Abstract. 1 Introduction

Transcription

1 Performance index derivation for a self-organising fuzzy autopilot M.N. Polldnghorne*, R.S. Burns"*, G.N. Roberts' ^Plymouth Teaching Company Centre, University ofplymouth, Constantine Street, Plymouth PL4 8DE, UK *School ofmanufacturing, Materials and Mechanical Engineering, University ofplymouth, Plymouth, UK *Gwent College ofhigher Education, Allt-yr-yn Campus, Newport, UK Abstract The dynamic characteristics of marine vessels will alter with changes in environmental conditions and/or operating conditions. For a course-keeping autopilot to maintain a high level of performance it is necessary to achieve a form of on-line learning to enable the autopilot to determine any internal adjustments necessary as compensation. Considering a fuzzy logic design of autopilot, the formulation of a performance index is proposed to assess the level of vessel performance achieved, and to suggest suitable modifications as appropriate. 1 Introduction In general, ship autopilots still utilise the conventional Proportional plus Integral plus Derivative (PH>) control algorithm which is limited by fixed gain values. Whilst several new control techniques have been applied to the ship application in attempts to improve performance levels, few examples are intelligent and almost none are specifically for small vessels. Due to their limited draft and relatively short time constants in comparison to the tankers and freighters found on both the open sea and coastal waters across the world, the overall susceptibility of small vessels to incorrect controller action is of concern to current autopilot manufacturers. When external environmental disturbances are applied to the hull of a small vessel, the low inertia present creates little resistance to the induced heading change. The autopilot performance must therefore be particularly swift and decisive to counter any such effects by employing an opposing rudder condition, i.e. the autopilot must be working near its optimum performance level at all times.

2 758 Marine Technology and Transportation By designing a fiizzy logic autopilot for the small vessel application a significant increase in performance may be obtained when compared to the conventional PID alternative as demonstarted by Polkinghorae et al [1]. However, in order that this performance advantage may be maintained across the operating envelope it is a pre-requisite that on-line adaption must be present. The fundamental element of this type of self-organising fuzzy logic controller is the reliance on performance monitoring via a performance index Polkinghorne [2]. Polkinghorne et al [3] established the concept of the fuzzy logic foundation autopilot and validated its operation in comparison to the conventional PID controller. During sea trials this non-linear design of autopilot proved to be 50% faster when undertaking a 90 turn with a 25% reduction in rudder activity. This constituted a significant increase in performance, whilst also providing a much more efficient use of energy. Similarly, when attempting to maintain a desired course in moderate conditions, the novel design of fuzzy logic controller (FLC) improved performance by approximately 50%. It must be recognised that this new design of FLC still suffered from the main restriction associated with the PID version, i.e. the abscence of any online learning mechanism. The performance ability of the FLC controller, whilst improved across the operating envelope, remained dependant upon the settings for rudder ratio, counter rudder and trim. These values were input into the system by the installation engineer and could be subsequently altered by the mariner. The development of a learning mechanism which could be combined with the established foundation FLC design was therefore essential if the desired overall improvements in performance were to be obtained. Such a mechanism is called the self-organising controller (SOC) and is derived from an original application by Procyk and Mamdani [4]. 2 Fundamental Principles of SOC Operation The early SOC design has since been applied to a variety control applications Daley and Gill [5], Shao [6] and Mamdani and Stipaniciev [7]. Additional work by Yamazaki [8] and also by Sugiyama [9] has advanced the SOC performance capabilities to overcome early problems connected with the speed of learning and the SOC's poor ability to cope with steady-state errors. More recently marine applications have appeared Farbrother et al [10] and Sutton and Jess [11] which utilise the algorithm proposed by Sugiyama. In brief, this algorithm combines the two tasks of control and learning. Learning must be achieved by observing the operating environment and the controller's effect within that environment. By utilising this information, changes in the

