Possible Solution of Decoupling and Invariance of Multi-variable Control Loop by Using Binding and Correction Members

Transcription

1 WEA TANACTION on CICUIT and YTEM Poible olution of Decoupling and Invariance of Multi-variable Control Loop b Uing Binding and Correction Member PAVEL NAVATIL LIBO PEKA Department of Automation and Control Toma Bata Univerit in Zlin nam. T.. Maarka Zlin CZECH EPUBLIC pnavratil@fai.utb.cz pekar@fai.utb.cz Abtract: - The paper decribe one of poible method how to control of multi-variable control loop. In thi cae the ued method of control ue the o called main controller binding member and correction member. Thi control method combine claical approach for enuring decoupling of multi-variable control loop b mean of binding member and the ue of the correction member for enuring invariance of multi-variable control loop b mean of two approache. Main controller can be propoed b arbitrar ingle-variable nthei method. imulation verification of the ued control method i carried out for example of threevariable loop of a team turbine. Ke-Word: - Decoupling of control loop control invariance of control loop imulation. Introduction It i often required at large number controlled plant that their input and output variable have to be controlled imultaneoul. The example thee controlled plant are e.g. aircraft autopilot airconditioning plant chemical procee ditillation column team boiler pacecraft team turbine etc. []. In thee cae it mean that there i not onl larger number of independent IO (inglevariable control loop. Thee control loop are complex with everal controlled variable where eparate variable are not mutuall independent. Mutual coupling of controlled variable i uuall given b imultaneou action of each of input variable of controlled plant (manipulated variable and diturbance variable to all controlled variable. Thee control loop are called MIMO (multi-variable control loop and the are a complex of mutuall influencing impler control loop []. pecial cae of MIMO control loop i IO control loop that have onl one input ignal (diturbance variable manipulated variable and one output ignal (controlled variable [] []. One of poible example of MIMO controlled plant i alo an above mentioned team turbine [4] [6]. In the experimental part of the paper i conidered three-variable controlled plant of team turbine [4]. The elected method of control of the MIMO controlled plant ue the o called main controller binding member and correction member []. The main controller can be deigned via arbitrar IO nthei method e.g. [] [7] []. Binding member are determined from main controller and from parameter of MIMO controlled plant and enuring decoupling of MIMO control loop. Correction member are determined from parameter of MIMO controlled plant and enure an elimination of influence of diturbance variable on MIMO control loop i.e. the correction member enure invariance of MIMO control loop. In the next part of the paper are decribed two approache for enuring invariance of MIMO control loop b mean of correction member. The control method of MIMO control loop decribed in the next part of thi paper i conidered for MIMO controlled plant with ame number input ignal and output ignal. All imulation experiment were performed in the imulation mathematical education and reearch oftware MATLAB/IMULINK []. MATLAB i a widel ued tool not in education but alo in reearch; in addition to that man reearcher have produced a wide variet of educational tool baed on MATLAB [4] [5]. Multi-Variable Control Loop. Decription of ued multi-variable control loop It will be conidered multi-variable control loop with meaurement of diturbance variable via the following figure (ee Fig. []. IN: Iue 6 Volume June

