planmäßig
on schedule
Taking place exactly according to a previously established plan, timetable, or program.
Der Zug erreichte sein Ziel planmäßig um 18:30 Uhr.
The train reached its destination on schedule at 6:30 p.m.

scheduled / according to plan
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on schedule
Taking place exactly according to a previously established plan, timetable, or program.
Der Zug erreichte sein Ziel planmäßig um 18:30 Uhr.
The train reached its destination on schedule at 6:30 p.m.

The word is made up of 'Plan' (plan) and the ending '-mäßig'. The ending '-mäßig' means 'according to' or 'in accordance with', so 'planmäßig' literally means 'according to the plan'.
Die Bauarbeiten verlaufen bisher absolut planmäßig.
The construction work has been proceeding completely according to plan so far.
'Planmäßig' is very often used as an adverb to describe how an action is carried out. It answers the question 'How?'.
Wir sind planmäßig um 14 Uhr in Berlin angekommen.
We arrived in Berlin on schedule at 2 p.m.
In connection with timetables and schedules, 'planmäßig' is often combined with verbs of movement or sequence. Typical phrases are: 'planmäßig ankommen' (to arrive on schedule), 'planmäßig starten' (to start on schedule), or 'planmäßig enden' (to end on schedule).
Das Meeting begann planmäßig um Punkt 9 Uhr.
The meeting began on schedule at exactly 9 o'clock.
plan
'der Plan' and 'planmäßig' are directly related, but they have different grammatical roles. 'der Plan' is a noun and means the idea or organization for something you intend to do. 'planmäßig' is an adjective or adverb and describes that something happens according to a plan or schedule. Learners may confuse the words because both contain the same idea. You say 'einen Plan haben' (to have a plan), but 'etwas läuft planmäßig' (something is going according to plan). If you mean the thing itself, use 'Plan'. If you are describing how something proceeds, use 'planmäßig'.

Auf dem Amt ist das Gespräch planmäßig um zehn Uhr begonnen.
At the government office, the meeting started on schedule at ten o'clock.
Wegen des wichtigen Termins hat Frau Meier einen genauen Plan für den Vormittag.
Because of the important appointment, Ms. Meier has a detailed plan for the morning.