3 Marine Technology and Transportation 759 fuzzy rulebase were determined in order that future activations of those rules will generate an improved level of performance. Having predetermined which observations are acceptable, and which are not, this information may be stored in a matrix format called a performance index (PI). If the observations of the operating environment indicate that the process is maintaining a satisfactory level of performance then no rule alterations will be required. Conversely, as the performance level deteriorates, then the magnitude of the rule changes increases. 3 Aspects of Learning The concept of the rulebase being empty, with subsequent learning to generate the correct rules, is not practical for this application. A vessel at sea with no control initially, then poor control during learning, followed by optimal control after convergence would create considerable safety problems. No vessel should be at sea under autopilot control unless that control is both predictable to other vessels, and corrective in nature with respect to the heading error. It could be argued that such learning would be a "one off' operation with the results being subsequently recalled from memory when the autopilot routine was activated. In practice, due to the time-variant nature of both the vessel dynamics and of the environmental conditions, such learning only meets the vessel's requirements at that particular time and will thus represent only a rough guide to the vessel's control requirements at any point in the future. Since a rough estimate of the performance requirements is already available in the form of the pre-set gain values for rudder ratio, counter rudder and trim, it is more realistic to attempt to incorporate this information into an elementary rulebase which could befinelytuned on-line using the SOC learning mechanism. By this means the autopilot may always retain the capability to control the vessel. Safety, predictability and minimum performance levels can thus be ensured at all times. The form of FLC used for this study employed two rulebases, one for the gain of counter rudder (derivative term), and the other for rudder ratio (proportional term). Having established the function of the two rulebases, it is important to realise that vessel performance will only be satisfactory if the contents of each rulebase is correct. In order to ensure that the rulebases are capable of correct operation, the performance indices are employed. Observations of the vessel performance are passed to the performance index in terms of the fuzzified heading error and fuzzified rate of change of heading error. Based on these observations, the performance index can enforce any required modifications to each rulebase. The ability of the SOC to achieve the correct modifications to the rulebases is fundamental to the its successful operation and is therefore dependant upon the content of the performance index utilised.

4 760 Marine Technology and Transportation 4 Performance Index Development Other SOC applications cited previously, have employed a single performance index (PI) to adjust their individual fuzzy rulebase. The PI design utilised here was based upon the traditional structure with the inputs being derived from the fuzzified heading error and rate of change of heading error information. The content of the Pis was set to zero for acceptable performance levels so that no change to the either enhancement matrix would result. When the performance level observed from the input data appeared to represent an aggregate gain being too high, then a negative PI value was set, thus reducing the rulebase value identified, and therefore generating a reduction in the aggregate gain. Similarly, for low performance levels, then the PI value was set positive to induce an increase in the rulebase value and a subsequent increase in the aggregate gain (Tables 1 & 2). Table 1. Performance Index for Rudder Ratio RateMError NB NM NS NT PT PS PM PB NB NM NS NT PT PS PM PB The magnitude of each element in the respective Pis was determined based upon experience, observations and an understanding of the nature of the learning required and as such may be considered to be application dependant. Poor performances are penalised by large magnitude whilst desirable performance levels generate no modification. Between these two extremes is a variety of permutations which reflect the non-linear set point positions in the fuzzy input windows. It is essential to take into account poor performances which are being modified correctly, e.g. a large heading error which is reducing at a large rate of change of heading error is an acceptable performance. However, why the large heading error was present could be related to either earlier incorrect control, or alternatively due to disturbance effects.

5 Marine Technology and Transportation 761 Table 2. Performance Index for Counter Rudder Rate\Error NB NM NS NT PT PS PM PB NB NM -1.6 NS -0.4 NT PT PS -0.4 PM -1.6 PB When the sea conditions become rough it is unrealistic to expect the vessel's performance to be maintained with the same quality of response possible during calm conditions. Given that the only external indicators concerning weather and vessel performance are the heading error and the rate of change of heading error, then an element of uncertainty regarding the exact cause of any irregularities in performance will remain. Assumptions regarding the learning required for generalised performance conditions are therefore a firm basis to initiate the development of the Pis The four key assumptions utilised for this study are: 1. If heading error and rate of change of heading error are approximately zero, then decrease the rulebase values slowly until a deterioration in performance is detected. Then increase them slightly to regain the previous performance level. 2. If heading error is NB with rate of change of heading error NB, or if heading error is PB with rate of change of heading error PB, then the performance is very poor and the rulebase values responsible are increased significantly. 3. If heading error is PB with rate of change of heading error NB, or if heading error is NB with rate of change of heading error PB, then the performance is very satisfactory and no modifications are required. 4. If the heading error is approximately zero, i.e. NT or PT, but the rate of change of heading error is NB or PB, then a medium size modification is required.

