1. Introduction

The conventional control of the dc motor supposes the use of the modulus and symmetric criteria, adapted to the fast processes (Kessler variant), by the optimum choosing of the tuning parameters of the corresponding controllers. Therefore, the cascaded control loops are the most appropriate choice for the conventional dc drive system. The advantages of using the conventional drive are: the complex process is divided into simple subprocesses having only one significant time constant compensated by an independent controller; it assures the minimum time response; thanks to the feedback path of the control loop, the stability of the dc drive system is maintained; the null steady state error; the fast compensation of the dc drive perturbations.

The main disadvantage of the conventional control is its inadaptability to the parameters variations of the processes. Taking into account that the normal operation of the processes is

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

assured through the electric motors, the values of the electric parameters are not constant. It is well-known that the parameters of the controllers depend on the parameters of the process. Therefore, a change of the process parameters conducts to the deterioration of the drive system performances. Moreover, the uncertainness of the parameters and the structural mismatch of the processes are the main barriers of avoiding the use of the conventional control. In these particular cases the conventional control, even the robust control is inefficient due to the invariance of the controller parameters. An adaptive control is desired in order to maintain the imposed performances on the electric drive. Consequently, an additional adaptive loop is inserted to the conventional feedback system. The purpose of inserting the adaptive loop is to update the controller parameters related to the parameter variations of the process or to the modified structure of the physical process. According to the exogenous variation (reference and perturbation), the adaptive mechanism of the regulation part is performed by the minimization of the specific performance criterion. The result of the designed regulation algorithm consists of a new set of the controller parameters. The closed loop adaptive systems (widely spread) assure the appropriate control correlation with the process uncertainness (modified parameters or structure). The adaptive loop delivers the real time control based on the designed on-line controller.

In this chapter the adaptive control with supraunitary relative degree is introduced through

Matlab-Simulink-Based Compound Model Reference Adaptive Control for DC Motor

http://dx.doi.org/10.5772/intechopen.71758

119

The design procedure of the adaptive control is based on the strictly positive real (SPR) concept. In order to attain the SPR condition, the equivalent transfer function should satisfy the follow-

3. Re[Hm(jω)] ≥ 0, for any ω > 0, i.e., the transfer function of the reference model, Hm(s), should be minimum of phase (without dead time and zero situated in the right half plane).

vanishes, and the relative degree of the reference model should be greater or at least of the

n∗ <sup>m</sup> ≥ n<sup>∗</sup>

In this Section the control methodology of the conventional dc drive system is presented.

tors), at high power, the natural commutation is used (based on thyristors).

2.1. Assumptions for mathematical modeling of the dc motor

The drive system consists of the full controlled dc motor connected to the load. At the high power, the controlled six pulses full bridge ac-dc power converter is involved; at the low – medium power the full bridge dc-dc power converter connected in series with the uncontrolled ac-dc power rectifier is used. From the point of view of commutation, there is a substantial difference between the above presented solutions: while at low and medium power, the force commutation is used (based on the high frequency switching power transis-

In order to design the conventional control for fast processes, the entire system should be

The magnetizing flux is maintained at the rated value; the permeability of the ferromagnetic core is infinite; the unsaturated magnetic circuit is considered, a compensated dc motor is taken into consideration; there are auxiliaries poles; the brushes are situated on the neutral

e0ðÞ!t 0, the asymptotic limit of the tracking error

<sup>p</sup> (1)

1. strictly stable (the poles are situated in the left half plane of the complex space);

The model reference adaptive control (MRAC) contains three aspects:

the dc drive system.

2. the relative degree must be 0 or 1;

1. MRAC in simple form;

3. compound MRAC.

2. variable structure form; and

In order to obtain a perfect tracking, lim<sup>t</sup>!<sup>0</sup>

2. Conventional dc drive system

modeled under certain assumptions:

axis; and the brush droop voltage is neglected.

same order with the relative degree of the process:

ing tasks:

The signals in Figure 1 are defined as follows: r- the reference signal; ym- the output signal of the reference model; u- the adaptive control; y-the output of the process (the measurable signals); e0 – the tracking error vector; θ<sup>p</sup> – the parameters of the process.

In this manner, the structural mismatch and the parametric uncertainness are compensated. In the mechatronic domain or the rolling mill the adaptive control is mandatory.

The name of the adaptive control structure comes from the use of the on-line parameters estimator. Based on it, the process parameters are provided by measuring the control, the process output and the tracking error. Taking into account the reference signal and the process parameters, the adaptive algorithm delivers the appropriate estimation of the control.

There are two types of the adaptive control structures [2]. The adaptive control can be in explicit (indirect) form or in implicit (direct) form. The indirect adaptive control delivers the estimation of the process parameters. The direct adaptive control delivers the estimation of the controller parameters.

Figure 1. The principle of the adaptive control [1].

In this chapter the adaptive control with supraunitary relative degree is introduced through the dc drive system.

The design procedure of the adaptive control is based on the strictly positive real (SPR) concept.

In order to attain the SPR condition, the equivalent transfer function should satisfy the following tasks:


The model reference adaptive control (MRAC) contains three aspects:

1. MRAC in simple form;

assured through the electric motors, the values of the electric parameters are not constant. It is well-known that the parameters of the controllers depend on the parameters of the process. Therefore, a change of the process parameters conducts to the deterioration of the drive system performances. Moreover, the uncertainness of the parameters and the structural mismatch of the processes are the main barriers of avoiding the use of the conventional control. In these particular cases the conventional control, even the robust control is inefficient due to the invariance of the controller parameters. An adaptive control is desired in order to maintain the imposed performances on the electric drive. Consequently, an additional adaptive loop is inserted to the conventional feedback system. The purpose of inserting the adaptive loop is to update the controller parameters related to the parameter variations of the process or to the modified structure of the physical process. According to the exogenous variation (reference and perturbation), the adaptive mechanism of the regulation part is performed by the minimization of the specific performance criterion. The result of the designed regulation algorithm consists of a new set of the controller parameters. The closed loop adaptive systems (widely spread) assure the appropriate control correlation with the process uncertainness (modified parameters or structure). The adaptive loop delivers the real time control based on the designed

The signals in Figure 1 are defined as follows: r- the reference signal; ym- the output signal of the reference model; u- the adaptive control; y-the output of the process (the measurable

In this manner, the structural mismatch and the parametric uncertainness are compensated. In

The name of the adaptive control structure comes from the use of the on-line parameters estimator. Based on it, the process parameters are provided by measuring the control, the process output and the tracking error. Taking into account the reference signal and the process

There are two types of the adaptive control structures [2]. The adaptive control can be in explicit (indirect) form or in implicit (direct) form. The indirect adaptive control delivers the estimation of the process parameters. The direct adaptive control delivers the estimation of the

parameters, the adaptive algorithm delivers the appropriate estimation of the control.

signals); e0 – the tracking error vector; θ<sup>p</sup> – the parameters of the process.

the mechatronic domain or the rolling mill the adaptive control is mandatory.

on-line controller.

118 Adaptive Robust Control Systems

controller parameters.

Figure 1. The principle of the adaptive control [1].


In order to obtain a perfect tracking, lim<sup>t</sup>!<sup>0</sup> e0ðÞ!t 0, the asymptotic limit of the tracking error vanishes, and the relative degree of the reference model should be greater or at least of the same order with the relative degree of the process:

$$m^\*\_{\
u} \ge n^\*\_{\
u} \tag{1}$$
