The analysis is also performed with the state space approach to overcome the limitations of the DF method. The load disturbance is successfully rejected by the continuous action of the integral-loop controller and the Fourier transform based curve fitting technique is used to obtain the denoised limit cycle from the noisy one. A diagonal transfer function model of process dynamics is identified for decentralized/ed controller design, if the interaction between loops affects the accuracy of the iiKulel process.
4.8(a) Closed loop responses to step input and load disturbance for example b) Closed loop responses to step input and load disturbance.
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Nyqiiist curves of process models for example IL2 Nyqmsl curves of proeess models for example B.3
Closed loop responses to step input and load disturbance
- Nyquist curves of the uneompensated proeess , the process with the modified
- Recovered and noisy output signal with SNR=20dB for example 5.1 1 13
- Recovered and noisy output signal with SNR=20dB for example 5,2 116 Closed loop responses to step input and load disturbance for example 5.2 1 17
- Controller, limit cycle and process model parameters for example 34 2.8 Controller, limit cycle and process model parameters for example 2.8 35
- Aim of the Research Work
However, a lower-order transfer function model for the process dynamics can be obtained from the feedback relay experiment. It is used to find the dynamic information of the process and thus to set up the feedback controller. Therefore, two degrees of freedom controllers (Pl-PD, PID-P, weiuhtcd PID setpoint) are designed to overcome the structural limitations of the PID controller.
1 1 Controller and process model parameters for example 2.1 1
It shows that the proposed noise lllter method obtains superior estimates of model parameters in the presence of. In this chapter, three new on-line identification methods for stable and unstable SISO processes are proposed. The modified identification structure yields significantly more accurate estimates of the model parameters, especially for unsteady processes.
In section 2.2.2, an exact method using state space analysis for the online identification of stable and unstable processes is proposed. The advantage of this method is that no approximation such as DP is required to estimate the model parameters. Simulation examples show that the exact identification method provides better estimates than the descriptive function method.
Furthermore, one must solve a series of nonlinear equations simultaneously to identify a parametric model of the process dynamics. The sial load taken during the online idcnlllcalion is successfully removed due to the continuous operation of the integral controller in the loop. The online identification method is further improved by inserting an adaptive noise filter into the feedback path.
The method can accurately estimate model parameters even in the presence of static load disturbances and measurement noise.
Chapter 3
For easier implementation of Hold, it is desirable to identify two models of the SISO transfer function of the flTO process. The methods overcome several limitations of conventional automatic relay tuning techniques available in iileralLire. A modified identification method is given in subsection 3.2.2 by introducing proportional controllers in the internal feedback loop.
Two pre-load relays are inserted into the structure in the error paths and two integral fillers are used in the feedback paths. Based on the measurements of the limit cycle outputs, two SISO lumsler lunction models have been identified for the dynamics of the process. In this subsection an attempt is made to identify two models of the second-order transfer function SISO plus time delay of the TITO process from relay experiments.
In the above expression, /i is the derived filter constant for the i''' loop and neglected i. Tlio philosophy of estimating the stable stale gain for the SISO proeess described in siihseelion 2.2.1.2 is extended to the TITO process. The presence of the controllers in the loops during identification results in zero steady state value of the outputs of the step load disturbance inputs, which implies symmetrical stationary limit cycle outputs around the set points.
1 , T,] = 1 and The final model of the process is obtained by the procedure given in subsection 3.2.
The method provides unperturbed limit cycle measurements of the TITO G'(.v) process in the presence of measurement noise and various loop interactions. Based on tdteicd output cycle measurements, a two by two TITO pioee diagonal transfer function matrix model. So the diagonal process model is identified using critical amplification and critical liquidity or comparative study.
The height of the relay in the lesten starts with the parameters Z?, - 2. cicn innsfer functional models of the TITO process can be. 3.3 Identification of TITO processes using P_relay. Usiim ibe ibird order Padc approximalion for time delay, the Nyqiiist eurver of the diagonal elements is shown in Fig. The Nyquist curves of the process models obtained by the. proposed method, Palmor et al.'s method and Wang et al.'s method are shown in fig.
The proposed method requires no prior knowledge of the process and can identify equivalent second order plus delay SISO transfer function tnodcls of the process in the presence of load disturbances and measurement noise. A modification of the identification method is given in subsection 3.2. 2 by inserting proportional controllers in the inner leadbaek loops. The proportional controllers stabilize the process and reduce the ..ot)p interaction at critical I'requency thereby increasing the aeeuracy of the proeess model.
The most important thing is that the steady states of the transfer function models are estimated in a simple way.
