| Just about every real-world dynamical system is nonlinear. Present methods of controller design entail linearizing the nonlinear plant and then using the wealth of tools available for controlling a linear system. These tools have been well understood for many decades now. The problem with this is not in the tools, but in the linearization itself. Large disturbances in the system may cause the plant to operate well away from the pre-selected linearized operating point; in which case, the designed controller may be quite erroneous.; Neural networks have emerged as a viable method for the control of nonlinear dynamic systems. The backpropagation-through-time algorithm trains neural network controllers to perform nonlinear optimal control. Here, we discuss the conventional optimization technique for finding an optimal control profile (steepest descent dynamic optimization) and discuss its relationship to the backpropagation-through-time training algorithm for neural networks. The point is made that a properly trained neural network controller finds a mapping between the states and an optimal control profile (in the dynamic optimization sense). This relationship is exploited to discover a rule-of-thumb for the number of weights to use in the neural network.; Also discussed are practical issues relating to control systems. Using potential functions it is shown how to handle linear saturation and incorporate typical performance objectives of a control system, such as rise time, settling time and overshoot, into the neural network training process. The end result is a neural network controller which produces near optimal solutions which can handle linear saturation and meet performance specifications, automatically.; These contributions are applied to a simulated electric power system. A large disturbance is introduced to the system, which causes output voltage to swing and can even cause destabilization of one or more generators. A neural network controller is trained to work on top of existing controls in the power system, to improve voltage regulation and stability. Results indicate improved regulation and stability over conventional controls, and near optimal performance (compared with dynamic optimization). |
