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It is hard to design robust control systems for interacting multivariable processes. When processes are ill-conditioned, difficulties become more serious due to sensitivities on plant variations. For robust control systems, we decompose systems to slow subsystems and fast subsystems. When the slow subsystem is detuned and maintained to be slow, the fast subsystems can be made to be robust to plant variations. On the other hand, the slow loop is sensitive to plant variations. Adaptive control technique is introduced to the slow loop to maintain performances of the slow loop. Because the slow subsystem is chosen to be single-input single-output and controlled to be slow, the adaptive control scheme is very simple. Simulations show that the proposed control system has nominal performances similar to usual multivariable control systems while maintaining better robustness.

Recently, Chen et al. (Systems Control Lett. 24 (1995) 19) proposed conditions for D-stability and strong D-stability in terms of structured singular values. In this paper, simpler conditions for the strong D-stability are derived.

Many industrial chemical process control systems consist of conventional PID and nonlinear controllers, even though many advanced control strategies have been proposed. In addition, nonlinear control methods are widely used even for linear processes to achieve better control performance compared with linear PID controllers. However, there are few tuning methods for these nonlinear controllers. In this work, we suggest new controller tuning methods for the error square type of nonlinear PI controller. These control methods can be applied to a large number of linear and nonlinear processes without changing control structures. We also propose new tuning rules for integrating processes. In addition, we suggest application guidelines for performing the proposed tuning rules at the pilot scale multistage level control system. Finally, in this work we confirmed good control performances of the proposed tuning methods through both simulation studies and experimental studies.

For some pH processes, components and concentrations of influent streams are time-varing, causing dramatic changes of their dynamic characteristics. To track dynamic characteristics of time-varing pH processes adaptively, in-line mixer system has been introduced. Output of the in-line mixer implemented in front of mixed tank reactor can be used for the feedforward control and further can be perturbed for reliable adaptation without disturbing pH process much. Here, effectiveness of pH control systems with in-line mixers is illustrated experimentally.

Nonminimum-phase parts are better removed in the feedback loop like the time delay term. For this, Wright and Kravaris [1992] proposed the concept of optimal minimum-phase output to control nonlinear nonminimumphase processes. However, their optimal minimum-phase output has no analytic solutions for processes with more than three state variables. Here, methods for analytic minimum-phase outputs approximating the optimal ones are proposed, having no limitations in the number of state variables. The proposed methods provide analytic solutions for processes with three state variables and simple numerical solutions for those with more state variables.

For some ill-conditioned processes, small element errors due to the classical element-by-element identification cannot be tolerated and control systems based on models with such errors can suffer f...

Components and concentrations of the influent stream are often varying in pH processes and changes of components and concentrations alter the nonlinear characteristics of pH processes severely. Hence adaptation coping with such influent stream changes is required for most pH control systems. As in linear adaptive control systems, bursting phenomenon of the estimator is a serious problem in the adaptive control of pH processes. One reliable method avoiding this problem is to excite the process to some extents intentionally. However, it may not be obvious how much the input should be perturbed. Too large perturbation can deteriorate control performances much. To avoid the bursting phenomenon of the estimator without deteriorating control performances, we introduce a small in-line static mixer which is easily implemented and whose output can be excited persistently for the reliable estimation of process parameters. Furthermore, it can be used for the feedforward action to compensate effectively the influent stream changes, which are the major disturbances. Improvements in control performances will justify the additional investment of the in-line static mixer.

Utilizing the concepts of the internal model control and the structured singular value, Grosdidier and Morari (1986) have proposed the μ -interaction measure for multiloop control system designs. Under the μ -interaction measure plot that constrains the magnitude of each closed-loop transfer function, a stable multiloop control system can be designed. However, for some processes, the plot fails to provide a stable multiloop control system with integral action and a dynamically better control system is discarded. Here we introduce a phase stability condition that reduces the above possibility when used together with the μ -interaction measure. The small gain theorem with linear fractional transformations is used to calculate the phase condition. As in the gain margin and phase margin design for single-input single-output processes, a reliable multiloop control system can be designed with the gain constraints of the μ -interaction measure and the proposed phase constraints.

