**3. Tuning method**

In this study, GA tuning approach has been invoked to tune the gain matrix of LQR controller used to approximate the gain parameters of PID controller for 3DOF helicopter system. GA is a global search optimization technique bases on the strategy of natural selection. This optimization method is utilized to obtain an optimum global solution for more control and manipulating problems. The procedure of GA approach includes three basic steps: selection, crossover and mutation, that constitute the main core of GA with powerful searching ability.

**Selection:** This step includes choosing individual genomes with high adaptive value from the current population to create mating pool. At present, there mainly are: sequencing choice, adaptive value proportional choice, tournament choice and so on. In order to avoid the best individuals of current population missing in the next generation due to destruction influence of crossover and mutation or selection error, De Jong put forward to the cream choice strategy [3xxx];

**Crossover:** This operation is the process of mimicking gene recombination of natural sexual reproduction, through combining the genetic information of two gens to create a new offspring contining more complicated gene structur. Reproduction may proceed in three stages as follows: (1) two newly reproduced strings are randomly selected from a Mating Pool; (2) a number of crossover positions along each string are uniformly selected at random and (3) two new strings are created and copied to the next generation by swapping string characters between the crossover positions defined before.

**Mutation:** In this process one or more indivisual values in a chromosome are altered from its initial state. This can result in entirely new gene values being added to the gene pool. This stage is also important by the view of preventing the genes local optimal points.

Applying these main operations creates new individuals which could be better than their parents. Based on the requirements of desired response, the sequence of GA optimization technique is repeated for many iterations and finally stops at generating optimum solution elements for the application problems. The sequence of the GA tuning method is presented in **Figure 3** [13, 14]. The steps of the GA loop are defined as follows:

1. Initial set of population.

2.Choose individuals for mating.

**Figure 3.** *Process loop of GA optimization method.*

*A Hybrid Control Approach Based on the Combination of PID Control with LQR Optimal Control DOI: http://dx.doi.org/10.5772/intechopen.94907*

3.Mating the population to create progeny.

4.Mutate progeny.

for a compromise between the best control performance and minimum control input effort. Based on the LQR controller an optimum tracking performance can be investigated by a proper setting of the feedback gain matrix. To achieve this, the LQR controller is optimised by using GA tuning method which is adopted to obtain

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

In this study, GA tuning approach has been invoked to tune the gain matrix of LQR controller used to approximate the gain parameters of PID controller for 3DOF helicopter system. GA is a global search optimization technique bases on the strategy of natural selection. This optimization method is utilized to obtain an optimum global solution for more control and manipulating problems. The procedure of GA approach includes three basic steps: selection, crossover and mutation, that consti-

**Selection:** This step includes choosing individual genomes with high adaptive value from the current population to create mating pool. At present, there mainly are: sequencing choice, adaptive value proportional choice, tournament choice and so on. In order to avoid the best individuals of current population missing in the next generation due to destruction influence of crossover and mutation or selection

**Crossover:** This operation is the process of mimicking gene recombination of natural sexual reproduction, through combining the genetic information of two gens to create a new offspring contining more complicated gene structur. Reproduction may proceed in three stages as follows: (1) two newly reproduced strings are randomly selected from a Mating Pool; (2) a number of crossover positions along each string are uniformly selected at random and (3) two new strings are created and copied to the next generation by swapping string characters between

**Mutation:** In this process one or more indivisual values in a chromosome are altered from its initial state. This can result in entirely new gene values being added to the gene pool. This stage is also important by the view of preventing the genes

Applying these main operations creates new individuals which could be better than their parents. Based on the requirements of desired response, the sequence of GA optimization technique is repeated for many iterations and finally stops at generating optimum solution elements for the application problems. The sequence of the GA tuning method is presented in **Figure 3** [13, 14]. The steps of the GA loop

optimum elements values for of Q and R weighting matrices.

tute the main core of GA with powerful searching ability.

error, De Jong put forward to the cream choice strategy [3xxx];

the crossover positions defined before.

local optimal points.

are defined as follows:

**Figure 3.**

**22**

1. Initial set of population.

*Process loop of GA optimization method.*

2.Choose individuals for mating.

**3. Tuning method**

5. Inserting new generated individuals into populations.

6.Are the system fitness function satisfied?

7.End search process for solution.

In this study, the aim of using GA optimization method is to tune the elements of the state weighting matrix *Q* and input weighting matrix *R* of the optimal LQR controller based on a selected fitness function which, should be minimised to a smallest value. The fitness function should be formulated based on the required performance characteristics. These optimized LQR elements are then employed to calculate the optimum values for PID controller gain parameters, which are used to stabilize the control system. The implementation procedure of the GA tuning method begins with the definition step of the chromosome representation. Each chromosome is represented by a strip of cells. Each cell corresponds to an element of the controller gain parameters. These cells are formed by real positive numbers and characterize the individual to be evaluated [13].
