the MPC problem for betterdescription of the vehicle behavior 2. To avoid the computational burden infinding the optimal solution of the MPC problem using the constrained optimalcontrol theory, the desired states and inputs as references are generated sincethe solution of the MPC problem can be easily obtained in a closed form withoutusing numeric solvers using these reference values.
The suggested method controlsthe vehicle to follow the generated reference values to maintain the vehicleyaw stability while the vehicle turns as the driver intended. The superiorityof the proposed method is verified through comparisons with an ESC method basedon ordinary MPC in the simulation environments on both high- and low-? surfacesusing the vehicle dynamics. Designand implementation of a stabilization algorithm for a car like robot performinghigh speed turns require control of such a kind of system 5. It is ratherdifficult because of the complexity of the physical wheel soil interactionmodel.
In this paper, it is planned to analyze the complex dynamic model ofthis process to elaborate a stabilization algorithm only based on the measurementof the system yaw rate. Finally, simulation is performed to evaluate theefficiency of this designed stabilization algorithmB, Model Predictive Control Symmetry in Linear Model Predictive Control (MPC) and defines a symmetryfor model predictive control laws and for model predictive control problems.Properties of MPC symmetries are studied by using a group theory formalismsuggested by Claus Danielson, Francesco Borrelli 1.
It showhow to efficiently compute MPC symmetries by transforming the search of MPCsymmetry generators into a graph automorphism problem. MPC symmetries are thenused to design model predictive control algorithms with reduced complexity. Theeffectiveness of the proposed approach is shown through a simple large-scaleMPC problem whose explicit solution can only be found with the methodA newapproach of employing model predictive control (MPC) where the difficultiesimposed by actuator limitations in a range of active vibration and noisecontrol problems are well recognized by Adrain G Wills and Dale Bates. MPC permits limitations on allowable control action to be explicitlyincluded in the computation of an optimal control action. Such techniques havebeen widely and successfully applied in many other areas. However, due to therelatively high computational requirements of MPC, existing applications havebeen limited to systems with slow dynamics.
It illustrates that MPC can beimplemented on inexpensive hardware at high sampling rates using traditionalonline quadratic programming methods for nontrivial models and with significantcontrol performance dividends. The problem of steering a non holonomic mobile robotto a desired position and orientation is discussed by KarlWorthmann, Mohamed W. A Model Predictive Control(MPC) scheme based on tailored non quadratic stage cost is proposed to fulfillthis control task. We rigorously prove asymptotic stability while neitherstabilizing constraints nor costs are used. To this end, we first designsuitable maneuvers to construct bounds on the value function.
Second, thesebounds are exploited to determine a prediction horizon length such that theasymptotic stability of the MPC closed loop is guaranteed. Finally, numericalsimulations are conducted to explain the necessity of having non quadraticrunning costs. C. Trajectory Tracking .Based on the kinematic equations of the mobile robot, a tracking error model isobtained by LIN Fengda1, LIN Zijian 4.This nonlinear model is linearized around origin.
Based on local linearizedmodel, an optimal controller is designed for the trajectory tracking problem byusing optimal linear quadratic (LQ) design approach. The simulation shows theeffectiveness of optimal LQR (linear quadratic regulator) controller for thecases where the robot tracks both straight and curve trajectories.