Chapter 4
Several methods are available in the literature for the control of single input single output processes [23-44] and two input two output processes [59-69], However, it is found that the eontroller design based on the gain and phase margin criteria robust. The idea of eontroller design for SISO and TITO processes based on loop phase and gain margin was proposed in and in respectively. In this chapter, the phase and gain margin criteria are used to design the SISO controllers or the identified translator function models of SISO and.
In subsection 4.4.1, we use the loop phase and gain margin philosophy to obtain c-presses for the PID controller parameters for both stable and unstable FOPDTs. However, the PID controller gives excessive overshoot, especially for the servo problem, for minimum overshoot, two-stage Ireedom controllers are used [40-44].
- Fstimntion of Controller Parameters
The reference path controller {G, (.v)) does not affect the roots of the characteristic equation of the system. 1 the perlormanee of the system can be easily improx ed b>' inserting a controller in a suitable place within the structure of the system. I'hc time domain perlormanee is usually obtained from the response of the process to a test signal.
Furthermore, the derived effect can be used for proee.ss' stabili i/aticm. So the control signal is the combination of the weighted error, the time integral of the error, and the lime rate change of the error. To eliminate this problem, a bit is used with the .. derived action of the controller.
They required solving four design equations of looj") gain and phase margin criteria to obtain two unknown controller parameters due to the presence of two other unknown parameters, gain and phase transition frequencies in the design equations. Using the identification method discussed in Chapter 2, a FOPDT is called -transfer function model (2.6) of the process identified. Let the phase crossover and gain crossover Ircqueneies of the loop transfer function be a) and (t)^, respectively.
Set the relay height to zero m t^ig- -A. To begin with, the forms of PI and PD controls are given. v ^ .. ic Hpsiancd based on the stability characteristics of the process internal feedback PD controller is design approx.
I. The Pi-PD control method piopos
The closed loop responds to the input and step load. disturbances with 10 and -10 % changes in process parameters are shown in Fig. The controller parameters are designed for the TITO process ShSO models for the specified cycle stage and profit margins. The controller scheme is modified by introducing proportional controllers in the internal feedback paths, thus reducing the loop interaction and improving the process stability.
IIorc that do not require a malhematic model of the lie aiiH)-iiiininu of PID-coiilroiicis which is ao nu i. In the proposed method, the ratios of the amplitudes of the harmonic components to the fundamental ones decrease due to the integral operation of the PI controllers in the modified relay. Let
Due to the integral action in the loop in the proposed scheme, the effects of load disturbance are successfully eliminated, as described in subsection 2.2.1.5 of Chapter 2. The design parameter c satisfies both the gain margin and phase margin requirements because c and > cos '(1/^)-^hc closed loop performance of the process can be improved with the appropriate choice of g. The amplitude A and the frequency of the limit cycle output are measured in the second phase of the auto-tuning test.
A relay with height h - tlcrivative time constant of the PID '•'^Tivative filter eonstant is chosen to.
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Closed loop responses on step input and loaddislurbanee Ibr example 5.2. The melodies of 2iegler and Nichols and Ho ct al. show more. elearn from ^jisn„.bance rejection ability. shooting \N ilh nlmosl simi ai the responses are slow, however. bm and l lagglon*-' redllees l^su^r .capons.^ with shorter ones. zero coinpiii --'br'w .ujihy compared to the othei thiee.
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Chapter 6
- We proposed a modilicd ichy existing techniques. So, the
The proposed method identifies two phis delay SISO iransfer fitnelion models of the second-order process in the presence of load disturbances and measurement noise. The Nyquist curves of the actual process and the process models by the above methods are shown in Figure B.2. The accuracy of the identified model is shown in Example B.6 and compared with other methods.
In this section, the llic controller pcrrorinancc for the high-order process given in example B.2 is illustrated and compared with the aiilo-liining method of Leva et al. [79], where the controller parameters are obtained from the characteristics of the eluted loop. of the process. The characteristics of the response in the relay feedback test for linear and non-linear processes (Wiener and Hammerstein types) are given in Table C.l. The nonlinear process can be identified in any of the structures mentioned above (Wiener or I Fimnierstein types).
1 I'K-' proposed auto-tuning scheme can be extended for identification and control of the non-linear process. The block diagrams of the proposed online identification method for nonlinear processes are shown in Fig. The advantage of the infusion method is that the drug level in the body can be kept more constant, in contrast to.
On a new measure of interaction for multivariable process control, .. 68] Shinskey, F.G., The stability of interacting control loops with and without decoupling, /h-oc.. from IF AC Mnltivariahle Techno!.
