ADAPTIVE POLE ASSIGNMENT CONTROL OF CD PLAYER ARM

Transcription

1 Vol. (5), 00, ADAPIVE POLE ASSIGNMEN CONROL OF CD PLAYER ARM A.Ara Khaael Department of Electrical Engineering University echnology Malaysia Skudai, Malaysia M.Nasiradeh* Department of Electrical Engineering University echnology Malaysia Skudai, Malaysia ABSRAC his study provides a design procedure for the self tuning adaptive control of a CD arm controller. he inputs are the forces of the mechanical actuators while the outputs are related to the tracking accuracy of the arm. he data was measured in closed loop, and then through a two-step procedure converted to open loop equivalent data the inputs are highly colored. Rely on the otained model, the parameters of the CD player arm will e estimated online and according to those parameters a self tuning poles assignment controller is designed to force the output to track a desire response. Keywords: Adaptive Controller, Pole Assignment Controller, Recursive Parameter Estimator, CD Player Arm. Introduction his study provides a design procedure for the self tuning adaptive control of a CD arm controller Data which is used to find the model structure of CD player arm has een taken from the mechanical construction of a CD player arm which Contriuted y Mechanical Engineering Systems and Control group of Delft University. he pole assignment control method is a common approach for designing closed-loop controllers in order to meet desired control specifications. Closed-loop poles are often replaced y assigning a characteristic polynomial ecause this polynomial plays a significant role as a closed loop characteristic equation of the system in the staility analysis of linear control systems and polynomial coefficients are simply related to controller and plant parameters. Another important issue in adaptive pole assignment controller design is to reduce the sensitivity of a system output to disturances with is achievale trough designing a feedack controller and making adaptive closed loop controlled system. he general structure of a self-tuning control scheme is shown in Fig.. Figure.. General structure of a Self uning Controller ISSN:

2 Vol. (5), 00, It consists of a parameter estimation module and a controller design module. Process model parameters are estimated from the input and output measurements. he estimated parameters are utilied to calculate the parameters of the control algorithm (Schumann, 985). he control signal is then generated and fed ack into the process/plant. he followings are the main principles of a Self uning control system: Plant s parameters (which are unknown or time-varying) are estimated using a parameter estimator ased on the control input signal, u (t), and plant s output signal, y (t). he estimated parameters are used in the design of the controller parameters via the controller design algorithm module i.e. the controller parameters are adjusted according to the estimated plant parameters. Any parameter estimation algorithm can e comined with any control algorithm. his results in SC eing a more flexile and powerful design. As it can e seen in Fig. adaptive control involves modifying the control law used y a controller to cope with the fact that the parameters of the system eing controlled are slowly time-varying or uncertain.. RECURSIVE PARAMEER ESIMAION Parameter estimation is a process of determining the values of coefficients relating different signals in a system. In SC, the aim of parameter estimation is to otain the coefficients of the transfer function of the plant to e controlled. he estimation process usually involves processing the input and the corresponding output signals of the plant. In this study, the force signal as an input and tracking signal as an output signals are fed into a parameter estimator, to processes them and produce the estimated transfer function of the plant. RLS is used to estimate the parameters of a transfer function in an online manner where the estimated parameters are updated at every sampling interval. Consider a discrete-time (D-) system in the form: N 0... N y( k) u( k) () which can e N a a... a N a written as: yk ( ) ayk ( ) a yk ( )... a N yk ( N a ) a () uk 0 ( ) uk ( ) N uk ( N ) 0,..., N and a,..., a N can e estimated using RLS algorithm y first transforming Eq. into a a regression equation, a a Na yk ( ) [ yk ( )... yk ( Na) uk ( )... uk ( Na)] (3) Na ( k ) he regression equation in Eq.3 aove is then used in the RLS algorithm, ( k ) L( k) ( k) (4) Current estimate is otained y adding a correction to the previous estimate Pk ( ) ( k) Lk ( ) (5) ( kpk ) ( ) ( k) L is known as the least squares weighting factor, which tells how the correction and the previous estimate should e comined. ISSN:

