How to give application pool account permissions to search service application

try this one

$principal = New-SPClaimsPrincipal "contosojane" -IdentityType WindowsSamAccountName
$spapp = Get-SPServiceApplication –Name "Contoso Visio Graphics"
$security = Get-SPServiceApplicationSecurity $spapp –Admin
Grant-SPObjectSecurity $security $principal "Full Control"
Set-SPServiceApplicationSecurity $spapp $security –Admin
(Get-SPServiceApplicationSecurity $spapp -Admin).AccessRules

https://social.technet.microsoft.com/Forums/sharepoint/en-US/591d57a3-8925-41b8-9b54-63cad32ad084/how-to-add-an-administrator-for-search-service-application-sharepoint-2013-powershell?forum=sharepointadmin