A secondary measurement is usually used in the form of cascade control to effectively reject disturbances to the manipulated variable. In the cascade control system, the inner loop is tuned first and then the outer loop is tuned with the inner loop closed. When the dynamics of the inner process is slow, this tuning procedure does not provide the best control performance. Here, for slow inner processes, parallel compensation similar to the Smith predictor and the internal model control is shown to be more effective than the cascade control. A very simple tuning rule and a simple anti-reset windup are feasible in this control structure. It can be used in its own structure or to tune the cascade control system systematically. For automatic tuning of the proposed control system, an identification method which finds two process models with the relay feedback and P-control tests is also proposed.

An accurate and realistic model for transient diffusion and adsorption in a biporous pellet is typically represented by two coupled second-order partial differential equations. The model, however, has been rarely used in practice because of its mathematical complexity and bulky numerical computation, and approximations of the model have been used instead. But the accuracy of the available approximations has been limited and not enough for detailed analysis and simulation of the mass transfer process. Therefore, in this study, we develop for the first time high-order approximations, of up to third order, for noncyclic and cyclic adsorption in a biporous pellet, respectively. The approximations are in the form of a state equation which consists of first-order differential equations ; the number of the equations is the same as the approximation order. The approximations are easy to use and their accuracy dramatically increases with increasing approximation order, so that the second-or the third-order approximations can effectively substitute the complex biporous diffusion model.

A trial-and-error method that is a variation of Ziegler–Nichols tuning has been employed in the past for field tuning of PID controllers. This method is now extended for tuning of multiloop PI controllers. The Nyquist array method is refined to determine ultimate gains for multiloop tuning. The proposed method is simple to use and simulation results show that it avoids sluggish responses and unbalanced responses between loops that occur with other tuning methods such as BLT and sequential autotuning.

We propose a simple on-line process identification method for the automatic design of PID controllers. It can identify general time-invariant linear systems with time and frequency weighting, while retaining simplicity. We then use a model reduction method to tune PID controllers using usual tuning rules based on the first or second order plus time delay model. It can efficiently incorporate initial value problems of previous identification methods for autotuning by assigning zero weight to the initial state. The proposed method shows an acceptable robustness to measurement noises and disturbances.

For noncyclic and cyclic transient diffusion and adsorption in a particle, respectively, a sequence of linear approximations is developed. In the case of noncyclic adsorption, the Pade summation on the Taylor series of the transfer function of the diffusion and adsorption system is used to derive approximations with constant coefficients. And in the case of cyclic adsorption, a frequency response matching method is developed to approximate the transfer function and applied to derive approximations with theoretical frequency-dependent coefficients. All the approximations are in the form of a state equation that consists of first-order differential equations, the number of which is the same as the approximation order. For noncyclic adsorption, the first element in the sequence, a first-order approximation, is identical to the linear driving force (LDF) equation, and for cyclic adsorption, it is identical to the approximation by Kim (1996, Chem. Engng Sci. 51, 4137). For each increment in the order, the approximation error is found to decrease roughly by an order of magnitude, and the second- or third-order approximations are shown to yield responses very close to those from the pore diffusion model. The high-order approximations for noncyclic adsorption are shown to be applicable to the cyclic adsorption over a wide range of cycle frequencies. Application of the approximations for cyclic adsorption to the cases where the effective diffusivity varies between steps within a cycle is discussed.

Some ill-conditioned processes are very sensitive to small elementwise uncertainties arising in classical element-by-element model identifications. For such processes, accurate identification of singular values and right singular vectors are more important than those of the elements themselves. Singular values and right singular vectors can be found by iterative identification methods that implement the input and output transformations iteratively. Methods based on SVD decomposition, QR decomposition, and LU decomposition are proposed and compared with Kuong and MacGregor's method. Convergence proofs are given. These SVD and QR methods use orthogonal matrices for the transformations that cannot be calculated analytically in general, and so they are hard to apply to dynamic processes, whereas the LU method uses simple analytic transformations and can be directly applied to dynamic processes.

For some practical disturbances and uncertainties, acceptable control systems can be designed even for MIMO ill-conditioned processes. A class of ill-conditioned processes has been studied where an inversion-based control system is not sensitive to the diagonal input uncertainties. We show for this class that element uncertainties arising from usual element-by-element model identification do not significantly degrade the control performance. Some useful measures for uncertainty effects on the control performance, stability, and inversion are proposed.

