Adaptive Neural Network Control of Engine RPM Steve Rogers, Institute for Scientific Research, srogers@isr.us Abstract Conventional fixed controllers in combination with adaptive neural networks provide a powerful controller architecture. By utilizing the existing controller designs and augmenting them with adaptive neural networks engineers may exploit the merits of both control approaches. By adding on an adaptive component to the existing controller the range of operating conditions is increased and robustness to system degradation is improved. One of the simplest neural network controllers is the adaptive linear combiner. In this paper the adaptive linear combiner is described and the controller architecture is applied to an engine rpm controller. Results are given. Keywords: engine control, adaptive linear combiner controllers Introduction Adaptive neural networks (ANN) are used in system identification and control, among other applications. To achieve quality tracking in control applications or accurate identification requires responsive adaptation rules. A linear combiner is a subset of a radial basis function neural network. ANN’s have been most successful when used as an add-on component to an existing controller1. The general diagram is shown below. The objective is for the neural network to adapt as necessary to account for anomalies outside the capability of the conventional controller. It is necessary for the control system to maintain performance criteria in the face of
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Figure 1, Neural Network controller in conjunction with a conventional controller1 anomalies including equipment degradation, wear, fouling, sensor faults, etc. Adaptive linear combiners are a good candidate for this application due to their capabilities to model and control a wide variety of operating conditions. This paper presents an adaptive linear combiner in conjunction with a linear
conventional controller applied to an engine rpm control system. The paper is organized as: 1) introduction, 2) linear combiner fundamentals, 3) engine rpm model, 4) simulation, and 5) conclusion. Linear Combiner Fundamentals If the linear combiner update mechanism is considered a plant to be controlled, control system principles may be applied. Figure 1 illustrates the idea of the linear combiner. The basic linear combiner equations are shown below: e = y − yˆ yˆ = wφ w& = µφe
where e is the error to be driven to zero, y is the actual signal to be tracked, yhat is the estimate, ϕ is an appropriate set of plant measurements, w is the connection weight vector, and µ is the learning rate.
Figure 1 Linear Combiner with and without control circuit The bottom part of the figure shows how a control structure may be inserted into the linear combiner. The simplest control structure is the standard learning rate µ. A proportional integral (PI) structure is the next simplest controller. It has the form: Kp
(s + a ) , which gives another integrator plus a zero. Note also that s
Kp may be combined with µ. This structure has been used to improve state estimators. Obviously, any control structure may be used including lead-lag, PID, servo type PID’s, etc. Engine RPM Model
The engine rpm model is in simulink and is part of the set of demonstrations provided in the mathworks software package. The top-level code is shown in Figure 2 below.
Figure 2 High level simulink model from Mathworks Note that it has variable timing so that normal linearization techniques will not apply without modification of the timing block. The Controller block at the left of Figure 1 was modified for optimization. The drag torque block at the lower right of Figure 2 produces the load disturbances to the simulation.
Figure 3, Lead-lag controller with ANN controller Note how the ANN control block is integrated with the controller in Figure 3 as is shown in Figure 1.
Figure 4, Simulink code for adaptive linear combiner Simulation
Figure 5, Engine RPM simulation results with and without the adaptive linear combiner The model described above was simulated to test the concept for a throttle valve that was suddenly, at 50 seconds into the simulation, restricted to 20% of its original capacity. The results of the simulation are shown in Figures 5-8. The sum of the absolute setpoint error was used as a performance criterion. The rpm setpo int − rpm measured , where PF is the performance criterion. PF with an adaptive equation is PF =
∑
linear combiner = 1.3027e+04. PF without an adaptive linear combiner = 4.1633e+004, which shows a significant improvement and a possible direction for future research.
Figure 6, Simulation results showing load variation, command throttle degrees, and rpm error without adaptive controller
Figure 7, Simulation results showing load variation, command throttle degrees, and rpm error with adaptive controller
Figure 8, Adaptive controller command signals Conclusions An approach to using adaptive neural network controllers to offset the effects of throttle valve degradation applied to engine idle control has been presented. The approach uses the solution for a discrete lyapunov equation for the adaptive weight update laws. It is shown to help converge very quickly to offset the throttle valve degradation. Further areas of investigation include improved weight update criteria, addition of nonlinear ‘squashing’ functions, and applications to other types or causes of engine performance degradations. References: 1) Lewis, F., ‘Nonlinear Network Structures for Feedback Control,’ http://ARRI.uta.edu/acs. 2) Spooner, J and Passino, K., ‘Decentralized Adaptive Control of Nonlinear Systems Using Radial Basis Neural Networks,’ IEEE Transactions on Automatic Control, v. 44 ,no. 11, Nov., 1999. 3) Eric N. Johnson and Anthony J. Calise. ‘Limited Authority Adaptive Flight Control for Reusable Launch Vehicles’ AIAA Journal of Guidance, Control, and Dynamics, 26(6):993-1002, Nov-Dec 2003 4) Naira Hovakimyan and Anthony J. Calise. ‘Adaptive Output Feedback Control of Uncertain MultiInput Multi-Output Systems using Single Hidden Layer Neural Networks,’ International Journal of Control, 2002.