2 WEA TANACTION on CICUIT and YTEM V( W( E( ( ( U ( U ( U( V ( ( Y ( Y V ( Y( Fig. - Multi-variable control loop with meaurement of diturbance variable The decription of the eparate parameter in the above mentioned multi-variable control i following i.e. ( V ( ( and ( are tranfer function matrice of a controlled plant diturbance variable controller and correction member. ignal Y( [n ] i a vector of controlled variable W( [n ] i a vector of etpoint U( [n ] i a vector of manipulated variable and V( [m ] i a vector of diturbance variable and it i conidered m n. Tranfer function matrice of controlled plant ( and diturbance variable V ( are conidered in form n Y ( n U n n nn where i j <... n> and i j ( ( ( V V Vm Y ( ( V V V m V i V V ( V j ( Vn Vn Vnm where i <... n> j <... m> m n. Tranfer function matrice of controller ( and correction member ( are conidered in form n ( n n n nn where i j <... n> and U i ( E ( j ( m U ( ( m i (4 V j ( n n nm where i <... n> j <... m> m n.. Decoupling of multi-variable control loop and invariance of multi-variable control loop It i often required at nthei of multi-variable control loop beide tabilit and qualit of control that one control variable caue a change of onl one correponding controlled variable i.e. elimination of effect of loop interaction. uch multi-variable control loop i called decoupled. Other requirement at nthei of multi-variable control loop can alo be elimination of influence of meaurable diturbance variable on controlled variable. uch multi-variable control loop i called invariant. Control loop at which the influence of diturbance variable i eliminated onl partiall (e.g. onl in tead tate are called approximatel invariant. The are often called alo invariant up to ε where ε i an error caued b incomplete elimination of influence of diturbance. Control loop at which the influence of diturbance on controlled variable i completel eliminated are called abolutel invariant. [] In order to enure decoupling and invariance of multi-variable control loop a cloed loop tranfer function matrix W/Y ( and tranfer function matrix of diturbance variable V/Y ( are ued therefore W/Y V/Y ( ( [ I + ( ( ] ( ( [ I + ( ( ] [ ( ( ( ] V (5 (6 For enuring decoupling of control loop tranfer function matrix W/Y ( mut be a diagonal matrix. Becaue the um and product of two diagonal matrice are diagonal matrice and the invere of diagonal matrix i alo diagonal matrix then the requirement can be enured if tranfer function matrix ( ( i diagonal. Thi condition i realized if (7 i valid kj ji jk i jk < n > jk (7 where kj are eparate member of a tranfer function matrix of controller ( and ji jk are algebraic upplement of eparate element of a tranfer function matrix of controlled plant (. It i conidered that diagonal i.e. main controller ii (i n are alread known from the firt deign of conception of control. Thee main controller are deigned via arbitrar IO nthei method [] [9]. elation (7 i ued to calculation of aide from diagonal member of a tranfer function matrix of controller ( (binding member which mean that above IN: 9-74 Iue 6 Volume June

3 WEA TANACTION on CICUIT and YTEM mentioned relation can be rewritten into the following form ji jj jj jj i j < n > (8 The other trateg how to enure decoupling of MIMO control loop can be found e.g. in [6] [9]. Abolute invariance of control loop can be enure if the tranfer function matrix of diturbance variable V/Y ( (6 i zero. Thi i poible if the following relation i valid ( ( V ( (9 Correction member of tranfer function matrix of correction member ( can be determined from ( n ki V kj det k det i < n > j < m > m n ( where det i a determinant of tranfer function matrix of controlled plant ( Vkj are eparate member of a tranfer function matrix of diturbance variable V ( and ki are algebraic upplement of eparate element of a tranfer function matrix of controlled plant (. In cae diagonal member of a tranfer function matrix of diturbance variable V ( are conidered a a dominant it i poible to implif the above mentioned relation. In thi cae it i conidered that internal coupling are omitted at MIMO control loop and thu n IO branched control loop with meaurement of a diturbance variable are gained. Connection of all IO branched control loop i the ame and the differ in eparate tranfer function of controlled plant controller correction member diturbance variable manipulated variable etpoint and controlled variable (ee Fig.. [] v i w i e i ii ii u i Vii Fig. - ingle-variable branched control loop with meaurement of diturbance variable Tranfer of correction member i then determined b uing the following equation ii i ii V ii ii i < n > ii i j i < n > j < m > m n ( where Vii are eparate member of tranfer function matrix of diturbance variable V ( and ii are eparate member of tranfer function matrix of controlled plant (.. Control of multi-variable control loop One of the poible method of control of MIMO control loop i decribed in thi part of the paper. The decribed method i demontrated on imulation example of three-variable of control loop of team turbine. The method of control i poible to divide into three baic part i.e. determination of parameter of main controller then enuring decoupling of control loop and finall enuring invariance of control loop. [] Main controller which are diagonal element of tranfer function matrix of controller ( are deigned b an nthei method of IO control loop. That mean parameter of main controller are determined for n IO control loop ( nn b mean of an nthei method of IO control loop. It i conidered that original diagonal tranfer function ii (i n of tranfer function matrix of controlled plant ( are modified to diagonal tranfer function iix (i n. In thee modified tranfer function influence of aide-fromdiagonal tranfer function of tranfer function matrix of controlled plant ( i.e. (i j i j n on original diagonal tranfer function i.e. ii (i n are included. Modified tranfer function iix i.e. x x x etc. are determined from ( b uing (5 and (7. n ii x i < n > ii j ii ( where ii are algebraic upplement of eparate element of a tranfer function matrix of controlled plant ( and are eparate member of a tranfer function matrix of controlled plant (. Decoupling of control loop i enured b mean of binding member (8 which are aide from diagonal member of a tranfer function matrix of controller (. Invariance of control loop which i elimination of influence of diturbance variable in the control loop i enured b mean of correction member b uing of equation ( or (. elation ( can be ued when influence of aide from diagonal element of a tranfer function matrix of diturbance IN: 9-74 Iue 6 Volume June

4 WEA TANACTION on CICUIT and YTEM variable V ( are not dominant. In thi cae invariance of control loop i enured b uing n IO branched control loop with meaurement of diturbance variable. imulation Verification of Decribed Method of Control of Multi-variable Control Loop. Three-variable controlled plant of team turbine Tpical example of MIMO controlled plant i a team turbine [5] [6]. In thi cae it i conidered the team turbine with two controlled withdrawal which drive electric generator uppling determined part of electric network which mean the turbine operate without phaing into power network []. The cheme of three-variable controlled plant of team turbine i hown in the Fig. [4]. ω VT VT m p M T NT ~ T NT m p Fig. - Three-variable control plant of team turbine Decription of eparate parameter which are in the cheme of three-variable control plant of team turbine are following: ω i a change of angular peed of turbo-generator p p are change of team preure in correponding withdrawal VT T NT are change of opening poition of control valve of high-preure (VT medium-preure (T and low-preure part of turbine (NT M i a change of electric load of turbo-generator and m m are change of ma flow of withdrawn team. Thee parameter repreent variable in three-variable control loop with meaurement of diturbance variable. Controlled variable (i are parameter ω p p manipulated variable (u i are parameter VT T NT and diturbance variable (v i are parameter M m m.. Mathematical model of three-variable controlled plant of team turbine Mathematical model of the controlled plant of team turbine i given b three differential equation ( - (5. Thee differential equation were gained alread after deriving and uing linearization from project OTOKOVICE elaborated b the firm ALTOM Power [4]. The firt differential equation repreent moment balance which i in the form 58.4 ω 6. ω p p M VT T NT ( econd and third differential equation repreent flow through flow pace which are in form.865 p.6 p.6 m' T.45 p.56 p. m' NT +.67 p.57 p VT T (4 (5 It i poible to rewrite the above differential equation ( - (5 into better form (8 - ( b introducing relative value i.e. with regard to tarting table tate-operational the o called calculated point at which relation of value can be generall written in the form X ϕ X X ϕ X ( X (6 ( X where eparate operational parameter of controlled plant of team turbine in the calculated point are following ( ω 68. [rad/] ( p 4 [bar] ( p.55 [bar] ( VT 9.5 [mm] ( T 59.9 [mm] ( NT 69.8 [mm] ( M 9789 [Nm] ( m' 6.94 [kg/] ( m' 6.94 [kg/] hence 57.7 ϕ 977.4ϕ ϕ ω ϕ ϕ 6. ϕ p ϕ.848 ϕ p +.64ϕ p NT ω ϕ 9789ϕ.54ϕ VT p.64ϕ.88ϕ T p 5.496ϕ VT M p + 5.9ϕ +.59ϕ T p 6.94ϕ 6.ϕ NT p 6.94ϕ m' m'. T (7 (8 (9 ( In the next tep it i carried out the Laplace tranform of the modified differential equation IN: 9-74 Iue 6 Volume June

5 WEA TANACTION on CICUIT and YTEM (8 - (. The are gained three algebraic equation out of which after arrangement it i poible to put together tranfer function matrix of the controlled plant ( ( and tranfer function matrix of diturbance variable V ( (4. The Laplace tranform of a vector of output variable i.e. vector of controlled variable i generall given b (. Y ( ( U( + ( V ( V ( where Y( i a vector of controlled variable U( i vector of manipulated variable and V( i a vector of diturbance variable. T Further it i conidered Y ( [ Φ ω Φ p Φ p ] ( T T U [ Φ Φ ] VT Φ T and V ( [ Φ NT M Φ m' Φ m' ]. After ubtitution it i poible to re-write ( in the following form (. Φ ω Φ Φ VT M Φ p + ( Φ V ( Φ m' ( T Φ p Φ NT Φ m' where ( ( ( V (4 tep repone and impule repone of tranfer function matrix of the controlled plant ( ( and tranfer function matrix of diturbance variable V ( (4 are hown in the following figure (ee Fig. 4 - Fig. 7. To: Out( Amplitude To: Out( To: Out( To: Out( Amplitude To: Out( To: Out( From: In( Impule epone From: In( From: In( Time Fig. 5 - Impule repone of tranfer function matrix of the controlled plant ( ( From: In( tep epone From: In( From: In( Time Fig. 6 - tep repone of tranfer function matrix of the diturbance variable V ( (4 To: Out( Amplitude To: Out( From: In( Impule epone From: In( From: In(. From: In( tep epone From: In( From: In( To: Out( Amplitude To: Out( To: Out( To: Out( Time Fig. 4 - tep repone of tranfer function matrix of the controlled plant ( ( Time Fig. 7 - Impule repone of tranfer function matrix the diturbance variable V ( (4. Control of three-variable control loop of a team turbine The procedure of control decribed in the paragraph Control of multi-variable control loop i ued at control of the three-variable control loop of a team turbine. Firt of all tranfer function of IN: 9-74 Iue 6 Volume June

6 WEA TANACTION on CICUIT and YTEM main controller are determined b mean of arbitrar IO nthei method for modified diagonal tranfer function x x a x (. After that binding member are determined b uing of (8. Thi relation erve to enuring decoupling of control loop. Finall parameter of correction member which enured invariance of control loop are calculated b uing of ( (abolute invariance or ( (approximate invariance. To determination of modified tranfer function (i wa ued ( then iix x x x ( ( ( hence ( x x x. ( At deign of parameter of main controller and which are diagonal element of tranfer function matrix of controller ( the following IO nthei method were ued a Whitele method [] [] b method of optimal module [] [8] c method of deired model [8] d pole placement method [9] []. It i ued a polnomial approach at deign of parameter of main controller b mean of pole placement method. Further it i conidered that root of the cloed control loop (pole which influence qualit and tabilit of the cloed control loop are elected like multiple root. It i poible to ue alo other method of parameter deign of main (diagonal controller of tranfer function matrix of controller ( e.g. Ziegler-Nichol method Nalin method the mmetrical optimum method IMC method etc. [] [7] []. To calculation of binding member (i j which enuring decoupling of control loop wa ued (8. It mean thee binding member were gained from the following relation ( ( ( ( ( ( (7 To determine of correction member which enuring invariance of control loop wa ued ( and (. elation ( enure abolute invariance of control loop e.g. the firt four correction member are following ( det ( det ( det ( det ( + + V ( + + V ( + + V ( + + V V V V V V V V V (8 where det i a determinant of tranfer function matrix of controlled plant ( and ki (k i are algebraic upplement of eparate element of a tranfer function matrix of controlled plant ( (ee (5 or (7. elation ( enure that control loop i approximatel invariant hence V V V i j i j < >. (9 Tranfer function matrix of controller ( with utilization of four choen IO nthei method for deign of parameter of main controller i following IN: Iue 6 Volume June

7 WEA TANACTION on CICUIT and YTEM a Whitele method ( ( ( ( ( ( The cheme of three-variable control loop i generall conidered according to the following figure (ee Fig. 8. b method of optimal module ( ( ( ( ( ( c method of deired model ( ( ( ( ( ( d pole placement method ( ( ( ( ( ( where aide from diagonal element of tranfer function matrix of controller ( wa calculated from (7. Tranfer function matrix of correction member ( i given b the relation (8 or (9. Correponding relation i alwa ued for all imulation experiment. elation (8 enure abolute invariance of control loop hence ( (4 elation (9 enure that control loop i approximatel invariant hence ( (5 Fig. 8 - Three-variable branched control loop with meaurement of diturbance variable.4 imulation reult Mathematical oftware MATLAB/IMULINK [] i ued for imulating verification of propoed control method of MIMO control loop. imulation cheme hown in the Fig. 9 i utilized for thee purpoe. Tranfer matrix of correction member v Tranfer matrix of diturbance variable Tranfer matrix of controlled plant Tranfer matrix of controller M ux D Diturbance variable Demux P etpoint Diturbance variable - v Controlled variable - M anipulated variable - u etpoint - w Fig. 9 - imulation cheme of three-variable control loop in the program MATLAB/IMULINK IN: Iue 6 Volume June

8 WEA TANACTION on CICUIT and YTEM imulation coure of three-variable control loop of a team turbine with utilization of choen IO nthei method at deign of parameter of main controller are preented in the following figure (ee Fig. - Fig. 7. Fig. - Fig. how imulation coure of three-variable control loop where abolute invariance (8 i enured. Fig. 4 - Fig. 7 how imulation coure of three-variable control loop where approximate invariance (9 i enured. The following parameter were choen and ued at all imulation experiment (ee Fig. - Fig. 7 etpoint vector (t w t w t w : [ 4] etpoint vector (w w w : [.8.8.8] diturbance vector (tv t v t v : [4 5] diturbance vector (v v v : [.5.5.5] tep (k:.5 total imulation (t : 6 u w v u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. - imulation coure of control loop with utilization of method of deired model for deign of parameter of main controller b enuring abolute invariance of control loop via (4 u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. - imulation coure of control loop with utilization of Whitele method for deign of parameter of main controller b enuring abolute invariance of control loop via (4 u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. - imulation coure of control loop with utilization of pole placement method for deign of parameter of main controller b enuring abolute invariance of control loop via (4 u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. - imulation coure of control loop with utilization of method of optimal module for deign of parameter of main controller b enuring abolute invariance of control loop via (4 u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. 4 - imulation coure of control loop with utilization of Whitele method for deign of parameter of main controller b enuring approximate invariance of control loop via (5 IN: Iue 6 Volume June

9 WEA TANACTION on CICUIT and YTEM u w v u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. 5 - imulation coure of control loop with utilization of method of optimal module for deign of parameter of main controller b enuring approximate invariance of control loop via (5 u w v u w v u w v u w v u w v u w v controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. 6 - imulation coure of control loop with utilization of method of deired model for deign of parameter of main controller b enuring approximate invariance of control loop via ( controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable controlled variable u - manipulated variable w - etpoint v - diturbance variable Fig. 7 - imulation coure of control loop with utilization of pole placement method for deign of parameter of main controller b enuring approximate invariance of control loop via (5 Variable in the figure (ee Fig. - Fig. 7 correpond to variable decribed in the threevariable control loop of team turbine (ee Fig. i.e. controlled variable: ϕ ϕ ϕ manipulated variable: u etpoint: w ϕ w ω p p ϕ u ϕ VT u T ϕ w ϕ ω p p ϕ diturbance variable: v ϕ v ϕ v ϕ NT M m' m'.5 Evaluation of imulation experiment obtained b uing of decribed method of control of multi-variable control loop To comparion imulation experiment the IE criterion (6 and ITAE criterion (7 were ued (ee Table and Table i.e. J J K K [ ] w( t ( t dt IE e ( t dt e ( t dt (6 ITAE t t e( t dt t e( t dt t t ( w( t ( t dt (7 where t r i of control t i of imulation w(t i etpoint (t i controlled variable e(t i control error (ee Fig. 8. (t ( t r (t (t w(t ( t δ ( (δ -5% Fig. 8 - Poible coure of control loop Table - Qualit of control for imulation example of three-variable control loop b enuring invariance of control loop via (4 nthei method * JK JK JK IE ITAE IE ITAE IE ITAE t IN: Iue 6 Volume June

10 WEA TANACTION on CICUIT and YTEM Table - Qualit of control for imulation example of three-variable control loop b enuring invariance of control loop via (5 nthei method * JK JK JK IE ITAE IE ITAE IE ITAE * Number in the previou table (Table and Table in the column nthei method repreent the ued IO nthei method of at deign of parameter of main controller i.e.: - Whitele method - method of optimal module - method of deired model 4 - pole placement method. Optimal adjutment of control loop i conidered here from the point of view of minimal ize of IE criterion or ITAE criterion (Table and Table. However quite different point of view can be rall conidered for optimal adjutment. Namel requirement for the mallet overhooting and for the hortet of control are generall valid for optimal adjutment. However thee requirement are antagonitic and therefore the optimal adjutment of controller i alwa a compromie between them. Degree of internal coupling of MIMO controlled plant i often evaluated via A (elative ain Arra [8] [] []. A value are depended on frequenc. Thee value are uuall determined for frequenc equal to zero i.e. for tead tate. From the point of view of control it i ideal tate when value of diagonal element of A matrix are approaching to the value of one and aide-fromdiagonal element of A matrix approaching to the value of zero. The A matrix (Λ can be calculated from the following equation Λ (j T T ω ( (jω ( ( ( (8 where ( i a tranfer function matrix of examined object ( jω e.g. MIMO controlled plant MIMO cloed loop operator implie an element b element multiplication (chur product. It i poible to ue A value to compare propertie of original MIMO controlled plant and MIMO control loop from the point of view degree internal coupling. A matrix of three-variable controlled plant i following Λ ( ( ( and A matrix of cloed loop tranfer function matrix W/Y ( of three-variable control loop for all MIMO controller ( - ( i in the form ( / Y Λ W ( (4 It i obviou from the imulation of control loop hown above (ee Fig. - Fig. 7 that the condition of decoupling of control loop wa fulfilled. Fulfilment of thi condition wa enured via binding member which are aide-fromdiagonal element of tranfer function matrix of controller ( ( - (. Binding member were determined from o called main controller which are main diagonal element of the tranfer function matrix of controller. The determination of main controller i carried out b an IO nthei method for modified diagonal element of the tranfer function matrix of controlled plant. From the imulation of control loop i alo obviou that the control loop i abolute invariant (ee Fig. - Fig. and (4 let u a approximate invariant (ee Fig. 4 - Fig. 7 and (5. In thi econd cae influence of diturbance variable i eliminated onl at tead tate. Fulfilment of thi condition wa enured via eparate element of tranfer function matrix of correction member ( (4 - (5 i.e. via correction member. Correction member were determined from tranfer function matrix of the controlled plant and diturbance variable. 4 Concluion In thi paper wa to decribed and hown the one of poible approache to control of MIMO control loop. Advantage of decribed and ued control method i it implicit. Thi control method enable to ue an known IO nthei method to deign of main controller. The control method combine claical wa of enuring decoupling of control loop via binding member which are aidefrom-diagonal element of tranfer function matrix of controller ( and the ue of the correction member for enuring abolute invariance or approximate invariance of MIMO control loop. imulation verification of propoed control method wa preented on three-variable control loop of team turbine. Deigned parameter of matrix controller and correction member have good reult of the control and fulfilled baic control requirement uch a the IN: Iue 6 Volume June

11 WEA TANACTION on CICUIT and YTEM tabilit the reference ignal tracking and diturbance attenuation. The decribed and ued control method i valid under the following condition i.e. thi method can be ued onl for MIMO controlled tem with ame number of input and output ignal. MIMO controlled plant containing tranport dela nonminimal phae or having high order dnamic can be alo caue of certain limitation of the control method. The future work will be focued on the reduction of limitation of propoed control method verification of alternative approach to enuring decoupling of control loop [9] and alo imulation verification of propoed let u a modified verion of control method for other MIMO controlled plant e.g. model of balance platform tem [] model of heating tem []. Acknowledgement Thi work wa upported b the Minitr of Education Education Youth and port of the Czech epublic under grant No. MM eference: [] J. Balate Automatic Control nd edition. Praha: BEN - technical literature 4. (in Czech [] K. Dutton. Thompon and B. Barraclough The art of control engineering. Eex: Addiion Wele Longman Pearon Education 997. [].C. oodwin. F. raebe and M. E. algado Control tem deign. New Jere: Prentice Hall Upper addle ive. [4] ALTOM Power Ltd. Material of the compan from the project OTOKOVICE 998. (in Czech [5] J. Kadrnozka and L. Ochrana Combined heat and power production. Brno: CEM. (in Czech [6] J. Kadrnozka Thermal-turbine and turbocompreor. Brno: CEM 4. (in Czech [7] K. Åtröm and T. Hägglund PID Controller: Theor Deign and Tuning nd edition North Carolina: Intrument ociet of America eearch Triangle Park 995. [8] M. Viteckova and A. Vitecek Bae of automatic control nd edition Otrava: VŠB- Technical univerit Otrava 8. (in Czech [9] K. K. Kiong W. Q. uo H. C. Chien and T. Hägglund Advance in PID control. London: pringer-verlag 999. [] A. Datta M.T. Ho and. P. Bhattachara tructure and nthei of PID controller London: pringer-verlag. []. Prokop. Matuu and Z. Prokopova Automatic control theor - linear continuou dnamic tem. Zlin: TBU in Zlin 6. (in Czech []. Wagnerova and M. Minar nthei of control loop [Online] Available from: nteza/index.htm (in Czech [] P. Karban Computing and imulation in program Matlab and imulink. Brno: Computer Pre 6. (in Czech [4] M. Popecu A. Bitoleanu and M. Dobriceanu Matlab UI application in energetic performance anali of induction motor driving tem WEA Tran. on Advance in Engineering Education Vol. No. 56 pp. 4-. [5] A. Datfan Implementation and Aement of Interactive Power Electronic Coure WEA Tran. on Advance in Engineering Education iue 8 Volume 4 7 pp [6] P. kupin W. Klopot and T. Klopot Dnamic Matrix Control with partial decoupling In: Proceeding of the th WEA Int. Conf. Automation & information pp [7]. eing Implementabilit of egulation and Partial Decoupling of MIMO Plant In: Proceeding of the 4th Mediterranean Conf. on Control and Automation 6 pp. -6. [8] F. Duek and D. Honc Tranform of tem with different number of input and output ignal for decentralized control Automatization Vol. 5 No pp (in Czech [9] K. Warwick and D. ee Indutrial Digital Control tem nd edition. Intitution Of Engineering And Technolog 988. [] J. Lee D.H. Kim and T.F. Edgar tatic Decoupler for Control of Multivariable Procee AIChE Journal Vol. 5 No. 5 pp []. kogetad and M. Morari Implication of large A element on control element Ind Eng ChemFundam 987 pp. -. [] A. Kot and A. Nawrocka Balace Platform tem Modeling and imulation In: Proceeding of the International Carpathian Control Conference pp [] L. Pekar. Prokop and P. Dotalek Circuit heating plant model with internal dela WEA Tran. on tem Vol. 8 No. 9 9 pp IN: Iue 6 Volume June