This paper presents a novel approach to extract and to characterize steady state interaction by means of closed-loop structural analysis. A steady state interaction measure equivalent to the relative gain array is obtained. Due to the broad derivation basis and structural significance, the new measure allows for unified characterization of steady state interaction and systematic analysis of the impact of loop interaction on decentralized control systems. Important issues, such as the absolute and relative interaction, the size and the direction of interaction, positive and negative interaction, one way interaction problem, and the usefulness as well as the limitations of steady state interaction measures are systematically addressed. The impact of steady state interaction on closed-loop performance and stability is analyzed on the basis of individual loops within a classical paradigm. The analysis applies to nonrational processes. The use of steady state interaction measures as tools for variable pairing and controller design to counteract loop interaction for closed-loop performance and stability is demonstrated.

Most chemical processes are nonlinear in nature. When large set point changes or load disturbances occur frequently, nonlinear control systems are required. Instead of using the differential geometric method or nonlinear model predictive method, simple gain scheduling may be sufficient for many nonlinear single input-single output (SISO) processes. To design such simple control systems systematically, a nonlinear first-order plus time delay model is proposed for model-based control. A logarithmic transformation which is very useful for control of high purity distillation columns is shown to be effective in general. Several chemical process examples are also given.

Bioprocesses are often long-term experiments and their inspections are not easy. For these, the web cam can be very useful. It can analyze to continuous image data using webcam. For example, the height of the tank, or the growth of the organisms, the progress of the reaction. Specified pixel data show that red, green, blue, 16bit gray scale data and graph. It can analyze the result more easily and cheaply. In this paper, we describe our experiments with image analysis and applications.

In order to increase the active component, saponins, of the ginseng and improve the quality of it, the fresh ginseng is prepared to become the red ginseng through steaming ginseng and drying process. The steaming ginseng, which steam the fresh ginseng at 98~100°C for 3 hours, of the red ginseng process determine color and amounts of active components of the red ginseng. However, the red ginseng's quality will be low because the occurred cracks on the ginseng's surface expel active components. The cause of crack formation seems due to water absorbed into the ginseng. Therefore, in order to reduce cracks on the ginseng's surface, we propose a control system that maintains constantly the weight of water absorbed during steaming. To conduct the proposed method, an apparatus measuring the weight of ginseng in real-time is constructed and then a control system to keep the ginseng weight by manipulating the steam and hot-dried air is designed. As a result of steam and air inflow control, the crack formation would be minimized, improving yield of the high quality red ginseng.

A new identification method using the second order plus time delay model for the automatic tuning of the PID controller and a simple and explicit tuning method are proposed. We present a relay feedback test combined with a P controller to identify the process using the second order plus time delay model. Thus, the difficulty to determine the initial proportional gain is overcome. Since the proposed identification method uses the second order plus time delay model to identify the prodess, it can incorporate more various processes such as underdamped and high order processes than the identification method using the first order plus time delay model. In addition, a simple and explicit tuning relation for the second order plus time delay model is proposed in this paper. This tuning relation shows almost the same performance as the optimal tuning parameters. The proposed method needs no numerical technique and shows good performances in both simulation and experimental study.

For easier implementation of nonlinear pH controllers, we propose an on-line tuning method using the relay feedback with hysteresis. Since just two or three parameters are sufficient to characterize pH processes for practical applications (Williams et al., 1990; Lee et al., 1992), we parameterize pH processes with three parameters and then identify them with the relay feedback testing. The relay feedback method is very popular in on-line tuning of PID controllers (Astrom and Hagglund, 1984; Seborg et al., 1989). This on-line tuning method would reduce the efforts to obtain titration curves with off-line experiments

Methanol partial oxidation (POX) is highly exothermic. The reaction temperature in a reactor can increase fast when the reaction starts. So, it is needed to know the temperature dynamics for a stable operation of reactor. As the POX occurs in the coated-aluminum reactor, it has been reported that the reactor temperature shows various patterns. There are temperature patterns such that the reaction temperatures have rapid increase, regular oscillation, chaotic oscillation or constant value. In this paper, operating conditions showing such reactor temperature patterns in methanol partial oxidation are investigated experimentally.