3 Vol. (5), 00, ( k) y( k) ( k) ( k ) (6) he Eq.6 gives the current estimation error. Pk ( ) Pk ( ) Lk ( ) ( kpk ) ( ) (7) In which, P is a matrix that is proportional to the variance of the previous estimates. is the forgetting factor that determines how fast old data are forgotten. If ρ is, no data will e forgotten. herefore, if the parameters to e identified are time-varying, as in this study ρ should take a value less than. he smaller is its value, the faster old data is discarded. As a start-up procedure, the following values are used:. (0) 0.. P(0) I, which is normally a very large numer. his will speed up the convergence process of the estimates to their true values.he RLS algorithm can e comined with any control design algorithm to form a SC system, where the design is ased on assuming that the estimated parameters otained are correct. 3. SELF UNING POLE ASSIGNMEN CONROL he control parameters are calculated ased on the estimated system parameters, otainale from the parameter estimation module which is RLS parameter estimator. he structure of a self-tuning pole assignment control method is shown in Fig. Figure. Structure of a Self uning pole assignment control he ojective of the Self uning pole assignment control is to improve the system s transient response, which can e done y changing the locations of the closed-loop poles which can make the output to track the reference input. It can e assumed that the discrete transfer function of plant model which is CD arm player control is as fallow: Ay() t But () B (8) yt () ut () A Where, na A a... a n n B 0... n A controller of the following form is used ISSN:

4 Fu() t Hr() t Gy() t H G ut () rt () yt () F F Where, F f... f n G g0 g... gn n H h0 h... hn A.Ara Khaael et al. / International Journal of Engineering Science and echnology Vol. (5), 00, n f h n Which the closed-loop response is therefore given y BH y() t r() t FA BG g f h g hus, the characteristic equation of the closed-loop system is given y FA BG 0 () Finally, the desired closed-loop characteristic equation ecomes FA BG (3) In which, is a desired characteristic equation which is designed ase on desired dynamic characteristics of the output signal of the plant model which is CD arm player in this study. 4. RESULS AND ANALYSIS Data which is used to find the model structure of CD player arm has een taken from the mechanical construction of a CD player arm which Contriuted y Mechanical Engineering Systems and Control group of Delft University. he input is the forces of the mechanical actuators while the output is related to the tracking accuracy of the arm. Fig 3, 4 In this study a plant model is assumed as in Eq. (4) and the parameter are estimated using recursive least square algorithm, then the adaptive pole assignment controller produces a control signal to control the plant to have a minimum overshoot and minimum rise time to reach our desired output response. (9) (0) () 0 y( k) u( k) a a (4) Figure.3. Input signals to the plant model Fig.4. Output signal correspondingly to the input signal ISSN:

5 Vol. (5), 00, he estimated parameters of the CD player arm are given in ale and Fig, 5 and control parameter of self tuning pole assignment controller is shown in Fig.6 Figure.5. he estimated parameters of the CD player arm ale. Estimated parameter of model transfer function of plant Parameters Estimated values Min Max Mean a a Figure.6. Self uning control parameters ISSN:

6 Vol. (5), 00, During the experiments an attempt was made to choose the est optimal control parameter to optimie the CD arm controller as desired. he maximum overshoot was aout %. he overshoot can e adjusted y changing the place of desired poles. 5. CONCLUSION Figure.7. he controlled output of system It has een found that CD arm player dynamics can e estimated y recursive estimation procedures. he convergence of the estimated parameters is quite good. he CD arm control system ased on the comination of a recursive estimation algorithm with a pole assignment control law adapts well to changes of the environmental disturances. 6. REFERENCES [] Boál, V., J. Böhm, J. Prokop and J. Fessl (999a), Practical Aspects of Self- uning Controllers: Algorithms and Implementation, VUIUM Press, Brno University of echnology, Brno (in Cech). [] Boál, V., J. Böhm, and R. Prokop (999), Practical aspects of self-tuning controllers, International Journal of Adaptive Control and Signal Processing, 3, 999, [3] Kučera, V. (99), Analysis and Design of Discrete Linear Control Systems. London, Prentice Hall. [4] Nguyen, H.D. (000), Self-tuning Pole Assignment and Optimal Control Systems for Ships, okyo University of Marine Science and echnology, okyo. ISSN: