selection of operating conditions for the co-ordinated setting of robust fixed-parameter stabilisers

Selection of operating conditions for the co-ordiniated setting of robust fixed-parameter Stabilisers

H. F. Wa ng

Indexing ferms: FA CTS-liased s fdilisers, PSS, 0.rciNation s f ability, Rohur fness, Co-ordination

Abstract: The I S S U ~ the selectioii of operating conditions for :,tabiliser design in multimachine power systems is discussed, and a method is proposed to consduct the selection so as to achieve robust design of multiple fixed-parameter stabilisers. The co-ordination among different types of stabilisers, such as PSS, and FACTS- based stabilisers, is considered by the method proposed. An example three-machine power system is demonstrated in the paper, where a TCSC-based stabiliser and PSS are designed in co-ordination to damp two-mode oscillations. The correct selection of operating conditions for the stabiliser design has made them robust to the variations of sys .em operating conditions.

1 Introduction

In a multimachine power system, stabilisers are usually designed under a t>.pical operating condition. With the variations of system operating conditions, the effectiveness of the stabilisers changes. This problem of robustness of stabilisers to the variations of power system operating conditions has been known about for a long time. Great effort has been directed to the development of advanced stabilisers, such as adaptive, fuzzy logic and intelligent stabilisers, to increase stabiliser's robustness, which usually results in variable-structureiparam- eter stabilisers [l, 21.

However, the conventional method for ensuring a stabiliser's effectiveness is the careful selection of the typical operating condition under which stabilisers are designed. This method leads to fixed-parameter stabilisers and has been :;uccessful in single-machine power systems for power system stabilisers (PSS) design [3, 41. But, so far, further development of the method to the multimachine power system has not been investigated. A simple procedure of selecting the typical operating condition for stabiliser design in the multimachine power system is adopted sometimes by choosing the operating condition under which the power system has the worst oscillatioii damping. This selection is based on the hope that stabilisers would be able to handle the 0 IEE, 1998 IEE Pr0ceedinE.T online no 1998 1666 Paper received 9th June 1997 The author is with the Ur'iversity of Bath, Department of Electrical and Electronic Engineering, Claverton Down, Bath BA2 7AY, UK

cases when the power system has better oscillation damping, so that automatically they are robust to the changes of system operating conditions once they al-e designed at the operating condition with the worst oscillation damping.

With the recent development of flexible AC transmission systems (FACTS), the FACTS-based stabilisers, such as static var compensator (SVC)-based, thyristor controlled series compensator (TCSC)-based supple- mentary damping controllers, have shown great poten- tial in improving power system oscillation stability [5-lo]. So, in a multimachine power system installed with different types of stabilisers (FACTS-based stabilisers and PSS) to damp multimode oscillations, the investigation into the selection of typical operating point is more complicated. The difference in the changing pattern of the effectiveness of individual stabilisers to the variations of power system operating conditions would make it more difficult to choose a common typn- cal operating condition at which the co-ordination of multiple stabilisers can be achieved. Therefore, to obtain a co-ordinated design of multiple robust stabilisers in the multimachine power system, it is important to select proper typical operating conditions.

In this paper, the issue of the selection of operating conditions for stabiliser design in multimachine power systems is discussed, and a method is proposed to con- duct the selection to achieve robust design of multiple stabilisers. The co-ordination among different types of stabilisers in multimachine power is achieved by sequentially setting the phase of transfer function of every stabiliser and simultaneously tuning the gains of all stabilisers. The robustness of the stabilisers is ensured by the correct selection of the typical operating conditions for stabiliser design. In the paper, an example three-machine power system with two-mode oscillations is presented, where a robust PSS and TCSC- based stabiliser are successfully designed by the method proposed.

2 systems

The Phillips-Heffron model of an n-machine power system installed with M , FACTS-based stabilisers and M, PSSs is shown in Fig. 1 and can be expressed as [I 11:

Multichannel model of multimachine power

SA6 = w o a w

k = l

111 IBE Proc -Gener. Transni D, strib., Vol. 145, No. 2, March 1998

k=l

(1) where Au,, and nupk are the output control signal of the kth FACTS-based stabiliser and PSS respectively, K,, K2, K3, K4, K,, Kb E Rnxn are coefficient matrices determined by the system operating conditions, kpi,, kqk, kVl, E Rnx‘ are coefficient vectors related to the system operating condition and installing location of the kth FACTS-based stabiliser and:

Ii, = [0 . . . 0 10 . . . OIT E RnX1 kth column

if the kth PSS is installed on the kth machine.

TD = diag(Ti,,,) M = diag(2H,) EX(s) is the transfer function matrix with EX($) = diag[Ex,(s)], i = 1, 2, ..., n and Ex,(s) is the transfer function of the AVR of the ith machine in the power system. diag(z,) denotes an n-order diagonal matrix with diagonal element to be 2,.

EX (SI

Fig. 1 tem

Un2Jied form of Phillips-Heflron model of n-machine power sys-

From Fig. 1, we can obtain the forward path of the output control signal of the kth stabiliser (FACTS- based stabiliser or PSS) to the electromechanical oscillation loop to be:

F k ( S ) = k p i , - K2[KS + STD + EX(S)K6]-’

[ k q k + E X ( s ) k V k ] (FACTS-based stabiliser)

F k ( S ) = - Kz [ K3 + STD + E X ( S ) Ke] -’ E X ( S ) Ii,

(PSS) (2)

a u k = G(S)Yk ( 3 )

yk = yic,(s)Aw3 j = 1 , 2 , ..., n (4)

If the transfer function of the kth stabiliser is Gk(s) and the feedback signal is Y k , that is:

where nu,< is Au, or Au,,. Appendix 7.1 shows that any yk can be expressed as:

If it is assumed that there are L oscillation modes in the n-machine power system, which need to be damped

112

by M I + M2 stabilisers, to the ith oscillation mode A , the damping torque provided by the kth stabiliser to the electromechanical oscillation loop of the j th generator is:

A T D k a 3 = Re[Fkj(X,)Ykj ( X i ) G k ( A i ) ] A u j

j = 1 , 2 , ..., n (5) where Fkj(Ai) is thejth element of Fic(Ai) in eqn. 2.

Eqn. 5 indicates that, in the multimachine power system, the damping torque is contributed by a stabiliser to every machine through a single forward channel:

Fi,] (&)Ti,] (Ai) H k j i y k j (6) So, there are a total of 72 channels through which the stabiliser provides all machines the damping torque.

However, in the multimachine power system, the sources of the oscillations associated with different oscillation modes may be different. If a stabiliser provides a machine with a certain amount of damping torque which results in little improvement of the damping of an oscillation mode, we can believe that, to the oscillation mode, the machine is not the ‘source’. Based on this understanding, to the oscillation mode Ai = -ti k j q , the damping of which is mainly characterised by [i, we can define the sensitivity of 5, to an addition of the damping torque on the j th machine DGqAq as S,:

( 7 ) at , s,, = ~

8DGij So, the total improvement of the damping of the oscillation mode Ai due to the addition of a damping torque on all machines is:

From eqn. 5 we can have: M

ADG,, = R e [ F k , ( h ) Y k 3 iA,)aGk(A,)] (9)

where M = M I + M2. From eqns. 6, 8 and 9 we obtain: k=l

n M

j=1 k=l

According to eqn. 10, a model describing the pattern that M stabilisers in the n-machine power system provide L oscillation modes with damping is shown in Fig. 2.

No. 1

stabii isers machines oscillation modes

Fig. 2 modes in multimachine power system

Multichannel model of .stabilisers providing dumping to oscillation

IEE Psoc.-Genes. Tsansm Distrib.. Vol. 145, No. 2, March 1998

From Fig. 2 it can be seen that a stabiliser in the n- machine power sy8jtem provides damping to an oscillation mode through two groups of n channels. The first group of n channels are the forward paths through which the stabiliser supplies damping torque to every machine in the power system. The second group of n channels are the connections between the damping of the oscillation mDde and the addition of damping torque on machines, through which the damping torque is converted into the damping of the oscillation mode. Therefore, this model presents a full and clear picture about how a FACTS-based stabiliser or a PSS distributes and contributes damping to oscillation modes in the multimachine power system.

3 the co-ordinated setting of multiple robust stabilisers

Selection of a typical operation condition for

Assume that the set of all known operating conditions of the n-machine power system is Qo. For the kth stabiliser and the ith oscillation mode, at all operating conditions pcc(m) E no, we can calculate the weights attached to each channel in the multichannel model of Fig. 2, i!+k = SjiH,,,, . j = 1, 2, ..., n , and then obtain a total weight:

n n

j = 1 j=1

(11) Wi/< measures the damping provided by the kth stabiliser to the ith oscillation mode. So, it presents an index to estimate the effectiveness of the kth stabiliser to sup- press the oscillation associated with the ith oscillation mode in the power system. If we have:

K k ( 1 7 1 . t ) = r~lin[wzk(17~)] p & k ( m ) E 0 0 (12) m

we know that the stabiliser is least effective in damping the oscillation at the operating condition pil,(ml) E Qo. So, if we choose ~ ~ / < ( m ~ ) E Qo as the typical operating condition to design the stabiliser, an effective design of the stabiliser at pL,:(mr) E no can ensure the effectiveness of the stabiliser at all operating conditions pjlc(wz) E no due to eqn. 12. Therefore, by selecting the typical operating condition according to eqn. 12, the robustness of the stabiliser to the variations of power system operating conditions is achieved.

This selection m,zy result in different typical operating condition for different stabilisers and oscillation modes. So, it may be difficult or impossible to select a common typical operating condition at which all stabilisers can be designed simultaneously in co-ordination. On the other hand, if they are designed in co-ordination at a common operating condition simultaneously, their robustness may not be ensured, owing to the difference in the changing pattern of their effectiveness to the variations of system operating conditions. Such an example is given in this paper.

However, if stabilisers are designed one by one in a sequence, the problem of 'eigenvalue drift' [ 121 cannot be avoided. Therefxe, to achieve the co-ordinated setting of multiple fi xed-parameter robust stabilisers, a new method is proposed as follows.

3. I Sequential setting of the phase of the stabilisers For simplicity of expression, we use the conventional

IEE Proc.-Genei.. Trunsm l) istrih, VoI 145, No. 2, Murclz 1998

form of the transfer function of stabilisers:

= K k T k ( S ) (13) It is assumed that the kth stabiliser is designed mainly to improve the damping of the ith oscillation mode in the power system Ai = -ti k.jc0,. Without loss of gener- ality, we assume that, at the typical operating condition of the kth stabiliser selected by use of eqn. 12, S,, 2 Si2 2 ... 2 sin.

Then a compensation angle is chosen to satisfy: 90" > q5k - $9k3 > 0" j = 1 , 2 , ...,n (14)

If such a compensation angle cannot be obtained, the selection of the compensation angle @,' can be made among the first (n - 1) machines to satisfy:

This procedure can be continued until such a compensation angle is obtained. Then T,(s) is set to have a phase angle -@,<, that is, TIt(Ai) = TkL - 4k. So, from eqn. 10, the damping contribution by the kth stabiliser to A; can be expressed as:

90" > (bk - $9kj > 0" j = 1 , 2 , ...,?'- 1 (1,s)

n

a t z ( k ) = ~ s ~ ~ H ~ ~ T ~ c o s ~ ~ ~ A I x - ~ j = 1 , 2 , ...; n

(16) j=1

where Plcj = + qltj. The procedure above in selecting the compensation angle ensures that 0 > f i k j > -90" is tenable to the machines which are more sensitive to A, so that they are provided with a positive synchronising torque. Eqn. 16 shows the damping contribution to the ith oscillation mode by the kth stabiliser.

3.2 Simultaneous gain tuning From eqns. 8 and 16 we have:

M .M N

k=l iC=l3=1

(1'7) Eqn. 17 demonstrates the total damping iinprovemeiit by M stabilisers. It also indicates that, after every TL(s) is set, the damping improvement of the oscillation mode is determined by tuning stabilisers' gains, AKk = Kl< *

Assume that the target damping of the oscillation modes by the co-ordinated design of A4 stabilisers is -5,*, i = 1, 2, ..., L. An objective function can be formed to be:

L

J(W = sz[rdw - <,*I2 (18) 2 x 1

where K is the gain vector of the stabilisers K = [K, K2 ... KMIT. To find the solution of the objective function, the steepest descent algorithm is used here:

K ( n + 1) = K ( n ) - st x B J [ K ( n ) ] (19) where st is the single-dimension optimal searchirig length and VJ[K(n)] is the gradient of J(K> with respect to K as:

By using eqns. 18 and 19, the gains of M stabilisers are tuned simultaneously, which will assign L oscillation modes accurately to the positions on complex plane with target damping.

This simultaneous tuning of all gains of stabilisers is conducted at the typical operating condition of each stabiliser. At the typical operating condition of the first stabiliser, the initial values of the gains are simply taken to be zero. From the typical operating condition of the second stabiliser onwards, the gain values set by the previous tuning are taken to be the initial values to start the current tuning. Also in the tuning process, the following constraint is checked:

I&(WJ L IC1 2 = 1 , 2 , ..., L (21) If eqn. 21 is satisfied for any A,, 4 = 1, 2, ..., L, which is supposed to be damped by the kth stabiliser, we set Qe = 0 and d5e(K)ldKk = 0 in eqn. 19. This arrange- ment frees the eigenvalue drift towards the 'good' direction, the left half complex plane over the target value. Therefore, an unique final solution of gain tuning can be obtained.

~ "3

TCSC- based stabit iser

i' m 2 1 2

Fig.3 Example power system

4 Example

An example three-machine power system is shown in Fig. 3, the parameters of which are given in the Appen- dix (Section 7.2). The active power transferred along the main transmission line from bus 4 to 3 varies from P4, = 0.1p.u. to P43 = 0.9p.u. The example power system has one local mode and one interarea mode poorly damped, as shown in the third column of Table 1. It is decided that a PSS is to be installed on machine 3 to damp the local oscillation mode, and a TCSC-based stabiliser is to be installed on line 3-4 to improve the damping of the interarea. The locally available active power delivered along the transmission line is taken as the feedback signal of the stabilisers. For the selection of installing locations and feedback signals of stabilisers, the method proposed in [9] is used.

Table 1

From Table 1 it can be seen that, in this case of two- mode oscillations, the damping of two oscillation modes changes with system operating conditions in different pattern. There is no common operating condition at which two modes are of worst damping. Therefore, even the simple procedure to select the typical operating condition according to the damping of the oscillation modes cannot be used. Here, for demon- stration, a compromised operating condition for both oscillation modes p3 is selected to be the typical operating condition. At p3 two stabilisers are designed in co- ordination by use of eigenvalue assignment, which results in PSS:

K1 = 0.302p.u., T11 = 0 . 7 ~ , Ti2 = 0 . 6 7 ~ , Ti3 Ti4 = 0 .32~ , Ti = 0 . 0 2 5 ~ , T,, = 3.0s.

0 . 9 ~ ,

TCSC: K2 = 3.66p.u., T21 = 0 . 7 ~ , T22 = 0 .12~ , T23 = 0 . 9 ~ , T24 = 0 .11~ , T2 = 0 .025~ , Tw2 = 3.0s.

They move two modes to: A,ocal = -0.8574 kj8.5740, A,,,, = -0.4571 k j4.5710, both of which are of good damping 0. I . However, the results of eigenvalue calculation presented in the last column of Table 1 show that this design at p3 does not provide robust stabilisers to the variations of power system operating conditions.

Then the method proposed in the paper is used for the co-ordinated design of robust stabilisers.

Table 2

QO VVlocal.pss(m) Warea.TCSC(m) With robust stabilisers

PI 4.8521 0.2997 Liocal = -3.4821 k 17.2360 a,,,, = -0.4514 kj4.5155

~2 3.9417 0.9527 alocal = -2.9983 + p.6606 aa,,, = -0.7824 k j4.8455

p3 2.8903 1.7007 alocal = -2.31 18 +;8.1776 a,,,, = -1.0067 f p.0143

~4 2.0081 2.5512 Alocal = -1.6438 i j8 .5517 Larea = -1,1440 i j5.1281

ps 1.2308 3.7461 alocai = -I ,2474 i- j8.8460 a,,,, = -1.2472 ~ p . 2 1 1 7

(i) From the results of calculating Wlocal pss(m) and W,,,, Tcsc(m) in Table 2, it can be seen that, at p5, PSS is lea3 effective to damp the local mode and at pi TCSC-based stabiliser is least effective to damp the interarea mode. This estimation is confirmed by the results in the last column of Table 1, which demon- strate that the lower the level of power delivery on the