This chapter contains sections titled: Introduction to Process Control and Identification Properties of Linear Processes Laplace Transform Transfer Function and State-Space Systems Problems Bibliography

This chapter contains sections titled: Identification Methods Using Integral Transforms Prediction Error Identification Method Problems References

This chapter contains sections titled: Conventional Relay Feedback Methods Relay Feedback Method to Reject Static Disturbances Relay Feedback Method under Nonlinearity and Static Disturbances Relay Feedback Method for a Large Range of Operation Problems References

This chapter contains sections titled: Cascade Control Time-Delay Compensators Gain Scheduling Proportional-Integral-Derivative Control using Internal Feedback Loop Problems References Bibliography

This chapter contains sections titled: Low-Order Plus Time-Delay Processes Process Reaction Curve Method Poles and Zeroes Block Diagram Frequency Responses Problems Bibliography

The acid-base titration is used wide in the fields of chemical engineering, environmental engineering, agriculture, and medical science. The auto-titrator is a commercial apparatus that carries out the titration operation automatically and provides the equivalence point data. For some test samples and operating conditions, titration operations require up to around 5 minutes. Here we propose a method to reduce this operation time by one-fifth. For this, systems technologies such as reducing sensor time-constant with a lead-lag filter, parameter identification and alternative dosing of titrating and sample solutions have been applied. Test equipment that simulates commercial auto-titrators is introduced.

Heated press rollers are used to give tactility and gloss to papers, fabrics, nonwoven fabrics, films and so on. The surface temperature of the heated roller and its uniformity are especially important. Existing heated rollers have surface temperature profiles up to 10degC deviations, causing listing in fabrics. In order to suppress the surface temperature deviation to 1degC, we propose a heated roller system having multizone electric heaters and heating oil within the steel roller. The heated roller temperature control system is ill-conditioned. Because the controller performance is very sensitive on uncertainties in the model and disturbances, very accurate identification and elaborate controller design are required. For this, recent sequential relay feedback autotuning methods are applied for identification and controller design. Experimental results are given.

One proposes a new closed-loop tuning method for the PID controller. One improves the Yumana and Seborg method by identifying processes with a second-order plus dead-time model under closed-loop conditions. One also employes a more elaborate frequency domain tuning method. To tune the PID controller, a frequency domain method is applied, yielding controller settings much superior to the Ziegler-Nichols method or the first-order methods.

A general Schur vector method for solving a partial differential equation which appears in designing nonlinear optimal control laws for linear or nonlinear dynamical systems is proposed. The method reduces the dimensionality problem of the direct method. Numerical experiments show that it also reduces the numerical instability of the eigenvector method. >

For a class of non-linear dynamic systems, a quadratic regulator problem is considered in which the cost functional contains a small parameter multiplied to the control term. In the analysis of the problem, an appropriate transformation of the state variables and an eigenvector technique are utilized, which were devised originally for analysing complex linear cheap control problems and for solving a Lyapunov-type system of linear equations, respectively. In so doing, the class of nonlinear systems is characterized and extended in a mathematically simple way, for which the optimal cost becomes zero as the small parameter goes to zero.

The relay feedback method is now widely used in tuning proportional-integral-derivative controllers automatically. It usually uses point data such as the oscillation amplitude. As in the step response method which uses areas instead of point data, area and moment data of relay feedback response can also be used to extract process information. Here we propose identification methods involving various integrals of the conventional relay response and show their merits. Equations are very simple and can be applied easily to cheap commercial controllers.

Norms of differences in the sensitivity function matrices and the complementary sensitivity function matrices (closed-loop transfer function matrices) are used to determine better models in the context of iterative identification and model reduction. Some insights on the relative error matrix between the process transfer function matrix and its diagonal matrix, which has been used in analyzing dynamic interactions by several authors, are also obtained. Proposed interaction measures can be interpreted as the amounts of differences of the complementary sensitivity function matrices when loops are closed, extending the concept of gain changes in the relative gain array. To employ the interaction measures, control systems are designed in advance using internal model control. By changing the closed-loop time constant, proper pairings based on closed-loop response speeds can be obtained.