6 762 Marine Technology and Transportation Having established these performance assumptions, it is possible by interpolation to compute the detailed contents of each of the Pis. 5 SOC Performance Results By employing this design for the PI, in conjunction with the previously designed FLC, further sea trials were undertaken to identify how the SOC performed in comparison to the highly successful foundation fuzzy autopilot. Given the high level of performance obtained by the FLC, there was little anticipation of any signiifcant increase in peformance by utilising the full SOC. Learning was expected to occur in a gradual form which naturallyfiltersany incidental disturbance effects. Course-keeping tests were underaken for a 230 second period on a desired heading of 260 (Figures 1 to 4). SOC testing was caried out immediatley subsequent to the FLC tests to minimise any alterations in environmental conditions. The results for vessel heading and rudder responses are shown in Tables 3 and 4 respectively with comparison, where relevant, made between the SOC and the FLC results to indicate the magnitude of learning imposed. Given the quality of the previous FLC course-keeping response, the results obtained for the SOC are quite significant. As expected, there were no dramatic alterations in the controller's performance. However, after an analysis of the data, it is apparent that considerable further learning has occurred with notable consequences. In particular, when considering the vessels heading response, in comparison to the high performance obtained by the FLC, the range of 270 T Time (s) Figure 1: Heading Response for FLC Autopilot During Course-Keeping with a Desired Heading of 260?

7 Marine Technology and Transportation Time (s) Figure 2: Rudder Response for FLC Autopilot During Course-Keeping with a 270 T Desired Heading of 260? Time (s) Figure 3: Heading Response for SOC Autopilot During Course-Keeping with a Desired Heading of 260? movement, i.e. the heading error, has been restricted by the SOC a further 14%. Both the variance and the standard deviation of this response have also been reduced by 45% and 21% respectively. The course-keeping ability of the

8 764 Marine Technology and Transportation Time (s) Figure 4: Rudder Response for SOC Autopilot During Course-Keeping with a Desired Heading of 260? Table 3: Heading Results for SOC Course-Keeping Range of Error 0 Variance Standard Deviation SOC SOC/FLC % Table 4: Rudder Results for SOC Course-Keeping Range of Activity ( ) Variance Standard Deviation SOC SOC/FLC %

9 Marine Technology and Transportation 765 SOC is therefore far superior to that of the FLC. Since without learning in operation, the SOC and the FLC are the same controller, then this measured difference must be a reflection of the SOC's learning ability. It is therefore demonstrated that the SOC has the ability to learn on-line so that the vessel's performance may be improved to meet the relevant operational conditions. Having investigated the heading performance, it is also necessary to consider that of the SOC's rudder response. Clearly, to obtain such major performance improvements must require an alteration in the rudder movement. In comparison to the FLC, the results in Table 7.5 indicate that the range of rudder movement has increased by 28%. However, it is important to note that despite the greater range of movement being used, the rudder's variance and standard deviation have been reduced by a further 45% and 27% respectively compared to the FLC autopilot. References 1 Polkinghorne M.N., Bums R.S. and Roberts G.N. "Small Marine Vessel Application of a Fuzzy PID Autopilot." Proc. 12* IFAC World Congress, Sydney, Australia, Polkinghorne M.N. "A Self-Organising Fuzzy Logic Autopilot for Small Vessels." PhD Thesis, University of Plymouth, Polkinghorne M.N., Roberts G.N., Burns R.S. and Winwood D "The Implementation of Fixed Rulebase Fuzzy Logic to the Control of Small Surface Ships." IF AC Journal Control Engineering Practice, Vol. 3, No. 3, pp , Procyk T.J. and Mamdani E.H. "A Linguistic Self-Organising Process Controller." Automatica, Vol. 15, pp 15-30, Daley S. and Gill K.F. "A Design Study of a Self-Organising Fuzzy Logic Controller." Proc. IMechE, Part C, Vol. 200, pp 59-69, Shao S. "Fuzzy Self-Organising Controller and its Applications for Dynamic 7 Mamdani E.H. and Stipaniciev D. "Fuzzy Set Theory and Process Control, Past Present and Future." Proc. EFAC Symposium on Advanced Information Processing in Automatic Control, Frames, Yamazaki T. "An Improved Algorithm for a Self-Organising Controller." PhD Thesis, University of London, Sugiyama K. "Analysis and Synthesis of the Rulebased Self-Organising Controller." PhD Thesis, University of London, Farbrother H.N., Stacey B A and Sutton R. "Fuzzy Self-Organising Control of a Remotely Operated Submersible." Proc. EEE Int. Conference Control 91, Edinburgh, pp , Sutton R and Jess I.M. "Real-Time Application of a Self-Organising Autopilot to Warship Yaw Control." Proc. EEE Conference Control 91, Edinburgh, pp , 1990.