With stabilisers designed

condition p3 Qo p43 Without any stabiliser a t a common operating

ai,,,, = -1.2107 +;8.6064 a,,,, = -0.1766 +;4.4071

pLp P43 = 0.3p.u. a,,,,, = -0.3981 f j8.5666 ~,,,,, = -1.0483 i $3.5468 a,,,, = -0.3246 +;4.5516

h3 P~~ = 0.5p.u. aioca, = -0.4000 + j8.5686 a,,,,, = -0.8574 * j8.5740 a,,,, = -0.8574 i j8.5740

p4 f43 = 0.7p.u. Alocal = -0.4002 i j8.6028 = -0.6895 f j8.6278 a,,,, = -0.5593 i j4.5751

ps f43 = 0.9p.u. Alocal = -0.3987 i j8.6755 ~1,,,1 = -0.5172 f j8.7161

pd3 = 0.1 P.U. alocal = -0.3925 i- j8.6483 a,,,, = -0.0564 f j4 .3977

a,,,, = -0.0578 kj4.4925

a,,,, = -0.0543 i j4.4460

A,,,, = -0.0462 i j4.3787

a,,,, = -0.0319 i- j4.2681 aa,,, = -0.6530 ~ j 4 . 5 5 5 3

114 IEE ProcGener. Transm Distrib., Vol. 145. No. 2, March 1998

main transmission line P4?, the less effective the TCSC- based stabiliser is and the higher P43, the less effective the PSS. The changing pattern of the effectiveness of the stabilisers is totally different. Therefore, p, is chosen to be the typcal operating condition of the PSS and pl the typical operating condition of the TCSC- based stabiliser

(ii) At p5, the parameters of the PSS except its gain are set to be:

Til = 0.7 S , TI, = 0.68 S, TI, = 0.9 S, TI4 = 0.32 S,

TI = 0.025 S, T,, = 3.0 S.

and at pl, those of the TCSC-based stabiliser except its gain are set to be:

T,, = O . ~ S , T22 11 0.12~, T23 = 0 . 9 ~ , T24 = 0.11s, T2 = 0 .025~ , T,; = 3.0s. (iii) At pl, the gains of the PSS and the TCSC-based

stabiliser are tuned jointly by the algorithm of eqns. 18-21. The target damping for two oscillation modes is 0.1. The solution is Kpss = 1.28p.u., Krcsc = 2.26p.u., which moves two oscillation modes to:

a,,,,, = -0.8810 Itj8.8i4, a,,,, = -04410 +j4.4140 (iv) At p,, the ge.ins of the PSS and the TCSC-based

stabiliser are tuned jointly again by the algorithm of eqns. 18-21 with t i e same target damping of 0.1. The initial values of the gains are taken to be Kpss = 1.28p.u., ICTcsc = 2.26p.u. The final solution is:

Kpss = 1.28p.u., KTcSc = 12.Op.u. The last column in Table 2 presents the results of the

robustness of the stabilisers to the variations of system operating conditioris. Both stabilisers are robust.

Fig. 4 shows the results of nonlinear simulation. The oscillations are triggered by a three-phase short circuit occurring at bus 3 in the example power system at 0.1 s of the simulation, and is cleared after 120ms. They confirm all the reijults obtained above based on the eigenvalue calculation.

I P43 = 0.9 p.u.

, _.-_---

I

0 2 L 6 8 10 t ,s

Fig. 4 Nonlinear simuk tion ~~~- system installed with stabilisers designed a1 common operating condition

system inctallcd with robust stabilisers designed by inethod proposed

5 Conclusions

In this paper, a method is proposed to select the typical operating conditions at which multiple stabilisers are designed in co-ordmated to damp multimode oscillations in multimachine power systems. The robustness

IEE Proc.-Gener. Trunsm. Oistrih, Vol. 145, No 2, Murch 1958

of the stabilisers is ensured by the selection of the typical operating conditions. An example power system is presented in the paper, where a robust TCSC-based stabiliser and PSS are designed to damp multimode oscillations in co-ordination.

