Youla Parameterization for Feedback Systems

This paper presents an Internal model controller (IMC) for temperature control of heating, ventilation and air conditioning (HVAC) system. Firstly, the temperature of an air-conditioning system of the test room is controlled by using PID controller. The performance and stability of the control process are degraded due to the significant time delay of air-conditioning process. So, smith-predictor scheme is used to compensate the time delay. But when the process has larger system parameters and longer time delay, smith-predictor does not provide better results. To overcome this problem, an internal model (IMC) controller is developed. Simulation results compare the performance of internal model (IMC) controller with conventional PID controller and smith predictor controller. Simulation result shows that an internal model controller gives satisfactory performance with less overshoot and less settling time.

A systematic internal model control (IMC) controller design methodology has been developed for various types of multivariable processes. When we try to apply IMC to various systems several implementation problems are encountered. In this paper, we resolve these problems and suggest a systematic IMC controller design methodology. IMC shows very good performance and is easy to tune for open-loop stable systems. For unstable systems we apply IMC after stabilizing the systems using the pole placement technique. A combination of quadratic programming and IMC can handle constraints on manipulated and controlled variables.

Emulator-based control and internal model control: Complementary approaches to robust control design

The internal model control (IMC) proportional integral derivative (PID) controller tuning rules provide an excellent tracking of set-point, but sluggish disturbance rejection, as the conventional IMC filter introduces slow process pole. Disturbance rejection is significant than set-point tracking in many industrial applications. This paper proposes the design of IMC-PID controller, cascaded with lead–lag filter, with an improved IMC filter to provide effective disturbance rejection and robust operation of the first-order processes (FOPs). The simulation study was conducted to show the effectiveness of the proposed method on various structures of the FOPs, calculating the controller parameters, maintaining similar robustness in terms of maximum sensitivity MS. Perturbations were incorporated in the parameters of the plant model simultaneously, for the robustness analysis of the controller. The closed-loop performance was evaluated with the integral error criteria, namely, integral absolute error, integral square error, and integral time absolute error. The proposed IMC filter provided good disturbance rejection. The results of recently published design methods were compared with that obtained from the proposed method, validating the usefulness of the proposed method.

In this chapter, we consider briefly some important issues concerning the performance requirements to closed-loop linear systems and the fundamental design limitations in achieving the control aims. The performance specifications are formulated in continuous-time due to the clear physical interpretation in this case. First, we present the relatively simple case of single-input-single-output (SISO) systems which are well studied in the classical control theory. The trade-offs in the design of such systems are shown in some details. Then, we discuss the more complicated case of multiple-input-multiple-output (MIMO) systems whose performance is investigated by using the singular value plots of certain closed-loop transfer function matrices. An important issue in controller design is the closed-loop system performance in presence of different uncertainties. At the end of the chapter, we present some elements of the contemporary approach to the robustness analysis of uncertain linear systems based on the small gain theorem and structured singular value (SSV).

ROBUST CONTROL DESIGN USING THE ALGEBRAIC POLYNOMIAL APPROACH

The internal model control (IMC) scheme has been widely applied in the field of process control. This is due to its simple and straightforward controller design procedure as well as its good disturbance rejection capabilities and robustness properties. So far, IMC has been mainly applied to linear processes. This paper discusses the extension of the IMC scheme to nonlinear processes based on local linear models where the properties of the linear design procedures can be exploited directly. The resulting controllers are comparable to gain-scheduled PI or PID controllers which are the standard controllers in process industry. In practice, the tuning of conventional PI or PID controllers can be very time-consuming. In this paper, the design effort of the nonlinear IMC and conventional controller design methods are discussed and the control results are compared by applying it to a Hammerstein process and nonlinear temperature control of a heat exchanger.

