Controller design input-output linearization

The GMC control response can be designed via the tuning parameters K and K2 based on the tuning curve given by [24], It should be noted that the GMC approach is a special case of the global input output linearizing control technique in which a transformed control action is chosen properly with the external PI controller. The use of Eq. (16) forces y toward its set point, ysp, with zero offset. If Eq. (15) is differentiated, and the Eq. (16) is substituted into the resulting equation, the GMC control law is... 

Several process control design methods, such as the Generic Model Control (GMC) [41], the Globally Linearizing Control (GLC) [37], the Internal Decoupling Control (IDC) [7], the reference system synthesis [8], and the Nonlinear Internal Model Control (NIMC) [29], are based on input-output linearization. 

We used the model of the fast dynamics of the system in Equation (4.36) to design a nonlinear input-output linearizing output feedback controller with integral action (Daoutidis and Kravaris 1992) for x. The controller was designed to produce the critically damped second-order response... 

The non-stiff, low-dimensional model (6.63) is ideally suited for control purposes. We used it to design an input-output linearizing controller with integral action that manipulates QH and enforces a first-order response in the Tr dynamics, namely... 

With the outputs y and M, using the reduced-order model (7.38), a multi-variable input-output linearizing controller with integral action (Daoutidis and Kravaris 1994) was designed for the product purity and reactor holdup, requesting a decoupled first-order response ... 

In this work, therefore we aim to combine the stochastic observer to input/output prediction model so that it can be robust against the influence of noise. We employ the modified I/O data-based prediction model [3] as a linear part of Wimra" model to design the WMPC and these controllers are applied to a continuous mefihyl methacrylate (MMA) solution polymerization reactor to examine the performance of controller. 

As mentioned above, the backbone of the controller is the identified LTI part of Wiener model and the inverse of static nonlinear part just plays the role of converting the original output and reference of process to their linear counterpart. By doing so, the designed controller will try to make the linear counterpart of output follow that of reference. What should be advanced is, therefore, to obtain the linear input/output data-based prediction model, which is obtained by subspace identification. Let us consider the following state space model that can describe a general linear time invariant system ... 

A highly non-linear polymerization reactor can be controlled satisfactorily using controller designs based on the linearized case. Steady-state decoupling of outputs appears to be adequate under the conditions studies. It has also been shown that when the decoupling matrix is not square, some form of optimization technique can be used to provide "best" values of the input parameters. 

The alternative model development paradigm is based on developing relations based on process data. Input-output models are much less expensive to develop. However, they only describe the relationships between the process inputs and outputs, and their utility is limited to features that are included in the available data sets. There are numerous well-established techniques for linear input-output model development. Methods for development of linear models are easier to implement and more popular. Since most monitoring and control techniques are based on the linear framework, use of linear models is a natural choice. The design of experiments to collect data and the amount of data available have an impact on the accuracy and predictive capability of the model developed. Data collection experiments should be designed such that all key features of the process are excited in... 

Bode diagram, 330-31, 334-37 frequency response, 323-24 interacting capacities, 197-200 noninteracting capacities, 194-96 pulse transfer function, 619 Multiple-input multiple-output system, 20 discrete-time model, 586 discrete transfer function, 612 input-output model, 83-85, 163-68 linearization, 121-26 transfer-function matrix, 164, 166 Multiple loop control systems, 394-409 Multiplexer, 560, 564 Multivariable control systems, 461-62 alternative configurations, 467-84 decoupling of loops, 503-8 design questions, 461-62 interaction of loops, 487-94 selection of loops, 494-503 Multivariable process (see Multiple-input multiple-output system)... 

Control theory is well developed for systems well described by linear models (see, e.g., Zhou [8]). (A linear model is, essentially, one in which doubling the inputs, the actuator actions, will double the outputs, the measurements.) All systems are nonlinear, but for small excursions about equilibria or prescribed trajectories, many systems can be linearized and effectively controlled using linear control techniques. For systems that cannot be approximated as linear, nonlinear control techniques [9] are available to varying degrees of success for subclasses of systems for Hamiltonian systems (e.g., [10]), for nonlinear systems that can be made linear by a clever choice of variable transformation (e.g., [11], Chap. 10 in [12]), or other system subclasses. Nonlinear control design has been motivated by systems that commonly appear in applications these have traditionally been in electronic circuits and mechanical, fluid, and chemical systems on the macroscale. 

Hints Use the MATLAB MPC Toolbox, if desired, for this exercise. Two commands are used to produce a linear model of the plant in the representation needed for controller design. First, the dlinmod command obtains a state-space representation (A, B, C, D). To use this command, be sure that the Simuhnk diagram is drawn so that the process manipulated inputs and disturbances correspond to in ports on the top level of the Simulink flow sheet similarly, the outputs must correspond to out ports. Then the ss2mod command produces a model in MPC mod format, specifying inputs that are manipulated variables, measured disturbances, and unmeasured disturbances. The scmpc command simulates control of the hnearized plant with the MPC controller. 

If the loop interactions are not severe, then each single-loop controller can be designed using the techniques described earlier in this section. However, the presence of strong interactions requires that the controllers be detuned to reduce oscillations. There are multivariable control techniques, such as optimal control, that provide frameworks in which to handle the interactions between various inputs and outputs. Optimal control methods also allow one to deal directly with nonlinear system dynamics, rather than the linear model approximation required for the techniques discussed in this section. A thorough presentation of optimal control theory is given by Bryson and Ho (1975). Optimal control is discussed further in Section 9.5. 

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