6 References

1 NOROOZIAN, M., ANDERSSON, G., and TOMSOVIC, K.: ‘Robust, ncar time-optimal control of power system oscillati80n with fuzzy logic’, IEEE Trans., 1996, PI&-11, pp. 393400

2 WANC, H.F.: ‘Rule-based variable-gain power system stabiliser’, IEE Proc. C, 1995, (I), pp. 29-32

3 LARSEN, E.V., and SWANN, D.A.: ‘Applying power system stabiliser’, IEEE Trans., 1981, PAS-100, (I-HI), (6), pp. !-30

4 YU, Y.N.: ‘Electric power system dynamics’ (Acaclemic Press, 1983)

5 LARSEN, E.V., SANCHEZ-GASCA, J.J., and CHOW, J.H.: ‘Concept for design of FACTS controllers to damp power swings’, IEEE Trans., 1995, PWRS-IO, pp. 948-956

6 NOROOZIAN, M., and ANDERSSON, G.: ‘Damping of power system oscillations by use of controllable components’, ZEEE Trans., 1994, Pl3-9, (4), pp. 2046--2054 LERCH, E., POVH, D., and XU, L.: ‘Advanced SVC‘ control for damping power system oscillations’, IEEE Trans., 1991, PWRS- 6, (2 ) , pp. 524-535 XU, L., and ZAID, S.A.: ‘Tuning of power system controllers using symbolic eigensensitivity analysis and linear programming’, IEEE T v L ~ s . , 1995, PWRS--IO, (l), pp. 314-321 WANG, H.F., and SWIFT, F.J.: ‘Selection of installing locations and feedback signals of FACTS-based stabilisers in multimachine power systems by reduced-order modal analysis’, IEE Proc. C, 1997, (3), pp. 263-269

10 WANG, H.F., and SWIFT, F.J.: ‘A unified model for the analysis of FACTS devices in damping power system oscillations Part I: Single-machine infiniie-bus power systems’, IEEE Trans., 1997, PWRD-12, (2), pp. 941-946

11 WANG, H.F., and SWIFT, F.J.: ‘A unified model for the analysis of FACTS devices in damping power system oscillations Part 11: Multimachine power systems’, IEEE Trans., 1996, P W W I O ,

12 GOOI, H.B., HILL. E.F., MOBARAK, M.A., THONNE, D.H., and LEE, T.H.: ‘Co-ordinated multimachine stabilizer setting wiihout eigenvalue drift’, IEEE Trans., 1981, PAs--100, (lo), 3 879-3887

7

8

9

(1 1)

7 Appendix

7.1 Derivation of eqn. 4 For simplicity, only the case for the FACTS-based stabilisers is presented and subscript k is omitted.

From last two equations in eqn. 1 we can obtain: AE; =

- [(h; + S T D ) + E X ( S ) K p [ h 7 4 + EX(S)KS]A(T

- [ ( K 3 + S T D ) + E X ( s ) l G j - l [ k , + EX(S)k, ,]AU,f

= E(s)A6 + f ( s )Au ,

a = 1. 2, ..., ri i # j 115

and choose a pair A+, Aw,, the system model of eqn. 1 can be expressed as:

Thus we can obtain:

Substituting eqn. 24 into the last equation in eqns. 23 and 1 and then into the first equation in eqn. 23 we can obtain:

AE; = h 3 ~ ( ~ ) A 6 , + ~ ~ J ( s ) A z I ~

A E F D = & J ( S ) A ~ ~ + ~ G J ( S ) ~ U S

So, if the feedback signal of the FACTS-based stabiliser is:

(25) au, = hJ7(S )AhJ

7.2 Parameters of example power system (in p.u. except where indicated) Generator: 2Hl = 30.17s, 2H2 = 30.17s, 2H3 = 13.5s,

Tdol’ = 7.5s, Tdo2/ =7.5s, Tdo3’ = 4.7s, Dl = 0 2 1 0.0, 0 3 = 15.0

Xd1 = 0.19, X d z = 0.19, X d 3 = 0.41 Xql = 0.163, Xq2 = 0.163, X43 = 0.33, Xdl’ 0.0765, Xd2/ = 0.0765, Xd3’ 0.173 Exciter: Exl(s) = Ex2(s) = Ex?(s) = KA/l + . sTA , ,

Transmission lines: ZI3 = 0.0 + j0.6, XTl = X , = j0.03 The load condition: L 2 = 0.5 + j0.2, L3 = 1.0 + j0.6

T A 1 = T A , = T A 3 0 .01~ , K A 1 = KA2 = KA3 1 100

1 I6 IEE Proc.-Gener Transin. Distvib , Vol. 145, No. 2, Murch 1998

selection of operating conditions for the co-ordinated setting of robust fixed-parameter stabilisers

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