Combustion control system is a typical system with large time delays and complex couplings. The traditional PID control approach is a classical method often used. However, control performances of PID are unsatisfied such as overshoot and switch time. Internal model control (IMC) is a new control strategy with controller design based on process mathematical model. IMC is widely applied in combustion system because of its outstanding control performance and the simplicity of design. In this paper, an IMC structure is established firstly. Then, adaptive weight particle swarm optimization (AWPSO) algorithm is used in optimizing parameters of IMC and PID with the control evaluation index based on integral of time-weighted absolute value of the error (ITAE). Finally, these adjusted parameters are applied in process object. Result shows that the proposed approach can achieve better control performance than PID.

All the closed loop control system requires the controller for improvement of transient response of the error signal. Though the tuning of PID controller in real time is bit difficult and moreover it lacks the disturbance rejection capability. In order to compensate these internal design problems, internal model control (IMC) based tuning approach has been developed. The analytical method based on IMC principle for the design of PID controller is also developed. The IMC has a single tuning parameter to adjust the performance and robustness of the controller. The tuning method is very efficient in controlling the overshoot, stability and the dynamics of the speed-control system of the DC motor. The resulting structure of the control system is capable of controlling a fast dynamic process by integral control, which results in a striking improvement in performance.

Identification of transfer function matrices in a feedback system is discussed by using the singular value decomposition of Hankel matrix from the viewpoint of inverse problems. A method of model reduction is considered, and selection criteria are proposed for identification of them. Transformation formula between open loop and closed loop transfer function matrices are determined from the feedback loop structure, and they are needed for identification of open loop transfer function matrices under such a condition where the feedback system is in a minimum phase. Though the identifiability of open loop transfer function matrices can be examined in the framework of innovation model equivalent to the feedback system, there are pole-zero cancellations in the identification of them. The method to reduce a model order of an open loop transfer function is discussed by using the singular value decomposition of a gramian given by the open loop transfer function with higher degree. To check reliability of the present algorithm, a simulation study is performed for an example.

This paper proposes an approach of Internal Model Control (IMC) for the linear sampled multivariable non-square systems with outputs more than inputs. The proposed IMC, which is based on a specific inversion principle, is the extension of to the case of square systems, in the controller design, a simple method is presented to add a complementary transfer function matrix of the process to obtain a square transfer matrix. To guarantee the robust stability of the system and disturbance rejection, the controller design procedure is proposed to obtain the wish control. Simulation illustrate the effectiveness of the proposed method for non-square multivariable processes.

Risk-coherent H2-optimal disturbance rejection under model uncertainty

This chapter introduces the neoclassical method of controller design. It will discuss measures of stability and robustness followed by algebraic and analytical constraints in feedback design, revealing how Youla parameter could be utilized in designing a feedback control by considering the constraints and trade-offs in SISO control design.

We consider methods for synthesizing robust controllers that can be directly implemented in the Internal Model Control (IMC) scheme. We show how to put H design methods into the IMC scheme to improve its robustness. These methods include one degree-of-freedom (one d.o.f.) and two degrees-of-freedom (two d.o.f.) H designs. Explicit state-space formulae for the H one d.o.f. and two d.o.f. IMC-based controllers are derived in discrete time. We show that the IMC controller solves a special H control problem, namely a disturbance feedforward control problem, and it proves robust stability against coprime factor uncertainty and with a degree of robust performance for the two d.o.f. case, in the sense of making the closed-loop system match a pre-specified reference model. A design for a glass tube production process is presented as an illustrative example.

This paper is concerned with control design for a generalized discrete-time Takagi-Sugeno fuzzy system. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations. It is a great tool to analyze a nonlinear system and to design a stabilizing controller for it. However, there is a case where a controller design for a nonlinear system based on the Takagi-Sugeno fuzzy system becomes difficult due to its representation. A generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems, and gives a different representation from the standard Takagi-Sugeno fuzzy system, which leads to a rather easy controller design. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of nonlinear controllers. Then, the resulting closed-loop system becomes a fuzzy system with linear system structures locally, which makes the control design easier. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.