Nonlinear Optimal Control Technique Research Articles

Advanced motorcycle virtual rider

The target of this work is the development of a motorcycle virtual rider model that plans a trajectory and follows it. The reference speed and trajectory are obtained by applying the optimal manoeuvre method (i.e. a nonlinear optimal control technique) to a basic model of the motorcycle. Then, the vehicle control and guidance are obtained using a PID architecture and the gains vary with speed. Separated loops for speed and lateral motion controls have been implemented, the lateral motion control is complex because of the motorcycle instability, whereas the longitudinal control is simpler. The characteristics of the PID control are illustrated and discussed in detail, some examples are given for a cornering manoeuvre first and then for a run in the Mugello circuit.

Feedback linearization based computer controlled medication design for automatic treatment of parturient paresis of cows

Based on an existing model for calcium homeostatis (dynamics) and taking the help of feedback linearization philosophy of nonlinear control theory, two control design (medication) strategies are presented for automatic treatment of parturient paresis (milk fever) disease of cows. An important advantage of the new approach is that it results in a simple and straightforward method and eliminates the necessity of a significantly more complex neural network based nonlinear optimal control technique, as proposed by the author earlier. As an added advantage, unlike the neural network technique, the new approach leads to ‘closed form solution’ for the nonlinear controller. Moreover, global asymptotic stability of the closed loop system is always guaranteed. Besides theoretical justifications, the resulting controllers (medication strategies) are validated from numerical simulation studies of the nonlinear system as well. Moreover, from a numerical study about the robustness of the algorithms with respect to parametric uncertainty, it was observed that the optimal control formulation is a better option over the dynamic inversion formulation.

Optimal Trajectory Determination for Sagitally Symmetric Manual Lifting Tasks

A two dimensional, multi-link sagittally symmetric whole-body model was developed to simulate an optimal trajectory for manual material lifting. Non-linear optimal control techniques and genetic algorithms were utilized in the simulations to explore practical lifting patterns. The simulation results were then compared with the experimental data.

Implementation of linear and nonlinear optimal control techniques in a CO 2 absorption/desorption plant

A large-scale CO 2 Absorption/Desorption pilot plant has been used to investigate the feasibility of applying a Nonlinear Model Predictive Control technique — Receding Horizon Optimal Control (RHC) — and to investigate the performance of such algorithms when applied to a real system where mismatch between plant and model is always present. The performance, stability and robustness of the nonlinear algorithm are compared to those of a standard linear technique, Dynamic Matrix Control (DMC) applied to the same system. The critical nature of the various components of the RHC (model, estimator of unmeasured states and parameters, optimisation algorithm) has also been assessed. Moreover, the differences in performance of the algorithms in both simulations and experimental studies has been explored. Results showed that both the linear and nonlinear optimal control algorithms, performed extremely well in simulation studies and were able to achieve excellent control while minimising the overall cost. Implementation of the algorithms on the real plant, however, showed that good performance was critically dependent upon reducing the plant/model mismatch. This was especially true in the case of the nonlinear RHC algorithm. A problem which had to be resolved in on-line experimental implementation is the trade-off between improved model accuracy and computation time for both modelling and optimisation.

Nonlinear mixed H 2/H ∞ control for robust tracking design of robotic systems

A mixed H 2/H ∞ control design is proposed in this study for tracking of rigid 2 robotic systems under parameter perturbations and external disturbances. The design objective is that under a prescribed disturbance attenuation level (H ∞ attenuation constraint), the optimal least square error (H 2 optimal tracking) 2 must be achieved. Additionally, an explicit and global solution to this nonlinear time-varying mixed H 2/H ∞ control problem is presented by combining nonlinear minimax (Nash game) theory and LQ optimal control techniques. Moreover, by virtue of the skew symmetric property of robotic systems and adequate choice of state variable transformation, only two linear algebraic (instead of nonlinear timevarying) Riccati-like equations are required to construct the proposed mixed H 2/H ∞ tracking control law. Furthermore, these two linear algebraic equations 2 can be solved with a very simple method so that a closed-form nonlinear mixed H 2/H ∞ tracking controller can be constructed. Finally, extensive simulations are 2 made for mixed H 2/H ∞ tracking control of a two-link robotic manipulator. From the simulation results, the robust tracking performance of robotic systems by the proposed algorithm is remarkable.

Nonlinear optimal control of an alternating activated sludge process in a pilot plant

Abstract The application of a nonlinear optimal control technique to an alternating activated sludge process is presented. Faced with the time-varying features of the process, a parameter estimation procedure is designed and implemented based on a relatively simple process model established by the authors. New process variables are found and defined and a simplified state space model is developed to describe the nitrification and denitrification dynamics. The optimal control problem is formulated based on a criterion to minimize the daily average effluent nitrogen content in the face of a typical diurnal load variation. As the model and control problem exhibits strong nonlinearities, an iterative Newton-Raphson optimization method is applied to the problem. Simulation results and experiments in a pilot plant show that the new model and optimal control approach is successful and effective for improved nitrogen removal in the waste water treatment plant.

Synthesis of Optimal Control for an Infinite Dimensional Periodic Problem

We prove an existence and uniqueness result on periodic solutions of an infinite dimensional Riccati equation.